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<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodStartLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedNetLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTerseLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019e46d7-b342-7df1-a018-0777a1826671_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019e46d7-b3d9-7d63-8167-f5d2db12937b_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DomesticCountryMember_019e46d7-b341-7c40-9f70-fbef904ef4b2_terseLabel_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestic Tax Authority</link:label>
    <link:label id="lab_us-gaap_DomesticCountryMember_label_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction, Domestic Federal [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DomesticCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DomesticCountryMember" xlink:to="lab_us-gaap_DomesticCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019e46d7-b342-76b2-ad02-82d12b7e3cc7_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019e46d7-b3d9-78ae-a5c4-0bd436bdfecb_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019e46d7-b342-7d5d-bc55-89de56f4f366_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders and participating preferred stockholders, diluted</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice_019e46d7-b342-79dd-8b52-03e994a01e8b_terseLabel_en-US" xlink:label="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Optional prepayment, number of days written notice</link:label>
    <link:label id="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice_label_en-US" xlink:label="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Optional Prepayment, Number Of Days Written Notice</link:label>
    <link:label id="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice_documentation_en-US" xlink:label="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Optional Prepayment, Number Of Days Written Notice</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:href="vate-20260630.xsd#vate_OptionalPrepaymentNumberOfDaysWrittenNotice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:to="lab_vate_OptionalPrepaymentNumberOfDaysWrittenNotice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_019f64b3-7b10-749c-b945-6ec3ddc6c750_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotesDue202710.50Member_019e46d7-b342-779e-abe4-8e01fb285966_terseLabel_en-US" xlink:label="lab_vate_SeniorNotesDue202710.50Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">10.50% Senior Secured Notes</link:label>
    <link:label id="lab_vate_SeniorNotesDue202710.50Member_label_en-US" xlink:label="lab_vate_SeniorNotesDue202710.50Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes Due 2027, 10.50% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotesDue202710.50Member_documentation_en-US" xlink:label="lab_vate_SeniorNotesDue202710.50Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes Due 2027, 10.50%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotesDue202710.50Member" xlink:href="vate-20260630.xsd#vate_SeniorNotesDue202710.50Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotesDue202710.50Member" xlink:to="lab_vate_SeniorNotesDue202710.50Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_019e46d7-b342-7958-a4e7-e0e1c7a198a3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Measured on Not Measured at Fair Value</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Nonrecurring [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod_019e46d7-b342-780e-a2bf-7651b3f339c8_terseLabel_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock trading days to calculate volume weighted average price, trading day period</link:label>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod_label_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Trading Period To Calculate Volume Weighted Average Price, Trading Day Period</link:label>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod_documentation_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Trading Period To Calculate Volume Weighted Average Price, Trading Day Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:href="vate-20260630.xsd#vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:to="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePriceTradingDayPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019e46d7-b341-7103-81b8-7a7157e11efe_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_019e46d7-b27a-7304-a38d-1d17256252a8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsUnappropriatedMember_019e46d7-b3d9-77e7-86a3-f0679099ff47_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsUnappropriatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsUnappropriatedMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsUnappropriatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings, Unappropriated [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsUnappropriatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsUnappropriatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsUnappropriatedMember" xlink:to="lab_us-gaap_RetainedEarningsUnappropriatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue_019e46d7-b342-714e-9cf7-98496582e63a_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption value</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue_label_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Preferred, Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue" xlink:to="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable_019e46d7-b342-737a-93be-c3ecffec9b90_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from External Customers by Products and Services [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Product and Service, Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable" xlink:to="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_019e46d7-b46d-7c79-8d3c-ede7aa1ca8cc_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_019e46d7-b3d9-7661-9261-e41c81a5931b_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued payroll and employee benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNet_019e46d7-b341-7833-abe5-55c94444fe50_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNet_019e46d7-b341-722a-bf39-e174dda8f51e_totalLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNet_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNet" xlink:to="lab_us-gaap_ContractWithCustomerAssetNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_019e46d7-b27a-7a1b-8f90-d2b6ec522474_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_GainLossOnLeaseModification_019e46d7-b3d9-7941-9401-c8a371bb2329_negatedTerseLabel_en-US" xlink:label="lab_vate_GainLossOnLeaseModification" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on lease modifications</link:label>
    <link:label id="lab_vate_GainLossOnLeaseModification_label_en-US" xlink:label="lab_vate_GainLossOnLeaseModification" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Lease Modification</link:label>
    <link:label id="lab_vate_GainLossOnLeaseModification_documentation_en-US" xlink:label="lab_vate_GainLossOnLeaseModification" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Lease Modification</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_GainLossOnLeaseModification" xlink:href="vate-20260630.xsd#vate_GainLossOnLeaseModification"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_GainLossOnLeaseModification" xlink:to="lab_vate_GainLossOnLeaseModification" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings_019e46d7-b342-711e-972f-4dfd00e6d956_terseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost in excess of billings and estimated earnings</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings_label_en-US" xlink:label="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Cost In Excess Of Billings And Estimated Earnings</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Cost In Excess Of Billings And Estimated Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:to="lab_vate_ContractWithCustomerAssetCostInExcessOfBillingsAndEstimatedEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1_019e46d7-b341-74be-94d0-2182f6db130b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion price (in usd per share)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Conversion Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SupplierAMember_019e46d7-b46d-79fa-8c81-ed86c5019ce1_terseLabel_en-US" xlink:label="lab_vate_SupplierAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplier A</link:label>
    <link:label id="lab_vate_SupplierAMember_label_en-US" xlink:label="lab_vate_SupplierAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplier A [Member]</link:label>
    <link:label id="lab_vate_SupplierAMember_documentation_en-US" xlink:label="lab_vate_SupplierAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Supplier A</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SupplierAMember" xlink:href="vate-20260630.xsd#vate_SupplierAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SupplierAMember" xlink:to="lab_vate_SupplierAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019e46d7-b342-763f-aaae-9cf8aa4eb3c2_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability_019e46d7-b3d9-73e1-b2be-460df14ba170_negatedTerseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conditional retainage</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability_label_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Conditional Retainage, Liability</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Conditional Retainage, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerLiabilityConditionalRetainageLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:to="lab_vate_ContractWithCustomerLiabilityConditionalRetainageLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess_019e46d7-b3d9-7b0a-b419-c6378fca751c_terseLabel_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible notes and accrued interest converted to stock, in process</link:label>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess_label_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Notes And Accrued Interest Converted To Stock, In Process</link:label>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess_documentation_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Notes And Accrued Interest Converted To Stock, In Process</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:href="vate-20260630.xsd#vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:to="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStockInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_019e46d7-b46d-72f3-b3c7-0a9d8101f685_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_A2027ConvertibleNotesMember_019fa9ac-9f27-704b-98b9-657e74bbe6a4_terseLabel_en-US" xlink:label="lab_vate_A2027ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Convertible Notes</link:label>
    <link:label id="lab_vate_A2027ConvertibleNotesMember_label_en-US" xlink:label="lab_vate_A2027ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Convertible Notes [Member]</link:label>
    <link:label id="lab_vate_A2027ConvertibleNotesMember_documentation_en-US" xlink:label="lab_vate_A2027ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Convertible Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_A2027ConvertibleNotesMember" xlink:href="vate-20260630.xsd#vate_A2027ConvertibleNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_A2027ConvertibleNotesMember" xlink:to="lab_vate_A2027ConvertibleNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ThirdPartyMember_019e46d7-b3d9-7590-b028-a9fef97125c1_terseLabel_en-US" xlink:label="lab_vate_ThirdPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third-Party</link:label>
    <link:label id="lab_vate_ThirdPartyMember_label_en-US" xlink:label="lab_vate_ThirdPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third-Party [Member]</link:label>
    <link:label id="lab_vate_ThirdPartyMember_documentation_en-US" xlink:label="lab_vate_ThirdPartyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third-Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ThirdPartyMember" xlink:href="vate-20260630.xsd#vate_ThirdPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ThirdPartyMember" xlink:to="lab_vate_ThirdPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree_019e46d7-b342-7d8b-bfb4-ab1dd849094e_totalLabel_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities, Repayments Of Principal In Year Three</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree_documentation_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities, Repayments Of Principal In Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="vate-20260630.xsd#vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019e46d7-b341-7749-8ce6-559ddcfebe6f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Parties</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_019e46d7-b3d9-7424-9182-7eaef3dc7972_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_BroadcastStationRevenueMember_019e46d7-b3d9-751c-8e2a-3175e28292b0_terseLabel_en-US" xlink:label="lab_vate_BroadcastStationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Broadcast station</link:label>
    <link:label id="lab_vate_BroadcastStationRevenueMember_label_en-US" xlink:label="lab_vate_BroadcastStationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Broadcast Station Revenue [Member]</link:label>
    <link:label id="lab_vate_BroadcastStationRevenueMember_documentation_en-US" xlink:label="lab_vate_BroadcastStationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Broadcast Station Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_BroadcastStationRevenueMember" xlink:href="vate-20260630.xsd#vate_BroadcastStationRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_BroadcastStationRevenueMember" xlink:to="lab_vate_BroadcastStationRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019e46d7-b342-7853-87c5-945609435c85_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_019e46d7-b342-7d1d-a36f-55bcd01e6ee4_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_019e46d7-b342-7c9d-8c18-d50ab58423f3_periodStartLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents classified in Assets held for sale, beginning of period</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_019e46d7-b342-779e-8e1b-924deecde6f2_periodEndLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents classified in Assets held for sale, end of period</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DBMGiMember_019e46d7-b27a-7822-82df-ee3cdac8835e_terseLabel_en-US" xlink:label="lab_vate_DBMGiMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DBMGi</link:label>
    <link:label id="lab_vate_DBMGiMember_label_en-US" xlink:label="lab_vate_DBMGiMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DBMGi [Member]</link:label>
    <link:label id="lab_vate_DBMGiMember_documentation_en-US" xlink:label="lab_vate_DBMGiMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DBMGi [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DBMGiMember" xlink:href="vate-20260630.xsd#vate_DBMGiMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DBMGiMember" xlink:to="lab_vate_DBMGiMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_019e46d7-b342-7c66-a0a5-22a5bc7fd651_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangibles, net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019e46d7-b27a-71c3-bb93-573bfb57821f_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested at beginning of period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019e46d7-b27a-7491-a294-7079ef48ad99_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested at ending of period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableMember_019e46d7-b46d-7399-9fd8-138e8f64f912_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Receivable</link:label>
    <link:label id="lab_us-gaap_NotesReceivableMember_label_en-US" xlink:label="lab_us-gaap_NotesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableMember" xlink:to="lab_us-gaap_NotesReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019e46d7-b3d9-7175-9a93-39fba1152730_verboseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019e46d7-b3d9-73a9-b4e9-ab28a320b1ff_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_019e46d7-b342-7e69-9529-5c23c4207229_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_019e46d7-b342-7e60-a468-ade90607ddb6_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships and contracts</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_A12.0SeniorSecuredPromissoryNoteMember_019e46d7-b342-7888-9e3b-c3d773489d17_terseLabel_en-US" xlink:label="lab_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lancer Promissory Note</link:label>
    <link:label id="lab_vate_A12.0SeniorSecuredPromissoryNoteMember_label_en-US" xlink:label="lab_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">12.0% Senior Secured Promissory Note [Member]</link:label>
    <link:label id="lab_vate_A12.0SeniorSecuredPromissoryNoteMember_documentation_en-US" xlink:label="lab_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">12.0% Senior Secured Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:href="vate-20260630.xsd#vate_A12.0SeniorSecuredPromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:to="lab_vate_A12.0SeniorSecuredPromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_019e46d7-b46d-74be-8922-7bbb5335943c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsPolicyPolicyTextBlock_019e46d7-b3d9-7389-9171-ae6f088912e6_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SubsequentEventsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019e46d7-b342-7a59-bd69-619622ec4ddb_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019e46d7-b3d9-7834-980a-dd7db4102206_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_019e46d7-b3d9-7903-84e2-8953f152b151_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019e46d7-b342-75ee-a41a-44dc125110da_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentIssuedPercentageOfParValue_019e46d7-b342-7a19-969b-abd042b3a1f6_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issued, percentage of par value</link:label>
    <link:label id="lab_vate_DebtInstrumentIssuedPercentageOfParValue_label_en-US" xlink:label="lab_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Issued, Percentage Of Par Value</link:label>
    <link:label id="lab_vate_DebtInstrumentIssuedPercentageOfParValue_documentation_en-US" xlink:label="lab_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Issued, Percentage Of Par Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:href="vate-20260630.xsd#vate_DebtInstrumentIssuedPercentageOfParValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:to="lab_vate_DebtInstrumentIssuedPercentageOfParValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019e46d7-b3d9-730d-b110-cd2b8aa07e05_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e46d7-b27a-72bc-a614-822b2a07f9d7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019e46d7-b27a-79a6-b0d4-b147130b6c97_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesRevenueNetMember_019e46d7-b3d9-7e73-ab2b-c7fe65873e17_terseLabel_en-US" xlink:label="lab_us-gaap_SalesRevenueNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_SalesRevenueNetMember_label_en-US" xlink:label="lab_us-gaap_SalesRevenueNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesRevenueNetMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesRevenueNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesRevenueNetMember" xlink:to="lab_us-gaap_SalesRevenueNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentOptionExercisePeriod_019f4578-3493-72a3-a20b-d91f4d2c8038_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentOptionExercisePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Option exercise period</link:label>
    <link:label id="lab_vate_DebtInstrumentOptionExercisePeriod_label_en-US" xlink:label="lab_vate_DebtInstrumentOptionExercisePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument Option Exercise Period</link:label>
    <link:label id="lab_vate_DebtInstrumentOptionExercisePeriod_documentation_en-US" xlink:label="lab_vate_DebtInstrumentOptionExercisePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument Option Exercise Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentOptionExercisePeriod" xlink:href="vate-20260630.xsd#vate_DebtInstrumentOptionExercisePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentOptionExercisePeriod" xlink:to="lab_vate_DebtInstrumentOptionExercisePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_019f446f-76a6-7458-b8f9-2831c955fffd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_019e46d7-b3d9-76d2-8ba5-f8a8a84b5400_totalLabel_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2026 (remaining period)</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal Remainder Of Fiscal Year</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_documentation_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal Remainder Of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:href="vate-20260630.xsd#vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019f64b3-5374-7fea-b7ba-54ef6ec82013_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019e46d7-b342-7dfe-94f4-b324aa43fc26_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LancerPromissoryNoteMember_019e46d7-b341-746b-b0e5-001adfbb5b77_terseLabel_en-US" xlink:label="lab_vate_LancerPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lancer Promissory Note</link:label>
    <link:label id="lab_vate_LancerPromissoryNoteMember_label_en-US" xlink:label="lab_vate_LancerPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lancer Promissory Note [Member]</link:label>
    <link:label id="lab_vate_LancerPromissoryNoteMember_documentation_en-US" xlink:label="lab_vate_LancerPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lancer Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LancerPromissoryNoteMember" xlink:href="vate-20260630.xsd#vate_LancerPromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LancerPromissoryNoteMember" xlink:to="lab_vate_LancerPromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019e46d7-b3d9-77b2-91ba-b66db6e3aee6_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember_019e46d7-b3d9-7e84-9572-ed4d450f15c7_verboseLabel_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Within Three Years</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember_019e46d7-b3d9-7daa-ba51-14a55724a124_terseLabel_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Within Two to Five Years</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember_label_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period Two [Member]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember_documentation_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:href="vate-20260630.xsd#vate_RevenueRemainingPerformanceObligationPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:to="lab_vate_RevenueRemainingPerformanceObligationPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019e46d7-b342-74b2-8856-511f00d992ef_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operating Segments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019e46d7-b27a-733e-95ca-425eb69d6d70_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates and Assumptions</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019e46d7-b3d9-7f1c-aab0-e1edd49b1da5_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentThresholdPercentageOfOwnership_019f4578-3493-7132-a10d-d42fd1f36aee_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold percentage of ownership</link:label>
    <link:label id="lab_vate_DebtInstrumentThresholdPercentageOfOwnership_label_en-US" xlink:label="lab_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument Threshold Percentage Of Ownership</link:label>
    <link:label id="lab_vate_DebtInstrumentThresholdPercentageOfOwnership_documentation_en-US" xlink:label="lab_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument Threshold Percentage Of Ownership</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:href="vate-20260630.xsd#vate_DebtInstrumentThresholdPercentageOfOwnership"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:to="lab_vate_DebtInstrumentThresholdPercentageOfOwnership" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CustomerDMember_019e46d7-b46d-7809-acd6-4f99fe5e6f1b_terseLabel_en-US" xlink:label="lab_vate_CustomerDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer D</link:label>
    <link:label id="lab_vate_CustomerDMember_label_en-US" xlink:label="lab_vate_CustomerDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer D [Member]</link:label>
    <link:label id="lab_vate_CustomerDMember_documentation_en-US" xlink:label="lab_vate_CustomerDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer D</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CustomerDMember" xlink:href="vate-20260630.xsd#vate_CustomerDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CustomerDMember" xlink:to="lab_vate_CustomerDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_019e46d7-b3d9-7b38-aa58-82fc1d30457f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on lines of credit</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019e46d7-b342-7869-bbf1-df54e2ee5f5a_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operating Lease, Liability, Maturity</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019e46d7-b3d9-7b98-bc6a-f2860bcaa6bd_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e46d7-b3d9-7edb-96ea-c07e8c89f83a_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_019eaaaa-de24-7f0b-b199-435dee3b8d63_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019e46d7-b342-7a55-aaed-5da7249d8437_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019e46d7-b341-7836-8fc9-68d77e16b1bc_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019e46d7-b342-7577-ab2c-84891f7cf106_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019f91bb-e281-7862-8a76-bd625202584d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) per common share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019f4577-3542-78d5-9e5b-8ee3c63fff2f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock_019e46d7-b341-7f56-ac92-df8ca4886cb0_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Revenue from Segments to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciliation of Revenue by Segment to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_019e46d7-b3d9-7671-a9cd-2b35563b0710_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, at cost: 177,038 and 163,842 shares, respectively</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage_019fd2cb-61dc-77d4-a181-db14d84991a2_terseLabel_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3 and Series A-4 Preferred Stock (as a percent)</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage_label_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Preferred Stock, Allocation Percentage</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage_documentation_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Preferred Stock, Allocation Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:href="vate-20260630.xsd#vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:to="lab_vate_UndistributedEarningsLossAllocatedToPreferredStockAllocationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019e46d7-b3d9-7149-bdff-5435e4e0ea57_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate, effective percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_019e46d7-b46d-76ff-8d5a-8bde26a4003a_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_019e46d7-b342-7869-8e4a-58451535cd75_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining lease term (years) - finance leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_019e46d7-b342-73f2-9516-31ab1ee44a72_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate fair value of restricted common stock vested</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e46d7-b342-76a9-bf3f-7556a8b83a6b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019e46d7-b3d9-7230-ab4e-6c9c6166b6cc_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019e46d7-b3d8-7c3f-893e-bb83f4554869_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_019e46d7-b342-79d1-b119-de81ebfebbd4_netLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Current portion of operating lease</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_019e46d7-b342-77de-80e3-c2f7203e02f4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liability, current portion</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019e46d7-b3d9-78fa-aa61-f9971048c630_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic and Diluted Earnings (Loss) Per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnbilledContractsReceivable_019e46d7-b46d-72d7-9dae-e6e83fbfa2cc_terseLabel_en-US" xlink:label="lab_us-gaap_UnbilledContractsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unbilled retentions</link:label>
    <link:label id="lab_us-gaap_UnbilledContractsReceivable_label_en-US" xlink:label="lab_us-gaap_UnbilledContractsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unbilled Contracts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnbilledContractsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnbilledContractsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnbilledContractsReceivable" xlink:to="lab_us-gaap_UnbilledContractsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019e46d7-b3d9-7946-9738-21e7457cdd93_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019e46d7-b342-7ba5-9ce9-34ec762d0571_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems_019e46d7-b3d9-7f81-9469-aaf63874ebbb_terseLabel_en-US" xlink:label="lab_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Product and Service, Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems_label_en-US" xlink:label="lab_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Product and Service, Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems" xlink:to="lab_us-gaap_EntityWideInformationRevenueFromExternalCustomerLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders_019faf66-988c-711e-ae04-6d614ac27648_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares held by lenders (in shares)</link:label>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders_label_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Milestone Requirement, Number of Share Held by Lenders</link:label>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders_documentation_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Milestone Requirement, Number of Share Held by Lenders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:href="vate-20260630.xsd#vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:to="lab_vate_DebtInstrumentMilestoneRequirementNumberOfShareHeldByLenders" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019e46d7-b3d9-7d38-9205-8b1095c2ce70_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019e46d7-b342-7a95-9b2b-072f448f153c_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CONXMember_019f40fd-0479-7e7b-94d6-00455f853a2b_terseLabel_en-US" xlink:label="lab_vate_CONXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CONX</link:label>
    <link:label id="lab_vate_CONXMember_label_en-US" xlink:label="lab_vate_CONXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CONX [Member]</link:label>
    <link:label id="lab_vate_CONXMember_documentation_en-US" xlink:label="lab_vate_CONXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CONX</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CONXMember" xlink:href="vate-20260630.xsd#vate_CONXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CONXMember" xlink:to="lab_vate_CONXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019e46d7-b342-73bd-97bd-fde9d8ae8fa8_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_019e46d7-b3d9-76bb-8e24-66149eb4e3b3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract_019fae9a-3678-7d58-b80d-1d52890ff2ec_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_019e46d7-b3d9-78fe-b526-5634564b76c7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_019e46d7-b342-792a-acf5-79ac7a156071_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and restricted cash classified in Assets held for sale, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_019e46d7-b342-717f-8897-7306e6772db2_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and restricted cash classified in Assets held for sale, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_019e46d7-b27a-72eb-818a-c79be5defeb7_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherLiabilitiesCurrentOther_019e46d7-b3d9-7b7a-a135-ab216b633cd2_terseLabel_en-US" xlink:label="lab_vate_OtherLiabilitiesCurrentOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_vate_OtherLiabilitiesCurrentOther_label_en-US" xlink:label="lab_vate_OtherLiabilitiesCurrentOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current, Other</link:label>
    <link:label id="lab_vate_OtherLiabilitiesCurrentOther_documentation_en-US" xlink:label="lab_vate_OtherLiabilitiesCurrentOther" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherLiabilitiesCurrentOther" xlink:href="vate-20260630.xsd#vate_OtherLiabilitiesCurrentOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherLiabilitiesCurrentOther" xlink:to="lab_vate_OtherLiabilitiesCurrentOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits_019fd2b2-6d35-74b6-b770-b75f5cdc5bba_terseLabel_en-US" xlink:label="lab_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of assumed shares under the treasury stock method for stock options and unvested restricted stock</link:label>
    <link:label id="lab_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits_label_en-US" xlink:label="lab_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dilutive Securities, Effect on Basic Earnings Per Share, Options and Restrictive Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits" xlink:to="lab_us-gaap_AmountOfDilutiveSecuritiesStockOptionsAndRestrictiveStockUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour_019e46d7-b3d9-7f0f-976a-55ba6312fa1b_terseLabel_en-US" xlink:label="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:label id="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:href="vate-20260630.xsd#vate_FinanceLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_vate_FinanceLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_019e46d7-b3d9-757a-9668-7e428d21096c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019e46d7-b3d9-78b0-85bb-fb93376feb91_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_019e46d7-b27a-729e-b9b2-e57cd971a3d7_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019e46d7-b3d9-7919-a04d-708688894aa4_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_019eaa85-badd-7286-aa37-dddb692bb839_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_019e46d7-b342-7dfb-9b76-50c0f42f784f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_label_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables, Net, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivablesNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivablesNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivablesNetCurrent" xlink:to="lab_us-gaap_OtherReceivablesNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EliminationsAndReconcilingItemsMember_019e46d7-b27a-7a33-8eb3-5dc0f95a3a0d_terseLabel_en-US" xlink:label="lab_vate_EliminationsAndReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other and Eliminations</link:label>
    <link:label id="lab_vate_EliminationsAndReconcilingItemsMember_label_en-US" xlink:label="lab_vate_EliminationsAndReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Eliminations And Reconciling Items [Member]</link:label>
    <link:label id="lab_vate_EliminationsAndReconcilingItemsMember_documentation_en-US" xlink:label="lab_vate_EliminationsAndReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Eliminations And Reconciling Items</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EliminationsAndReconcilingItemsMember" xlink:href="vate-20260630.xsd#vate_EliminationsAndReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EliminationsAndReconcilingItemsMember" xlink:to="lab_vate_EliminationsAndReconcilingItemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock_019e46d7-b3d9-7d44-8633-a9d293342855_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Current Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Current Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_019e46d7-b3d9-7472-b770-796d7802659f_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_019eaa6a-849c-7745-aa8c-64828474a998_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_019e46d7-b342-7b8f-86cd-5043e50d61c8_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_019e46d7-b3d9-7312-b333-7654d5494f8f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwards" xlink:to="lab_us-gaap_OperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_019e46d7-b46d-7e60-afc1-3727b99c4b70_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_019ea719-33ec-724e-b432-23b6203c4e18_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Assets And Liabilities Held For Sale Of Spectrum Segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:to="lab_us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019e46d7-b3d9-77cb-9c8c-1619311ec737_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_019e46d7-b3d9-792a-b018-478c04fd507a_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_019e46d7-b27a-7ac5-ae20-b01b98d7aa89_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Dilutive common stock equivalents (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsReceivable_019fb173-41fd-7db2-be30-a1c17871d6fb_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Declared cash dividend receivable</link:label>
    <link:label id="lab_us-gaap_DividendsReceivable_label_en-US" xlink:label="lab_us-gaap_DividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsReceivable" xlink:to="lab_us-gaap_DividendsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_019e46d7-b3d9-7505-8e05-76040c44f93b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: amounts representing interest</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_019e46d7-b342-7dd7-8fb0-4978c2d7c14b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIntangibleAssetsMember" xlink:to="lab_us-gaap_OtherIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization_019e46d7-b342-7516-acb1-ae7306ddede5_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_019e46d7-b27a-7bcd-b62e-21eb872b4ed4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash flows for operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault_019e46d7-b3d9-79c0-a706-5aed268775b2_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Holders percentage required to declare default</link:label>
    <link:label id="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault_label_en-US" xlink:label="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Holders Percentage Required To Declare Default</link:label>
    <link:label id="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault_documentation_en-US" xlink:label="lab_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Holders Percentage Required To Declare Default</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault" xlink:href="vate-20260630.xsd#vate_DebtInstrumentHoldersPercentageRequiredToDeclareDefault"/>
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    <link:label id="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance_019e46d7-b3d9-7ddb-acb3-0e5e50c0c644_negatedLabel_en-US" xlink:label="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Loss (gain) on investments</link:label>
    <link:label id="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance_019e46d7-b3d9-72be-8a99-af7fe72bb9de_terseLabel_en-US" xlink:label="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of investments</link:label>
    <link:label id="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance_label_en-US" xlink:label="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Equity Method Investments, Equity Issuance</link:label>
    <link:label id="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance_documentation_en-US" xlink:label="lab_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Equity Method Investments, Equity Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance" xlink:href="vate-20260630.xsd#vate_RealizedGainLossEquityMethodInvestmentsEquityIssuance"/>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019e46d7-b3d9-743f-82d7-dc6a76c2439a_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019e46d7-b3d9-7099-9fe5-67868308da98_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices (Level 1)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_019e46d7-b3d9-7b1a-921f-43898b1b78fc_terseLabel_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Revenue Concentrations</link:label>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_label_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:to="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherIncomeExpenseNet_019e46d7-b3d9-7467-abca-4d591a4887e4_terseLabel_en-US" xlink:label="lab_vate_OtherIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_vate_OtherIncomeExpenseNet_label_en-US" xlink:label="lab_vate_OtherIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income (Expense), Net</link:label>
    <link:label id="lab_vate_OtherIncomeExpenseNet_documentation_en-US" xlink:label="lab_vate_OtherIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherIncomeExpenseNet" xlink:href="vate-20260630.xsd#vate_OtherIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherIncomeExpenseNet" xlink:to="lab_vate_OtherIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionRatio1_019e46d7-b3d9-78d5-b0a3-c2ccb45b11f7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionRatio1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible notes, conversion ratio</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionRatio1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionRatio1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentConvertibleConversionRatio1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleConversionRatio1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentConvertibleConversionRatio1" xlink:to="lab_us-gaap_DebtInstrumentConvertibleConversionRatio1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockConsentRightsPercentage_019e46d7-b342-7b46-85c0-8cae701611e8_terseLabel_en-US" xlink:label="lab_vate_PreferredStockConsentRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consent rights percentage (at least)</link:label>
    <link:label id="lab_vate_PreferredStockConsentRightsPercentage_label_en-US" xlink:label="lab_vate_PreferredStockConsentRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Consent Rights Percentage</link:label>
    <link:label id="lab_vate_PreferredStockConsentRightsPercentage_documentation_en-US" xlink:label="lab_vate_PreferredStockConsentRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Consent Rights Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockConsentRightsPercentage" xlink:href="vate-20260630.xsd#vate_PreferredStockConsentRightsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockConsentRightsPercentage" xlink:to="lab_vate_PreferredStockConsentRightsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays_019e46d7-b341-7b80-8979-f7ebd778d6ce_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Judgment default grace period days</link:label>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays_label_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Judgment Default Grace Period Days</link:label>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays_documentation_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Judgment Default Grace Period Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:href="vate-20260630.xsd#vate_DebtInstrumentJudgmentDefaultGracePeriodDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:to="lab_vate_DebtInstrumentJudgmentDefaultGracePeriodDays" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeCapitalized_019e46d7-b27a-7c62-9f06-e0ace7420ce3_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, extension fee</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeCapitalized_label_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee Capitalized</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeCapitalized_documentation_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeCapitalized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee Capitalized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentExtensionFeeCapitalized" xlink:href="vate-20260630.xsd#vate_DebtInstrumentExtensionFeeCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentExtensionFeeCapitalized" xlink:to="lab_vate_DebtInstrumentExtensionFeeCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019fd2bb-c576-7686-93e2-34a4bfc15c75_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of assumed shares under the treasury stock method for stock options and unvested restricted stock (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeriesA3PreferredStockMember_019e46d7-b3d9-76bd-80f8-5735a836e992_terseLabel_en-US" xlink:label="lab_vate_SeriesA3PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3 Preferred Stock</link:label>
    <link:label id="lab_vate_SeriesA3PreferredStockMember_label_en-US" xlink:label="lab_vate_SeriesA3PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-3 Preferred Stock [Member]</link:label>
    <link:label id="lab_vate_SeriesA3PreferredStockMember_documentation_en-US" xlink:label="lab_vate_SeriesA3PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-3 Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeriesA3PreferredStockMember" xlink:href="vate-20260630.xsd#vate_SeriesA3PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeriesA3PreferredStockMember" xlink:to="lab_vate_SeriesA3PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour_019e46d7-b342-76b9-97e5-d704984b8623_totalLabel_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities, Repayments Of Principal In Year Four</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour_documentation_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities, Repayments Of Principal In Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="vate-20260630.xsd#vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDividendsReceived_019fb170-a1ca-71a5-a534-436110991fd7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from dividends received</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDividendsReceived_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDividendsReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Dividends Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDividendsReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromDividendsReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDividendsReceived" xlink:to="lab_us-gaap_ProceedsFromDividendsReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_TermLoanMember_019e46d7-b341-71fe-be46-69dc9e53a98e_terseLabel_en-US" xlink:label="lab_vate_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:label id="lab_vate_TermLoanMember_label_en-US" xlink:label="lab_vate_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Loan [Member]</link:label>
    <link:label id="lab_vate_TermLoanMember_documentation_en-US" xlink:label="lab_vate_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">A loan from a bank for a specific amount that has a specified repayment schedule and a floating interest rate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_TermLoanMember" xlink:href="vate-20260630.xsd#vate_TermLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_TermLoanMember" xlink:to="lab_vate_TermLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019e46d7-b341-7edd-9a3e-9a9ad954d2d3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_019e46d7-b341-7725-96e5-a309080bf709_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPricePerShare_019e46d7-b3d9-7277-a6b1-2b4168cf4cfa_terseLabel_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock conversion price (in usd per share)</link:label>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPricePerShare_label_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock Conversion Price Per Share</link:label>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPricePerShare_documentation_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the conversion price for convertible preferred stock per share.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:href="vate-20260630.xsd#vate_ConvertiblePreferredStockConversionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:to="lab_vate_ConvertiblePreferredStockConversionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_019e46d7-b3d9-767d-b233-b96445208e75_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_019eaa85-badd-78b4-9d42-bfec9b2902ce_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019e46d7-b342-7cbc-bd19-7bb8cd523f6d_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019e46d7-b3d9-71c0-8370-53b13c673680_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding at beginning of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019e46d7-b3d9-765c-9b8e-5a255d58947e_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding at ending of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019e46d7-b341-701b-bc3c-555042925c2d_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Operating lease</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019e46d7-b341-789d-a0f1-671512f85fc2_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_019e46d7-b3d9-7ffa-93ef-cfa34f6d01e6_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwardsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:to="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019e46d7-b27a-7913-9175-f385dd842fe5_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsTable_019ea693-0d99-7895-8ccd-b4101336e75a_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table]</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTable_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTable" xlink:to="lab_us-gaap_OffsettingAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_019e46d7-b46d-73cf-bd48-2a3b918c531e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026And2027Member_019e46d7-b3d9-7b24-8ba8-81a27c9f5d1a_terseLabel_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2026 and 2027</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026And2027Member_label_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2026 and 2027 [Member]</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026And2027Member_documentation_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2026 and 2027</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:href="vate-20260630.xsd#vate_ConvertibleSeniorNotesDue2026And2027Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:to="lab_vate_ConvertibleSeniorNotesDue2026And2027Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019e46d7-b3d9-7455-85cc-ef14bf1b391e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LeaseRightOfUseAsset_019e46d7-b341-7962-8dea-7ba090709575_totalLabel_en-US" xlink:label="lab_vate_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total right-of-use assets</link:label>
    <link:label id="lab_vate_LeaseRightOfUseAsset_label_en-US" xlink:label="lab_vate_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Right-Of-Use Asset</link:label>
    <link:label id="lab_vate_LeaseRightOfUseAsset_documentation_en-US" xlink:label="lab_vate_LeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease, Right-Of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LeaseRightOfUseAsset" xlink:href="vate-20260630.xsd#vate_LeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LeaseRightOfUseAsset" xlink:to="lab_vate_LeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCredit_019e46d7-b3d9-7ebe-915f-028da1fdea1c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit outstanding</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EquipmentFurnitureAndFixturesMember_019e46d7-b27a-7130-8754-89a9fd7d6e5b_terseLabel_en-US" xlink:label="lab_vate_EquipmentFurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment, furniture and fixtures, and software</link:label>
    <link:label id="lab_vate_EquipmentFurnitureAndFixturesMember_label_en-US" xlink:label="lab_vate_EquipmentFurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Furniture And Fixtures [Member]</link:label>
    <link:label id="lab_vate_EquipmentFurnitureAndFixturesMember_documentation_en-US" xlink:label="lab_vate_EquipmentFurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment furniture and fixtures.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EquipmentFurnitureAndFixturesMember" xlink:href="vate-20260630.xsd#vate_EquipmentFurnitureAndFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EquipmentFurnitureAndFixturesMember" xlink:to="lab_vate_EquipmentFurnitureAndFixturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019e46d7-b342-7508-a3d0-2f73e642daf0_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice_019e46d7-b3d9-7478-be02-3e0f05a84cba_terseLabel_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock trading days to calculate volume weighted average price (at least)</link:label>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice_label_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Trading Period To Calculate Volume Weighted Average Price</link:label>
    <link:label id="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice_documentation_en-US" xlink:label="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the Preferred Stock trading period used to calculate volume weighted average price.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:href="vate-20260630.xsd#vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:to="lab_vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e46d7-b342-7e68-a853-2db50d95d1ad_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e46d7-b342-725b-b4c3-b0bc8ad43a63_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019e46d7-b342-7e91-85cd-c6d8e732bbf7_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_019e46d7-b341-7cec-a410-0a833d03f110_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operations [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operations [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_019e46d7-b3d9-7ca9-b192-0551f0553a44_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Exercisable at beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_019e46d7-b3d9-71fc-9db3-e903b2bd09a7_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Exercisable at ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_019e46d7-b342-769b-80a8-977a1981263f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_019e46d7-b3d9-7005-8845-d206a8b4fa2b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, unamortized premium, net</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019e46d7-b27a-7ad8-8435-410688d47bf6_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_019e46d7-b3d9-7da3-9d03-9340db8abf9d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019e46d7-b27a-763d-bae2-232c363c2456_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e46d7-b27a-7808-b920-0fa69c9e5620_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e46d7-b27a-7796-bd93-8badba294b64_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentAdditionalPrincipalAmount_019e46d7-b3d9-7849-b807-19f8377c068f_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional principal amount</link:label>
    <link:label id="lab_vate_DebtInstrumentAdditionalPrincipalAmount_label_en-US" xlink:label="lab_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Additional Principal Amount</link:label>
    <link:label id="lab_vate_DebtInstrumentAdditionalPrincipalAmount_documentation_en-US" xlink:label="lab_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Additional Principal Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:href="vate-20260630.xsd#vate_DebtInstrumentAdditionalPrincipalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:to="lab_vate_DebtInstrumentAdditionalPrincipalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019e46d7-b342-765e-8255-4cee1fc7cb5e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Obligations</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_019e46d7-b3d9-7ac3-86ac-d95700a1cbc5_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain" xlink:to="lab_us-gaap_DisposalGroupClassificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019f4578-f3d3-715c-923a-f800b345cfbb_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction cost, net</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplierConcentrationRiskMember_019e46d7-b342-7bfc-b014-c7a72928f42a_terseLabel_en-US" xlink:label="lab_us-gaap_SupplierConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplier Concentration Risk</link:label>
    <link:label id="lab_us-gaap_SupplierConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_SupplierConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplier Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplierConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplierConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplierConcentrationRiskMember" xlink:to="lab_us-gaap_SupplierConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OperatingLeaseModificationIncentive_019e46d7-b3d9-7d5d-ac0c-e92f1d55d4c3_terseLabel_en-US" xlink:label="lab_vate_OperatingLeaseModificationIncentive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease modification incentive</link:label>
    <link:label id="lab_vate_OperatingLeaseModificationIncentive_label_en-US" xlink:label="lab_vate_OperatingLeaseModificationIncentive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease Modification Incentive</link:label>
    <link:label id="lab_vate_OperatingLeaseModificationIncentive_documentation_en-US" xlink:label="lab_vate_OperatingLeaseModificationIncentive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Lease Modification Incentive</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OperatingLeaseModificationIncentive" xlink:href="vate-20260630.xsd#vate_OperatingLeaseModificationIncentive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OperatingLeaseModificationIncentive" xlink:to="lab_vate_OperatingLeaseModificationIncentive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_019e46d7-b46d-780f-a5f1-efa2618dab01_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects_019e46d7-b342-7a44-8676-97b84ad8313b_terseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities, increase due to new projects</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects_label_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Increase Due to New Projects</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Increase Due to New Projects</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:to="lab_vate_ContractWithCustomerLiabilityIncreaseDueToNewProjects" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_019e46d7-b46d-7e35-86ef-b31d3d9aee3a_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average discount rate - finance leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019e46d7-b46d-7ae7-9721-a6cee455e86c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019e46d7-b341-7456-81f3-3f2549a7201d_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total INNOVATE Corp. stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsLineItems_019ea693-0d99-70d5-9919-9b73b74f98b6_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsLineItems" xlink:to="lab_us-gaap_OffsettingAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019e46d7-b27a-746b-a06b-698377762fc5_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_019e46d7-b27a-77ea-8371-e13ad2e290ee_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019e46d7-b3d9-745d-8848-04b47e0516dc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax expense</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivatePlacementMember_019e46d7-b342-799c-8aef-e0c0095e85cb_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
    <link:label id="lab_us-gaap_PrivatePlacementMember_label_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivatePlacementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivatePlacementMember" xlink:to="lab_us-gaap_PrivatePlacementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract_019e46d7-b3d8-70f2-9b39-b931f424666d_terseLabel_en-US" xlink:label="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets obtained in exchange for new lease liabilities:</link:label>
    <link:label id="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract_label_en-US" xlink:label="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset Obtained In Exchange For Lease Liability [Abstract]</link:label>
    <link:label id="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract_documentation_en-US" xlink:label="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset Obtained In Exchange For Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:href="vate-20260630.xsd#vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:to="lab_vate_RightOfUseAssetObtainedInExchangeForLeaseLiabilityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_019f91ee-3155-7661-b18e-570160ac0996_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock_019f452a-bdde-7975-97b3-c912ce0739db_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held for Sale and Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Including Intangible Asset and Goodwill, Impairment and Disposal [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_019e46d7-b3d9-798c-b393-6ec34dbe6bea_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Geographical Area, Revenue and Long-Lived Asset [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Geographical Area, Revenue and Long-Lived Asset [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_A2026ConvertibleNotesMember_019fcb7d-f0f6-7f36-a20e-e7a428232f3f_terseLabel_en-US" xlink:label="lab_vate_A2026ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 Convertible Notes</link:label>
    <link:label id="lab_vate_A2026ConvertibleNotesMember_label_en-US" xlink:label="lab_vate_A2026ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2026 Convertible Notes [Member]</link:label>
    <link:label id="lab_vate_A2026ConvertibleNotesMember_documentation_en-US" xlink:label="lab_vate_A2026ConvertibleNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2026 Convertible Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_A2026ConvertibleNotesMember" xlink:href="vate-20260630.xsd#vate_A2026ConvertibleNotesMember"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019e46d7-b341-70a7-b0b5-23b446a55c79_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
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    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019e46d7-b27a-7b6a-a1c7-a85961caa1e5_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_019e46d7-b342-7122-8810-3d7dfd7613b0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in the Carrying Amount of Goodwill by Reporting Unit</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019e46d7-b3d9-71a5-bb1b-9cde92851b8f_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_019e46d7-b3d9-7306-9720-05961bc08446_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_019e46d7-b342-7659-9e66-9ef38b43e7af_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LeaseLiability_019e46d7-b3d9-77fd-b057-c738e7ce9c6c_totalLabel_en-US" xlink:label="lab_vate_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease liabilities</link:label>
    <link:label id="lab_vate_LeaseLiability_label_en-US" xlink:label="lab_vate_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Liability</link:label>
    <link:label id="lab_vate_LeaseLiability_documentation_en-US" xlink:label="lab_vate_LeaseLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LeaseLiability" xlink:href="vate-20260630.xsd#vate_LeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LeaseLiability" xlink:to="lab_vate_LeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NumberOfGeographicReportableSegments_019e46d7-b27a-7fcc-8b1c-37ff982425a4_terseLabel_en-US" xlink:label="lab_vate_NumberOfGeographicReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable geographic segments</link:label>
    <link:label id="lab_vate_NumberOfGeographicReportableSegments_label_en-US" xlink:label="lab_vate_NumberOfGeographicReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Geographic Reportable Segments</link:label>
    <link:label id="lab_vate_NumberOfGeographicReportableSegments_documentation_en-US" xlink:label="lab_vate_NumberOfGeographicReportableSegments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the number of reportable geographic segments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NumberOfGeographicReportableSegments" xlink:href="vate-20260630.xsd#vate_NumberOfGeographicReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NumberOfGeographicReportableSegments" xlink:to="lab_vate_NumberOfGeographicReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_019e46d7-b3d9-7379-bdc3-5765a5ee89ae_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (remaining period)</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_019eaa85-badd-7278-80a1-fb6427ea8554_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_019eaaaa-f305-7770-9008-234d6882a575_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward_019e46d7-b3d8-714d-8c51-18bd14c47c06_verboseLabel_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, And Restricted Cash Equivalents [Roll Forward]</link:label>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward_label_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, And Restricted Cash Equivalents [Roll Forward]</link:label>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward_documentation_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, And Restricted Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:href="vate-20260630.xsd#vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:to="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019e46d7-b46d-75df-a3fb-557de7a04fdb_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e46d7-b3d9-736b-b5bc-df2358df4ded_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_019e46d7-b3d9-74bb-b53f-06e5ffdeb9e4_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Dividend</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019e46d7-b341-72d8-9971-8fbbfdb83bef_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_019e46d7-b341-781a-9e93-27c5e8288e33_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock cumulative cash dividend rate</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock_019e46d7-b3d9-7435-b649-40f40096632e_terseLabel_en-US" xlink:label="lab_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments</link:label>
    <link:label id="lab_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Investment Holdings, Schedule of Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:to="lab_us-gaap_SummaryOfInvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_019e46d7-b342-71c2-9a18-74ac3b43cfa1_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Finance lease</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019e46d7-b342-78a2-abad-cf998511a089_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest_019e46d7-b342-711e-8c37-c33ec0766ad2_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension fee and accrued interest</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest_label_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee And Accrued Interest</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest_documentation_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee And Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:href="vate-20260630.xsd#vate_DebtInstrumentExtensionFeeAndAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:to="lab_vate_DebtInstrumentExtensionFeeAndAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019e46d7-b27a-777e-bf5d-ca9554b16af4_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Stock Options</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019e46d7-b46d-730d-8b07-6a60d4dba68c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis spread on variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_019e46d7-b342-7854-a5f5-82c96551466c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash, PIK and Special Cash Dividends</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDividendsPayableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_019e46d7-b3d9-791c-8cf1-1435d17745af_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_019e46d7-b27a-7c98-9cd4-e220c8df919a_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future minimum lease payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e46d7-b3d9-79fa-a2d3-34226e02450b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Comprehensive (Loss) Income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019e46d7-b3d9-7bf8-a650-8fdb3ace77c8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividend payments</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019e46d7-b3d9-7951-97bc-5eb7f7005d55_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend payments</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019e46d7-b27a-7081-88c5-efbfe34a5337_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense, period for recognition (in years)</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019e46d7-b342-767b-b054-0bb1ffe44661_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent_019e46d7-b3d9-7865-a493-c47b37046a15_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net, contracts with customers</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent" xlink:to="lab_us-gaap_ContractWithCustomerReceivableAfterAllowanceForCreditLossCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019e46d7-b27a-7212-a756-283511f8fa08_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019e46d7-b27a-7cf9-82c9-ba4eb34d1a81_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_019e46d7-b3d9-7cf3-a524-bfe7fb545f3d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale_019e46d7-b341-7698-b28b-e25b13f30658_totalLabel_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net decrease in cash and cash equivalents, including restricted cash and cash classified within assets held for sale</link:label>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale_label_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash And Restricted Cash Equivalents, Net Increase (Decrease) In Cash And Cash Equivalents, Including Cash Classified Within Assets Held For Sale</link:label>
    <link:label id="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale_documentation_en-US" xlink:label="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash And Restricted Cash Equivalents, Net Increase (Decrease) In Cash And Cash Equivalents, Including Cash Classified Within Assets Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:href="vate-20260630.xsd#vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:to="lab_vate_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsNetIncreaseDecreaseInCashAndCashEquivalentsIncludingCashClassifiedWithinAssetsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_019e46d7-b3d9-79cd-8b4c-121728dd979a_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Debt</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtMember" xlink:to="lab_us-gaap_ConvertibleDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis_019e46d7-b46d-71e7-b49f-1cd66036eea5_terseLabel_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period [Axis]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis_label_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period [Axis]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis_documentation_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:href="vate-20260630.xsd#vate_RevenueRemainingPerformanceObligationPeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:to="lab_vate_RevenueRemainingPerformanceObligationPeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019e46d7-b3d9-749f-8e79-a97d805201df_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019e46d7-b27a-77d2-af38-596f526250d0_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019e46d7-b27a-79c8-8bc3-7796616959d1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_019f446d-d26a-78b1-959f-cd96da40d151_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Goodwill, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_019e46d7-b3d9-7eb7-bfc1-a67faaa1f765_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Alternative</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities without Readily Determinable Fair Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:to="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract_019eab0b-5318-7655-bae7-f2bc997325bd_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019e46d7-b27a-73ca-957b-598220b21b3a_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount_019e46d7-b3d9-7a21-b50d-46b12c5cfe40_totalLabel_en-US" xlink:label="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total aggregate finance lease and debt principal payments</link:label>
    <link:label id="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount_label_en-US" xlink:label="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term, Combined Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtLongtermAndShorttermCombinedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:to="lab_us-gaap_DebtLongtermAndShorttermCombinedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019e46d7-b342-7adf-a94c-240bbbf125d9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_InterestCapitalized_019e46d7-b342-75e4-801a-e9280c3eb51d_terseLabel_en-US" xlink:label="lab_vate_InterestCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest and fees capitalized into principal debt</link:label>
    <link:label id="lab_vate_InterestCapitalized_label_en-US" xlink:label="lab_vate_InterestCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Capitalized</link:label>
    <link:label id="lab_vate_InterestCapitalized_documentation_en-US" xlink:label="lab_vate_InterestCapitalized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Capitalized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_InterestCapitalized" xlink:href="vate-20260630.xsd#vate_InterestCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_InterestCapitalized" xlink:to="lab_vate_InterestCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DTVAmericaCorporationMember_019e46d7-b342-71a1-84f1-c792cc0ed1e1_terseLabel_en-US" xlink:label="lab_vate_DTVAmericaCorporationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DTV America Corporation</link:label>
    <link:label id="lab_vate_DTVAmericaCorporationMember_label_en-US" xlink:label="lab_vate_DTVAmericaCorporationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DTV America Corporation [Member]</link:label>
    <link:label id="lab_vate_DTVAmericaCorporationMember_documentation_en-US" xlink:label="lab_vate_DTVAmericaCorporationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DTV America Corporation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DTVAmericaCorporationMember" xlink:href="vate-20260630.xsd#vate_DTVAmericaCorporationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DTVAmericaCorporationMember" xlink:to="lab_vate_DTVAmericaCorporationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019e46d7-b341-776b-8a01-a6caf94bb83b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019e46d7-b341-7cb3-8722-2bafa51f5bff_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions_019e46d7-b3d9-7a27-8a3e-851689b757d0_terseLabel_en-US" xlink:label="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating loss carryforwards, decrease for uncertain tax positions</link:label>
    <link:label id="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions_label_en-US" xlink:label="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards, Decrease For Uncertain Tax Positions</link:label>
    <link:label id="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions_documentation_en-US" xlink:label="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards, Decrease For Uncertain Tax Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:href="vate-20260630.xsd#vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:to="lab_vate_OperatingLossCarryforwardsDecreaseForUncertainTaxPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019e46d7-b341-7f66-8779-3f0ff01b4814_verboseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_019e46d7-b341-712f-8cb8-5db74741cf62_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_019e46d7-b341-73e2-8e2c-8cc105d28f16_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019e46d7-b3d9-7cb4-9ddf-b0160543afb1_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-current portion of operating lease</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019e46d7-b3d9-7569-8915-49736756556a_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liability, net of current portion</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019e46d7-b3d9-7830-99ec-fcf40bd6c205_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_019e46d7-b27a-7b37-bb5e-03e1cf7eee47_terseLabel_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Use Software</link:label>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_label_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software, In-Development, Internally Developed, and Purchased [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareAndSoftwareDevelopmentCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:to="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019e46d7-b3d9-76d4-96fc-63496259a5f5_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e46d7-b3d9-7653-8df3-d0d9de8cfa5d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e46d7-b3d9-7210-a56d-10abb0109f0e_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e46d7-b3d9-77a2-950d-a0a3cdf044e1_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019e46d7-b3d9-7d3d-bc78-064254b9a43a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent_019eaa85-badd-751d-a64b-0c911ad1121c_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of debt obligations</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Debt Obligations, Current</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Debt Obligations, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationDebtObligationsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestCostsCapitalized_019e46d7-b342-756e-a628-5c34f1f2d4f8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestCostsCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest costs capitalized</link:label>
    <link:label id="lab_us-gaap_InterestCostsCapitalized_label_en-US" xlink:label="lab_us-gaap_InterestCostsCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Costs Capitalized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestCostsCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestCostsCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestCostsCapitalized" xlink:to="lab_us-gaap_InterestCostsCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValueOutstanding_019e46d7-b3d9-7b09-b341-b54903f18de8_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock value outstanding</link:label>
    <link:label id="lab_us-gaap_PreferredStockValueOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValueOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValueOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValueOutstanding" xlink:to="lab_us-gaap_PreferredStockValueOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019e46d7-b341-70ea-bfc7-921f312cf6b1_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_019e46d7-b3d9-72be-b486-63e5015c5ec7_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019e46d7-b342-7b36-a8ab-c6366e1fd196_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock_019e46d7-b27a-7d42-bb86-b661b158911c_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3 and Series A-4 Preferred Stock (as converted) (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Conversion of Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_019e46d7-b342-73fc-a5c6-23da4fff15cf_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disclosure of Compensation Related Costs, Share-based Payments [Abstract]</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments_019e46d7-b342-7ee8-bbd0-b5ecb043bce1_negatedTerseLabel_en-US" xlink:label="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cumulative unrecognized loss on equity method investments</link:label>
    <link:label id="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments_label_en-US" xlink:label="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cumulative Unrecognized Gain (Loss) On Equity Method Investments</link:label>
    <link:label id="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments_documentation_en-US" xlink:label="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cumulative Unrecognized Gain (Loss) On Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:href="vate-20260630.xsd#vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:to="lab_vate_CumulativeUnrecognizedGainLossOnEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e46d7-b3d9-7b28-a394-01095e1c59e8_netLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total revenue from contracts with customers</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e46d7-b3d9-7e90-a523-95ea90a2ef7f_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Life Sciences segment revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019e46d7-b3d9-7559-bdf9-24fe64b71911_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotes850Member_019e46d7-b342-7c53-9b59-2c9340599fd9_terseLabel_en-US" xlink:label="lab_vate_SeniorNotes850Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.50% Note</link:label>
    <link:label id="lab_vate_SeniorNotes850Member_label_en-US" xlink:label="lab_vate_SeniorNotes850Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes, 8.50% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotes850Member_documentation_en-US" xlink:label="lab_vate_SeniorNotes850Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes, 8.50%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotes850Member" xlink:href="vate-20260630.xsd#vate_SeniorNotes850Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotes850Member" xlink:to="lab_vate_SeniorNotes850Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_019e46d7-b3d9-7f87-a68c-2521408bd505_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Availability for revolving loans</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold_019e46d7-b46d-794b-baea-5d0025171194_terseLabel_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accreting dividend threshold rate</link:label>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold_label_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Accreting Dividends Accruing Rate, Required Threshold</link:label>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold_documentation_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Accreting Dividends Accruing Rate, Required Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:href="vate-20260630.xsd#vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:to="lab_vate_PreferredStockAccretingDividendsAccruingRateRequiredThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_019e46d7-b341-718f-ba06-f052c74ca6b0_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Principal payments for other debt obligations</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfOtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EstimatedEarningsOnContracts_019e46d7-b341-7205-b696-188c2925fd9c_terseLabel_en-US" xlink:label="lab_vate_EstimatedEarningsOnContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated earnings</link:label>
    <link:label id="lab_vate_EstimatedEarningsOnContracts_label_en-US" xlink:label="lab_vate_EstimatedEarningsOnContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimated Earnings On Contracts</link:label>
    <link:label id="lab_vate_EstimatedEarningsOnContracts_documentation_en-US" xlink:label="lab_vate_EstimatedEarningsOnContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Estimated Earnings On Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EstimatedEarningsOnContracts" xlink:href="vate-20260630.xsd#vate_EstimatedEarningsOnContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EstimatedEarningsOnContracts" xlink:to="lab_vate_EstimatedEarningsOnContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019e46d7-b27a-70e4-986c-b8ef49de9eaa_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_019eaaaa-ab22-763d-b894-66392a28947c_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_InvestmentsExcludingAssetsHeldForSale_019fb54e-4201-7897-9e30-de20fdcbbaf4_terseLabel_en-US" xlink:label="lab_vate_InvestmentsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_vate_InvestmentsExcludingAssetsHeldForSale_label_en-US" xlink:label="lab_vate_InvestmentsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Excluding Assets Held for Sale</link:label>
    <link:label id="lab_vate_InvestmentsExcludingAssetsHeldForSale_documentation_en-US" xlink:label="lab_vate_InvestmentsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Excluding Assets Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_InvestmentsExcludingAssetsHeldForSale" xlink:href="vate-20260630.xsd#vate_InvestmentsExcludingAssetsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_InvestmentsExcludingAssetsHeldForSale" xlink:to="lab_vate_InvestmentsExcludingAssetsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_BusinessAndOrganizationLineItems_019e46d7-b27a-7bed-8f46-61ea8c92dd4a_terseLabel_en-US" xlink:label="lab_vate_BusinessAndOrganizationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business And Organization [Line Items]</link:label>
    <link:label id="lab_vate_BusinessAndOrganizationLineItems_label_en-US" xlink:label="lab_vate_BusinessAndOrganizationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business And Organization [Line Items]</link:label>
    <link:label id="lab_vate_BusinessAndOrganizationLineItems_documentation_en-US" xlink:label="lab_vate_BusinessAndOrganizationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business And Organization [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_BusinessAndOrganizationLineItems" xlink:href="vate-20260630.xsd#vate_BusinessAndOrganizationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_BusinessAndOrganizationLineItems" xlink:to="lab_vate_BusinessAndOrganizationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment_019fb54d-14e0-796d-a588-ae50fe2d6e7e_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, held for sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SpectrumSegmentMember_019e46d7-b3d9-72c6-84a0-74637496e1bf_terseLabel_en-US" xlink:label="lab_vate_SpectrumSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spectrum Segment</link:label>
    <link:label id="lab_vate_SpectrumSegmentMember_019e46d7-b3d9-7fab-b32b-60423898fd43_verboseLabel_en-US" xlink:label="lab_vate_SpectrumSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Spectrum</link:label>
    <link:label id="lab_vate_SpectrumSegmentMember_label_en-US" xlink:label="lab_vate_SpectrumSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Spectrum Segment [Member]</link:label>
    <link:label id="lab_vate_SpectrumSegmentMember_documentation_en-US" xlink:label="lab_vate_SpectrumSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Spectrum Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SpectrumSegmentMember" xlink:href="vate-20260630.xsd#vate_SpectrumSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SpectrumSegmentMember" xlink:to="lab_vate_SpectrumSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_019e46d7-b3d9-7ed6-ae2d-b026bef46b3c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Current Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherCurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_019e46d7-b27a-7723-89fc-847bc97e13df_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in progress</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionInProgressMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConstructionInProgressMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressMember" xlink:to="lab_us-gaap_ConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_019e46d7-b3d9-7cf5-a070-4f62423639f3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt conversion, share issued (in shares)</link:label>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_label_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent_019e46d7-b3d9-7d4d-9d8c-c9b55b95e4e1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RestrictedStockAndRestrictedStockUnitsMember_019e46d7-b3d9-7a4f-9214-af356fd28e4a_terseLabel_en-US" xlink:label="lab_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock and Restricted Stock Units</link:label>
    <link:label id="lab_vate_RestrictedStockAndRestrictedStockUnitsMember_label_en-US" xlink:label="lab_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock And Restricted Stock Units [Member]</link:label>
    <link:label id="lab_vate_RestrictedStockAndRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock And Restricted Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:href="vate-20260630.xsd#vate_RestrictedStockAndRestrictedStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:to="lab_vate_RestrictedStockAndRestrictedStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DTVAmericaMember_019e46d7-b3d9-7368-9ed7-38e8fea68eec_terseLabel_en-US" xlink:label="lab_vate_DTVAmericaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DTV America</link:label>
    <link:label id="lab_vate_DTVAmericaMember_label_en-US" xlink:label="lab_vate_DTVAmericaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DTV America [Member]</link:label>
    <link:label id="lab_vate_DTVAmericaMember_documentation_en-US" xlink:label="lab_vate_DTVAmericaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DTV America [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DTVAmericaMember" xlink:href="vate-20260630.xsd#vate_DTVAmericaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DTVAmericaMember" xlink:to="lab_vate_DTVAmericaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived_019e46d7-b27a-7186-9f88-517c71473cf8_terseLabel_en-US" xlink:label="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Surrender fees, number of equal installments to be received</link:label>
    <link:label id="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived_label_en-US" xlink:label="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surrender Fees, Number Of Equal Installments To Be Received</link:label>
    <link:label id="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived_documentation_en-US" xlink:label="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surrender Fees, Number Of Equal Installments To Be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:href="vate-20260630.xsd#vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:to="lab_vate_SurrenderFeesNumberOfEqualInstallmentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019e46d7-b3d9-749f-a1d4-081711766f15_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019e46d7-b341-7168-805b-cea0ace6ad98_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_019e46d7-b3d9-7e03-8086-ab8bc9e0dac4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other (expense) income:</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019e46d7-b3d9-7c4f-92c1-2a65e68760c3_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019e46d7-b3d9-7ec9-8808-44f60e0bbedf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_019e46d7-b341-789a-92e1-80cd651d713e_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining performance obligation amount</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_019e46d7-b341-7d52-bc79-d27e4567d5d8_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Remaining unsatisfied performance obligations</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_019e46d7-b342-7065-ab49-917b7764b98e_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finance Lease, Liability, Maturity</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_019e46d7-b3d9-78a5-89e1-cc0484e69e7e_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (remaining period)</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_BusinessAndOrganizationTable_019e46d7-b3d9-710f-ad5e-7cc59e4a6143_terseLabel_en-US" xlink:label="lab_vate_BusinessAndOrganizationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business And Organization [Table]</link:label>
    <link:label id="lab_vate_BusinessAndOrganizationTable_label_en-US" xlink:label="lab_vate_BusinessAndOrganizationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business And Organization [Table]</link:label>
    <link:label id="lab_vate_BusinessAndOrganizationTable_documentation_en-US" xlink:label="lab_vate_BusinessAndOrganizationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business And Organization [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_BusinessAndOrganizationTable" xlink:href="vate-20260630.xsd#vate_BusinessAndOrganizationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_BusinessAndOrganizationTable" xlink:to="lab_vate_BusinessAndOrganizationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings_019e46d7-b342-7595-b8b2-7d501e42b56b_negatedTerseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Billings in excess of costs and estimated earnings</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings_label_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Billings In Excess Of Costs And Estimated Earnings</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Billings In Excess Of Costs And Estimated Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:to="lab_vate_ContractWithCustomerLiabilityBillingsInExcessOfCostsAndEstimatedEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_019e46d7-b3d9-778c-a0e0-70229d03bc72_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_019e46d7-b3d9-7782-b197-89bc9c6a9517_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Dividends in Excess of Retained Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_TransportationRevenueMember_019e46d7-b342-7a55-a757-5feabee78815_terseLabel_en-US" xlink:label="lab_vate_TransportationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transportation</link:label>
    <link:label id="lab_vate_TransportationRevenueMember_019e46d7-b342-7cb6-9402-4b23cca7b877_verboseLabel_en-US" xlink:label="lab_vate_TransportationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Transportation</link:label>
    <link:label id="lab_vate_TransportationRevenueMember_label_en-US" xlink:label="lab_vate_TransportationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transportation Revenue [Member]</link:label>
    <link:label id="lab_vate_TransportationRevenueMember_documentation_en-US" xlink:label="lab_vate_TransportationRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transportation Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_TransportationRevenueMember" xlink:href="vate-20260630.xsd#vate_TransportationRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_TransportationRevenueMember" xlink:to="lab_vate_TransportationRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo_019e46d7-b27a-75a0-8132-efa4cfe71686_totalLabel_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal In Year Two</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo_documentation_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal In Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="vate-20260630.xsd#vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019e46d7-b341-78be-9ca1-d1c036f351c0_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019e46d7-b3d8-75a1-a29b-75433cbb46a0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ExitFeesPayable_019fcb85-480f-76c3-98a6-9b26939594f4_verboseLabel_en-US" xlink:label="lab_vate_ExitFeesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Exit fees</link:label>
    <link:label id="lab_vate_ExitFeesPayable_019e46d7-b3d9-7d96-bc78-e5141440c2d1_terseLabel_en-US" xlink:label="lab_vate_ExitFeesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit fees (non-current portion)</link:label>
    <link:label id="lab_vate_ExitFeesPayable_label_en-US" xlink:label="lab_vate_ExitFeesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exit Fees Payable</link:label>
    <link:label id="lab_vate_ExitFeesPayable_documentation_en-US" xlink:label="lab_vate_ExitFeesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exit Fees Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ExitFeesPayable" xlink:href="vate-20260630.xsd#vate_ExitFeesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ExitFeesPayable" xlink:to="lab_vate_ExitFeesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019e46d7-b342-7300-9d13-f38edf98c092_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_019e46d7-b46d-7e88-9cd4-591e76cdd229_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finished goods</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Finished Goods, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoods" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryFinishedGoods"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoods" xlink:to="lab_us-gaap_InventoryFinishedGoods" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDiscontinuedOperationsMember_019e46d7-b27a-76ed-9249-e8f36fd87885_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_SegmentDiscontinuedOperationsMember_label_en-US" xlink:label="lab_us-gaap_SegmentDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDiscontinuedOperationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDiscontinuedOperationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDiscontinuedOperationsMember" xlink:to="lab_us-gaap_SegmentDiscontinuedOperationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EmbeddedConversionFeatureFairValue_019e46d7-b342-759b-9eef-7d4ea8386e81_terseLabel_en-US" xlink:label="lab_vate_EmbeddedConversionFeatureFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Embedded conversion feature, fair value</link:label>
    <link:label id="lab_vate_EmbeddedConversionFeatureFairValue_label_en-US" xlink:label="lab_vate_EmbeddedConversionFeatureFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Embedded Conversion Feature, Fair Value</link:label>
    <link:label id="lab_vate_EmbeddedConversionFeatureFairValue_documentation_en-US" xlink:label="lab_vate_EmbeddedConversionFeatureFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Embedded Conversion Feature, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EmbeddedConversionFeatureFairValue" xlink:href="vate-20260630.xsd#vate_EmbeddedConversionFeatureFairValue"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_019e46d7-b342-7d6a-b4a9-5bf69f40b981_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019e46d7-b46d-79a2-b955-984bee39865c_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019e46d7-b342-770f-aa26-a8565d009823_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019e46d7-b3d9-7515-bf3b-ff44069f478b_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:to="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ProgressBillingOnContract_019e46d7-b341-7e59-91b7-9089f1a7f2ea_terseLabel_en-US" xlink:label="lab_vate_ProgressBillingOnContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: progress billings</link:label>
    <link:label id="lab_vate_ProgressBillingOnContract_label_en-US" xlink:label="lab_vate_ProgressBillingOnContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Progress Billing On Contract</link:label>
    <link:label id="lab_vate_ProgressBillingOnContract_documentation_en-US" xlink:label="lab_vate_ProgressBillingOnContract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Progress Billing On Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ProgressBillingOnContract" xlink:href="vate-20260630.xsd#vate_ProgressBillingOnContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ProgressBillingOnContract" xlink:to="lab_vate_ProgressBillingOnContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e46d7-b342-747c-a0e6-922bdaa8e4cf_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019e46d7-b3d9-76a0-a18f-3d2d67532905_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_019e46d7-b341-7188-a964-2fde7d50c52b_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019e46d7-b341-7886-bcd9-7a454defb8a7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_019e46d7-b27a-7e16-a1ef-7d2668224500_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt conversion, amount exchanged</link:label>
    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_label_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Original Debt, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionOriginalDebtAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_019e46d7-b3d9-7b2e-8c65-7b1224baac7f_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets and Liabilities Held for Sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_019e46d7-b342-7b00-9e05-0ff1b581d9ca_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_019e46d7-b342-7516-8f50-ca5464c2546a_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_019e46d7-b341-7ea9-85a3-b02c9280489e_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum contractual term of company's exercisable options</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_019e46d7-b46d-7d87-a875-51981389b272_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityLenderDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:to="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019e46d7-b342-7c72-82a6-3e793b24d42e_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019e46d7-b342-76a8-a0bb-fb575a89089c_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member_019e46d7-b3d9-7a92-b721-15e80ba2ea38_terseLabel_en-US" xlink:label="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SOFR plus 5.75% Revolving Line of Credit</link:label>
    <link:label id="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member_label_en-US" xlink:label="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SOFR plus 5.75% Revolving Line Of Credit Due 2026 [Member]</link:label>
    <link:label id="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member_documentation_en-US" xlink:label="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit 5.75% [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:href="vate-20260630.xsd#vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:to="lab_vate_SOFRPlus5.75RevolvingLineOfCreditDue2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019e46d7-b3d9-7c4e-93ee-93a1879b18b9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_019e46d7-b341-73d5-a258-dce911e8cb3c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGoodwillTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTable" xlink:to="lab_us-gaap_ScheduleOfGoodwillTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_019e46d7-b27a-78dd-abd0-8506d34a9e1d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019e46d7-b27a-77db-96dc-ac1bfc17f691_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019e46d7-b342-7d9d-a787-b6ccba160b1d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019e46d7-b3d9-7fc8-a1cc-4e6b2ed98721_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_019e46d7-b341-7815-a260-5310af59d678_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019e46d7-b27a-7e92-a636-0d8482b5c07b_verboseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_019e46d7-b27a-7ff1-adea-5e847443985c_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_019e46d7-b27a-7d90-8ea4-e6bf3ed868dd_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Infrastructure segment revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_019e46d7-b27a-7b67-b852-3906810ad01b_netLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019e46d7-b3d9-7fa8-8150-e0797b09d037_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_019e46d7-b3d9-77df-9833-58067d074fe9_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating loss carryforwards, U.S.</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Domestic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019e46d7-b46d-7d0a-a133-57910d3a41eb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss from equity investees</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019e46d7-b46d-7ef9-8f2f-297dab02bc7c_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Loss from equity investees</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AlternativeInvestment_019e46d7-b3d9-72a5-bd77-d291121b0076_terseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement alternative investment</link:label>
    <link:label id="lab_us-gaap_AlternativeInvestment_label_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alternative Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AlternativeInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AlternativeInvestment" xlink:to="lab_us-gaap_AlternativeInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_019e46d7-b27a-79bf-a3af-1435e6a1f2c8_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of right-of-use assets</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_019e46d7-b341-72bd-b4f5-fc2b4121a9d5_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019e46d7-b3d9-708a-8fbd-32f2c84e60b3_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeNamesMember_019e46d7-b3d9-77ed-a790-02867b351e5e_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade names</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019e46d7-b342-7ad1-9ea7-c26ddffdf718_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Award [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019e46d7-b342-7937-8748-c7eaf896103f_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (remaining period)</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019e46d7-b342-7934-99fc-fded8932490e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019e46d7-b342-7b51-8ec7-8a37b1ddbeaa_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019e46d7-b3d9-7061-8c55-c76a27491af2_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of proxy and voting rights from minority holders</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentConsentFeePercentage_019fa9ac-9f27-71bb-980f-09bbf7abaed7_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentConsentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consent fee percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentConsentFeePercentage_label_en-US" xlink:label="lab_vate_DebtInstrumentConsentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Consent Fee Percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentConsentFeePercentage_documentation_en-US" xlink:label="lab_vate_DebtInstrumentConsentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Consent Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentConsentFeePercentage" xlink:href="vate-20260630.xsd#vate_DebtInstrumentConsentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentConsentFeePercentage" xlink:to="lab_vate_DebtInstrumentConsentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_019e46d7-b27a-7eff-924b-fb8ee2619b0e_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_019e46d7-b27a-7919-97b3-7314c366ff59_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_019e46d7-b27a-7527-ae4d-0d687cb12bcc_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SOFRPlus2.75TermLoanDue2030Member_019e46d7-b27a-7c44-843f-14009dd296d8_terseLabel_en-US" xlink:label="lab_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Term Loan</link:label>
    <link:label id="lab_vate_SOFRPlus2.75TermLoanDue2030Member_label_en-US" xlink:label="lab_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Term Loan due 2030 [Member]</link:label>
    <link:label id="lab_vate_SOFRPlus2.75TermLoanDue2030Member_documentation_en-US" xlink:label="lab_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Term Loan due 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:href="vate-20260630.xsd#vate_SOFRPlus2.75TermLoanDue2030Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:to="lab_vate_SOFRPlus2.75TermLoanDue2030Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019e46d7-b27a-7990-87ae-dc6454e96826_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019e46d7-b3d9-7d47-a1fa-b5dccff43225_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, debt</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019e46d7-b3d9-734d-bda6-4fe629064b0b_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, debt (less than)</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_019e46d7-b3d9-75c5-8637-af7f13658c01_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract_019e46f0-e073-7c2b-a75d-50b746f2a1ab_terseLabel_en-US" xlink:label="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract_label_en-US" xlink:label="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maturities Of Long-Term Debt And Finance Lease Obligations [Abstract]</link:label>
    <link:label id="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract_documentation_en-US" xlink:label="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maturities Of Long-Term Debt And Finance Lease Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:href="vate-20260630.xsd#vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:to="lab_vate_MaturitiesOfLongTermDebtAndFinanceLeaseObligationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019e46d7-b3d9-7408-8b7b-7358cf7f634b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain_019e46d7-b3d9-7440-82e3-6c3227275ac6_terseLabel_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period [Domain]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain_label_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period [Domain]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain_documentation_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:href="vate-20260630.xsd#vate_RevenueRemainingPerformanceObligationPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:to="lab_vate_RevenueRemainingPerformanceObligationPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConventionRevenueMember_019e46d7-b3d9-7711-a7a2-8f93c91c5c07_verboseLabel_en-US" xlink:label="lab_vate_ConventionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Convention</link:label>
    <link:label id="lab_vate_ConventionRevenueMember_019e46d7-b3d9-717e-952b-484ac5573104_terseLabel_en-US" xlink:label="lab_vate_ConventionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convention</link:label>
    <link:label id="lab_vate_ConventionRevenueMember_label_en-US" xlink:label="lab_vate_ConventionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convention Revenue [Member]</link:label>
    <link:label id="lab_vate_ConventionRevenueMember_documentation_en-US" xlink:label="lab_vate_ConventionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convention Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConventionRevenueMember" xlink:href="vate-20260630.xsd#vate_ConventionRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConventionRevenueMember" xlink:to="lab_vate_ConventionRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019e46d7-b3d9-7b34-9c72-c592e6de5b0d_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Percentage of ownership (approximately)</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset_019eaa6a-849c-761d-ad75-8c25f011fe84_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal ownership, percentage</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Ownership Percentage in Disposed Asset</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Ownership Percentage in Disposed Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationOwnershipPercentageInDisposedAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_019e46d7-b3d9-7ef9-94f4-5ffe7a8fc4d6_terseLabel_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_label_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NameOfMajorCustomerDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NameOfMajorCustomerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NameOfMajorCustomerDomain" xlink:to="lab_srt_NameOfMajorCustomerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019e46d7-b342-7a66-9eb5-08c3bb4ece16_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_019e46d7-b342-7f7e-8dea-ce7417794c2a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Inventory</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Inventory, Current [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_019e46d7-b341-71a9-a1e1-cd606b06e518_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_019e46d7-b46d-7ae9-9423-e68528180ae1_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019e46d7-b341-7773-a679-8fe134e28fd8_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivableMaturityOfJuly52026Member_019fcba3-51d1-7067-86c8-887a876face2_terseLabel_en-US" xlink:label="lab_vate_NotesReceivableMaturityOfJuly52026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Receivable, Maturity of July 5, 2026</link:label>
    <link:label id="lab_vate_NotesReceivableMaturityOfJuly52026Member_label_en-US" xlink:label="lab_vate_NotesReceivableMaturityOfJuly52026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable, Maturity of July 5, 2026 [Member]</link:label>
    <link:label id="lab_vate_NotesReceivableMaturityOfJuly52026Member_documentation_en-US" xlink:label="lab_vate_NotesReceivableMaturityOfJuly52026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable, Maturity of July 5, 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivableMaturityOfJuly52026Member" xlink:href="vate-20260630.xsd#vate_NotesReceivableMaturityOfJuly52026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivableMaturityOfJuly52026Member" xlink:to="lab_vate_NotesReceivableMaturityOfJuly52026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryRawMaterials_019e46d7-b342-79ee-b63a-40a56d49f123_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterials" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Raw materials and consumables</link:label>
    <link:label id="lab_us-gaap_InventoryRawMaterials_label_en-US" xlink:label="lab_us-gaap_InventoryRawMaterials" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Raw Materials, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterials" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryRawMaterials"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryRawMaterials" xlink:to="lab_us-gaap_InventoryRawMaterials" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_019e46d7-b3d9-7a85-bf2b-421ed014823f_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e46d7-b3d9-7b31-962b-6e031d2d5398_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentExpectedInterestDue_019fb15e-8aad-74b6-a3a0-a953acef492f_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentExpectedInterestDue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected interest due</link:label>
    <link:label id="lab_vate_DebtInstrumentExpectedInterestDue_label_en-US" xlink:label="lab_vate_DebtInstrumentExpectedInterestDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Expected Interest Due</link:label>
    <link:label id="lab_vate_DebtInstrumentExpectedInterestDue_documentation_en-US" xlink:label="lab_vate_DebtInstrumentExpectedInterestDue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Expected Interest Due</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentExpectedInterestDue" xlink:href="vate-20260630.xsd#vate_DebtInstrumentExpectedInterestDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentExpectedInterestDue" xlink:to="lab_vate_DebtInstrumentExpectedInterestDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfRevenue_019e46d7-b3d9-73cb-889d-779481baaf22_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue</link:label>
    <link:label id="lab_us-gaap_CostOfRevenue_label_en-US" xlink:label="lab_us-gaap_CostOfRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfRevenue" xlink:to="lab_us-gaap_CostOfRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019e46d7-b342-762b-bfad-a765635084c1_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019e46d7-b3d9-75f2-902f-6ee20977cec2_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019e46d7-b342-7d35-8d2e-8cf24e4e0f47_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_019e46d7-b3d9-7015-83f0-f7d310690119_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash - non-current</link:label>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_019e46d7-b3d9-75b1-adbe-9b79bca2fe28_periodStartLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Restricted cash included in other assets (non-current), beginning of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_019e46d7-b3d9-734b-9f7f-88ebc7f0c96e_periodEndLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Restricted cash included in other assets (non-current), end of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_label_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashNoncurrent" xlink:to="lab_us-gaap_RestrictedCashNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PlantAndTransportationEquipmentMember_019e46d7-b46d-7ed5-8245-43643286df5c_terseLabel_en-US" xlink:label="lab_vate_PlantAndTransportationEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plant and transportation equipment</link:label>
    <link:label id="lab_vate_PlantAndTransportationEquipmentMember_label_en-US" xlink:label="lab_vate_PlantAndTransportationEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plant And Transportation Equipment [Member]</link:label>
    <link:label id="lab_vate_PlantAndTransportationEquipmentMember_documentation_en-US" xlink:label="lab_vate_PlantAndTransportationEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Plant and transportation equipment.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PlantAndTransportationEquipmentMember" xlink:href="vate-20260630.xsd#vate_PlantAndTransportationEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PlantAndTransportationEquipmentMember" xlink:to="lab_vate_PlantAndTransportationEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019e46d7-b341-7994-8440-b19fd8b885a8_netLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_019e46d7-b341-7437-855e-c5f54838f9a2_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultThreshold_019e46d7-b342-7633-8cd9-2d50a50c0699_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Judgment default threshold</link:label>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultThreshold_label_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Judgment Default Threshold</link:label>
    <link:label id="lab_vate_DebtInstrumentJudgmentDefaultThreshold_documentation_en-US" xlink:label="lab_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Judgment Default Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:href="vate-20260630.xsd#vate_DebtInstrumentJudgmentDefaultThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:to="lab_vate_DebtInstrumentJudgmentDefaultThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_019e46d7-b341-7c72-8168-15ab6d94aec6_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RevolvingCreditAgreementMember_019e46d7-b46d-7665-b006-3c85c5999846_terseLabel_en-US" xlink:label="lab_vate_RevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Agreement</link:label>
    <link:label id="lab_vate_RevolvingCreditAgreementMember_label_en-US" xlink:label="lab_vate_RevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Agreement [Member]</link:label>
    <link:label id="lab_vate_RevolvingCreditAgreementMember_documentation_en-US" xlink:label="lab_vate_RevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revolving Credit Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RevolvingCreditAgreementMember" xlink:href="vate-20260630.xsd#vate_RevolvingCreditAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RevolvingCreditAgreementMember" xlink:to="lab_vate_RevolvingCreditAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019e46d7-b3d9-748e-b6a6-01ec4d988e94_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_019e46d7-b27a-7430-819b-b41af122b6a3_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Translation adjustments</link:label>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Foreign Currency Translation, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillForeignCurrencyTranslationGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:to="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019e46d7-b3d9-773a-b642-05554087269c_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, temporary equity and stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_019e46d7-b3d9-70f5-82f0-4dc07a27d6a0_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease cost</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity_019e46d7-b3d9-7d8b-93ae-4b8980d85c67_verboseLabel_en-US" xlink:label="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity_label_en-US" xlink:label="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest, Excluding Temporary Equity</link:label>
    <link:label id="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity_documentation_en-US" xlink:label="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest, Excluding Temporary Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:href="vate-20260630.xsd#vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:to="lab_vate_NetIncomeLossIncludingPortionAttributabletoNoncontrollingInterestExcludingTemporaryEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019e46d7-b46d-74eb-89c7-f083ae846aaa_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_019e46d7-b342-7564-bf58-e9c9c6f3d33c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Geographical Area, Revenue and Long-Lived Asset [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Geographical Area, Revenue and Long-Lived Asset [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:to="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_019e46d7-b27a-757b-9838-406635b7ca86_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_019e46d7-b3d9-7178-a90b-2df7be70c101_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating losses subject to expiration</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_019e46d7-b342-7474-b778-c79e3d167daf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwardsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:to="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019e46d7-b3d9-794c-b2a1-79a33a571997_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019e46d7-b3d9-7c51-bec5-9dc878a3469a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_NoTradingSymbolFlag_019e46d7-b3d9-79a7-84e4-28779061e204_terseLabel_en-US" xlink:label="lab_dei_NoTradingSymbolFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">No Trading Symbol</link:label>
    <link:label id="lab_dei_NoTradingSymbolFlag_label_en-US" xlink:label="lab_dei_NoTradingSymbolFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">No Trading Symbol Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_NoTradingSymbolFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_NoTradingSymbolFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_NoTradingSymbolFlag" xlink:to="lab_dei_NoTradingSymbolFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesAndExciseTaxPayableCurrent_019e46d7-b3d9-74fc-87a7-fd8943fc844f_terseLabel_en-US" xlink:label="lab_us-gaap_SalesAndExciseTaxPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued sales and use taxes</link:label>
    <link:label id="lab_us-gaap_SalesAndExciseTaxPayableCurrent_label_en-US" xlink:label="lab_us-gaap_SalesAndExciseTaxPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales and Excise Tax Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesAndExciseTaxPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesAndExciseTaxPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesAndExciseTaxPayableCurrent" xlink:to="lab_us-gaap_SalesAndExciseTaxPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotes8.50And11.50Member_019faeb5-e11f-7e97-8386-e0bf9e12a3fc_terseLabel_en-US" xlink:label="lab_vate_SeniorNotes8.50And11.50Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes, 8.50% and 11.50%</link:label>
    <link:label id="lab_vate_SeniorNotes8.50And11.50Member_label_en-US" xlink:label="lab_vate_SeniorNotes8.50And11.50Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes, 8.50% and 11.50% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotes8.50And11.50Member_documentation_en-US" xlink:label="lab_vate_SeniorNotes8.50And11.50Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes, 8.50% and 11.50%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotes8.50And11.50Member" xlink:href="vate-20260630.xsd#vate_SeniorNotes8.50And11.50Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotes8.50And11.50Member" xlink:to="lab_vate_SeniorNotes8.50And11.50Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesReceivable_019e46d7-b3d9-75e4-9550-cf45bb84b7d4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax receivable</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesReceivable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Receivable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesReceivable" xlink:to="lab_us-gaap_IncomeTaxesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_019e46d7-b27a-7b6d-82f1-0a46545e978b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other operating loss (income)</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherOperatingIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:to="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_019e46d7-b3d8-7b78-a428-01757d7e28cc_verboseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Intrinsic value of options outstanding</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CONXAffiliateLetterAgreementMember_019eaa6a-d7af-7030-9000-058562706a3d_terseLabel_en-US" xlink:label="lab_vate_CONXAffiliateLetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CONX Affiliate Letter Agreement</link:label>
    <link:label id="lab_vate_CONXAffiliateLetterAgreementMember_label_en-US" xlink:label="lab_vate_CONXAffiliateLetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CONX Affiliate Letter Agreement [Member]</link:label>
    <link:label id="lab_vate_CONXAffiliateLetterAgreementMember_documentation_en-US" xlink:label="lab_vate_CONXAffiliateLetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CONX Affiliate Letter Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CONXAffiliateLetterAgreementMember" xlink:href="vate-20260630.xsd#vate_CONXAffiliateLetterAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CONXAffiliateLetterAgreementMember" xlink:to="lab_vate_CONXAffiliateLetterAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2_019e46d7-b3d9-7e66-9caa-2cfaeb34a9ea_terseLabel_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend payable, additional amount accrued, for prior period 2</link:label>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2_label_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Payable, Additional Amount Accrued, For Prior Period 2</link:label>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2_documentation_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Payable, Additional Amount Accrued, For Prior Period 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:href="vate-20260630.xsd#vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:to="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCurrentLiabilitiesTableTextBlock_019e46d7-b342-7027-8cd3-77598bbb1970_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCurrentLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Current Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherCurrentLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherCurrentLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Current Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCurrentLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCurrentLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCurrentLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OtherCurrentLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019e46d7-b27a-7c96-bed7-444a23857a4c_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PercentageOfLossAllocatedAbstract_019e46d7-b3d9-7a09-90b2-c6f17ea9c9a1_terseLabel_en-US" xlink:label="lab_vate_PercentageOfLossAllocatedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of earnings (loss) allocated to:</link:label>
    <link:label id="lab_vate_PercentageOfLossAllocatedAbstract_label_en-US" xlink:label="lab_vate_PercentageOfLossAllocatedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Loss Allocated [Abstract]</link:label>
    <link:label id="lab_vate_PercentageOfLossAllocatedAbstract_documentation_en-US" xlink:label="lab_vate_PercentageOfLossAllocatedAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage Of Loss Allocated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PercentageOfLossAllocatedAbstract" xlink:href="vate-20260630.xsd#vate_PercentageOfLossAllocatedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PercentageOfLossAllocatedAbstract" xlink:to="lab_vate_PercentageOfLossAllocatedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherDataAbstract_019e46d7-b3d9-78fc-85e1-b41c7157531c_terseLabel_en-US" xlink:label="lab_vate_OtherDataAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other data:</link:label>
    <link:label id="lab_vate_OtherDataAbstract_label_en-US" xlink:label="lab_vate_OtherDataAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Data [Abstract]</link:label>
    <link:label id="lab_vate_OtherDataAbstract_documentation_en-US" xlink:label="lab_vate_OtherDataAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Data</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherDataAbstract" xlink:href="vate-20260630.xsd#vate_OtherDataAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherDataAbstract" xlink:to="lab_vate_OtherDataAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_IncreaseDecreaseInAccruedPreferredStock_019e46d7-b3d9-7a5a-8f5e-597b9eaee68a_terseLabel_en-US" xlink:label="lab_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in accrued preferred stock</link:label>
    <link:label id="lab_vate_IncreaseDecreaseInAccruedPreferredStock_label_en-US" xlink:label="lab_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Accrued Preferred Stock</link:label>
    <link:label id="lab_vate_IncreaseDecreaseInAccruedPreferredStock_documentation_en-US" xlink:label="lab_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Accrued Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:href="vate-20260630.xsd#vate_IncreaseDecreaseInAccruedPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:to="lab_vate_IncreaseDecreaseInAccruedPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1_019e46d7-b341-7165-9ffa-4cfc5dcc1525_terseLabel_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend payable, additional amount accrued, for prior period 1</link:label>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1_label_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Payable, Additional Amount Accrued, For Prior Period 1</link:label>
    <link:label id="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1_documentation_en-US" xlink:label="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Payable, Additional Amount Accrued, For Prior Period 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:href="vate-20260630.xsd#vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:to="lab_vate_DividendPayableAdditionalAmountAccruedForPriorPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_019e46d7-b3d9-79b2-b6d2-769556cdc034_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss_019e46d7-b3d9-7775-84ae-ee8a928772ea_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketable securities unrealized (losses) gain</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss_019e46d7-b3d9-73bb-bdb3-d531e0e8202e_verboseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized fair value (loss) gain on securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Security, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketableSecuritiesUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:to="lab_us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019e46d7-b3d9-7eda-80ab-fa227e54b59a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_019e46d7-b3d9-7d2b-97bf-05a7c1744e5f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for asset acquisitions</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Productive Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireProductiveAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAmount_019f4578-f3d3-7c8a-b8fd-be2e4e51fbe1_terseLabel_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total debt payoff amount</link:label>
    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAmount_label_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extinguishment of Debt, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtinguishmentOfDebtAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ExtinguishmentOfDebtAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtinguishmentOfDebtAmount" xlink:to="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CGICMember_019e46d7-b342-779b-8d7d-deb6152715da_terseLabel_en-US" xlink:label="lab_vate_CGICMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CGIC</link:label>
    <link:label id="lab_vate_CGICMember_label_en-US" xlink:label="lab_vate_CGICMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CGIC [Member]</link:label>
    <link:label id="lab_vate_CGICMember_documentation_en-US" xlink:label="lab_vate_CGICMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CGIC [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CGICMember" xlink:href="vate-20260630.xsd#vate_CGICMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CGICMember" xlink:to="lab_vate_CGICMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019e46d7-b342-79f2-b1de-5c0a1cfd047b_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019e46d7-b27a-7d04-8443-fc8afe989f62_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets not accounted for at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_019e46d7-b46d-7b30-9013-18c8f2273454_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Debt obligations, net of current portion</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_019e46d7-b46d-736b-b79e-dfb469c9bda9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations, net of current portion</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019e46d7-b342-70ab-a59a-38a1990d75da_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage_019fb23f-1743-7385-8a24-66211d8c52ea_terseLabel_en-US" xlink:label="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes receivable convertible conversion price discount percentage</link:label>
    <link:label id="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage_label_en-US" xlink:label="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable, Convertible, Conversion Price Discount, Percentage</link:label>
    <link:label id="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage_documentation_en-US" xlink:label="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable, Convertible, Conversion Price Discount, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:href="vate-20260630.xsd#vate_NotesReceivableConvertibleConversionPriceDiscountPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:to="lab_vate_NotesReceivableConvertibleConversionPriceDiscountPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019e46d7-b342-784c-a0a0-88883361dcee_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssets_019e46d7-b3d9-7ce9-925c-27c02339ba44_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Current Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherCurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EquityMethodInvestmentInterest_019e46d7-b342-704d-a588-2faf7bb74322_terseLabel_en-US" xlink:label="lab_vate_EquityMethodInvestmentInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, interest</link:label>
    <link:label id="lab_vate_EquityMethodInvestmentInterest_label_en-US" xlink:label="lab_vate_EquityMethodInvestmentInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Interest</link:label>
    <link:label id="lab_vate_EquityMethodInvestmentInterest_documentation_en-US" xlink:label="lab_vate_EquityMethodInvestmentInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EquityMethodInvestmentInterest" xlink:href="vate-20260630.xsd#vate_EquityMethodInvestmentInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EquityMethodInvestmentInterest" xlink:to="lab_vate_EquityMethodInvestmentInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_FinanceLeaseCost_019e46d7-b342-705a-ae4f-3abbfc577c34_totalLabel_en-US" xlink:label="lab_vate_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net finance lease cost</link:label>
    <link:label id="lab_vate_FinanceLeaseCost_label_en-US" xlink:label="lab_vate_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost</link:label>
    <link:label id="lab_vate_FinanceLeaseCost_documentation_en-US" xlink:label="lab_vate_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_FinanceLeaseCost" xlink:href="vate-20260630.xsd#vate_FinanceLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_FinanceLeaseCost" xlink:to="lab_vate_FinanceLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019e46d7-b27a-70bf-adc4-575202742192_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-In Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EarlyLeaseTerminationPaymentReceivable_019e46d7-b27a-7988-bdf1-d85bd9ac1d57_terseLabel_en-US" xlink:label="lab_vate_EarlyLeaseTerminationPaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Early lease termination payment receivable</link:label>
    <link:label id="lab_vate_EarlyLeaseTerminationPaymentReceivable_label_en-US" xlink:label="lab_vate_EarlyLeaseTerminationPaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Early Lease Termination Payment Receivable</link:label>
    <link:label id="lab_vate_EarlyLeaseTerminationPaymentReceivable_documentation_en-US" xlink:label="lab_vate_EarlyLeaseTerminationPaymentReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Early Lease Termination Payment Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EarlyLeaseTerminationPaymentReceivable" xlink:href="vate-20260630.xsd#vate_EarlyLeaseTerminationPaymentReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EarlyLeaseTerminationPaymentReceivable" xlink:to="lab_vate_EarlyLeaseTerminationPaymentReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueNotFromContractWithCustomer_019e46d7-b3d9-7fd9-8065-217eacdc6cd2_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other revenue</link:label>
    <link:label id="lab_us-gaap_RevenueNotFromContractWithCustomer_label_en-US" xlink:label="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Not from Contract with Customer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueNotFromContractWithCustomer" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueNotFromContractWithCustomer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueNotFromContractWithCustomer" xlink:to="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019fcb85-92f2-708d-93ea-a72afaf0e763_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_019e46d7-b342-769e-ac07-ee1159dcc5bb_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_019e46d7-b3d9-705f-8b24-ddd611cbbf0d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Excluding Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e46d7-b3d9-71ae-a80f-4841c3e5e9f0_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e46d7-b3d9-7bdb-8b1e-855fcb0a0e08_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, beginning of the period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e46d7-b3d9-7bdc-8b5c-01f74b4658d0_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, end of the period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates_019e46d7-b342-7d6c-a88b-dd32c6f4cc95_terseLabel_en-US" xlink:label="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of property leases with amended termination dates</link:label>
    <link:label id="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates_label_en-US" xlink:label="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Property Leases With Amended Termination Dates</link:label>
    <link:label id="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates_documentation_en-US" xlink:label="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Property Leases With Amended Termination Dates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:href="vate-20260630.xsd#vate_NumberOfPropertyLeasesWithAmendedTerminationDates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:to="lab_vate_NumberOfPropertyLeasesWithAmendedTerminationDates" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UMBBankMember_019e46d7-b46d-7385-bc5e-c61995011d0b_terseLabel_en-US" xlink:label="lab_vate_UMBBankMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UMB Bank</link:label>
    <link:label id="lab_vate_UMBBankMember_label_en-US" xlink:label="lab_vate_UMBBankMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UMB Bank [Member]</link:label>
    <link:label id="lab_vate_UMBBankMember_documentation_en-US" xlink:label="lab_vate_UMBBankMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">UMB Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UMBBankMember" xlink:href="vate-20260630.xsd#vate_UMBBankMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UMBBankMember" xlink:to="lab_vate_UMBBankMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets_019e46d7-b342-7cf6-9381-fa598c42d551_terseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conditional retainage</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets_label_en-US" xlink:label="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Conditional Retainage, Assets</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Conditional Retainage, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerAssetConditionalRetainageAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:to="lab_vate_ContractWithCustomerAssetConditionalRetainageAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019e46d7-b3d9-7f2f-9aab-dc5736ad5a79_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization (including amounts in cost of revenue)</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit_019e46d7-b342-78bb-96da-a7c8090cfdac_terseLabel_en-US" xlink:label="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accordion feature to increase line of credit</link:label>
    <link:label id="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit_label_en-US" xlink:label="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:label id="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit_documentation_en-US" xlink:label="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:href="vate-20260630.xsd#vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:to="lab_vate_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_019e46d7-b46d-78f6-9e48-2be6287d9a2b_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance leases</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate_019e46d7-b46d-7502-9bd7-2bc78356c025_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized tax benefits that would impact effective tax rate</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits that Would Impact Effective Tax Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:to="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019e46d7-b3d9-7100-8828-809203f74bd4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining lease term (years) - operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod_019e46d7-b342-772a-9793-428decbf34c1_terseLabel_en-US" xlink:label="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining payment due period</link:label>
    <link:label id="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod_label_en-US" xlink:label="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Early Lease Termination, Remaining Payment Due Period</link:label>
    <link:label id="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod_documentation_en-US" xlink:label="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Early Lease Termination, Remaining Payment Due Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:href="vate-20260630.xsd#vate_EarlyLeaseTerminationRemainingPaymentDuePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:to="lab_vate_EarlyLeaseTerminationRemainingPaymentDuePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_019e46d7-b342-7550-8670-6e636c0f8e46_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation losses</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_FinanceLeaseInterestRate_019e46d7-b341-7ea0-a07a-09e4b7f9a20b_terseLabel_en-US" xlink:label="lab_vate_FinanceLeaseInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease, interest rate</link:label>
    <link:label id="lab_vate_FinanceLeaseInterestRate_label_en-US" xlink:label="lab_vate_FinanceLeaseInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Rate</link:label>
    <link:label id="lab_vate_FinanceLeaseInterestRate_documentation_en-US" xlink:label="lab_vate_FinanceLeaseInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_FinanceLeaseInterestRate" xlink:href="vate-20260630.xsd#vate_FinanceLeaseInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_FinanceLeaseInterestRate" xlink:to="lab_vate_FinanceLeaseInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_019e46d7-b27a-7c5a-b93f-5317aaa4cfc8_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e46d7-b27a-756d-b6f3-43083409dcfe_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net decrease in cash and cash equivalents, including restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeriesA3A4PreferredStockMember_019e46d7-b46d-7c34-ae2f-c159b8fecc36_terseLabel_en-US" xlink:label="lab_vate_SeriesA3A4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3 , A-4 Preferred Stock</link:label>
    <link:label id="lab_vate_SeriesA3A4PreferredStockMember_label_en-US" xlink:label="lab_vate_SeriesA3A4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-3 , A-4 Preferred Stock [Member]</link:label>
    <link:label id="lab_vate_SeriesA3A4PreferredStockMember_documentation_en-US" xlink:label="lab_vate_SeriesA3A4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-3 , A-4 Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeriesA3A4PreferredStockMember" xlink:href="vate-20260630.xsd#vate_SeriesA3A4PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeriesA3A4PreferredStockMember" xlink:to="lab_vate_SeriesA3A4PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract_019fae98-d588-7198-956d-b848bddf3f55_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-current assets</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e46d7-b341-7828-9916-f4e2efdd4777_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to INNOVATE Corp.</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019e46d7-b342-76d4-8625-f62681c84a75_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_019e46d7-b3d9-7419-9c8e-e0e0bb5e9cc7_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BridgeLoanMember_019eabc1-8e39-7599-8cc4-1f62a4bc46ab_terseLabel_en-US" xlink:label="lab_us-gaap_BridgeLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bridge Loan</link:label>
    <link:label id="lab_us-gaap_BridgeLoanMember_label_en-US" xlink:label="lab_us-gaap_BridgeLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bridge Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BridgeLoanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BridgeLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BridgeLoanMember" xlink:to="lab_us-gaap_BridgeLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_019e46d7-b27a-72d0-957b-ddd71d08c79a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from disposal of property, plant and equipment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019e46d7-b341-7b8a-9aad-10bbacff6ef4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedPremium_019e46d7-b342-7ccf-86bb-00071b5e0683_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedPremium" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized premium</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedPremium_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Premium</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedPremium" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedPremium"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedPremium" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedPremium" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_019e46d7-b341-7053-9aba-7604712ddf20_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Exercisable at beginning balance (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_019e46d7-b341-7d84-bd77-c5b94c854448_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Exercisable at ending balance (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CommercialRevenueMember_019e46d7-b341-7d9f-94b8-cc5192e1dd5f_verboseLabel_en-US" xlink:label="lab_vate_CommercialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial</link:label>
    <link:label id="lab_vate_CommercialRevenueMember_019e46d7-b341-7717-a7e9-6d72bb13fa10_terseLabel_en-US" xlink:label="lab_vate_CommercialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial</link:label>
    <link:label id="lab_vate_CommercialRevenueMember_label_en-US" xlink:label="lab_vate_CommercialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Revenue [Member]</link:label>
    <link:label id="lab_vate_CommercialRevenueMember_documentation_en-US" xlink:label="lab_vate_CommercialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CommercialRevenueMember" xlink:href="vate-20260630.xsd#vate_CommercialRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CommercialRevenueMember" xlink:to="lab_vate_CommercialRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares_019e46d7-b342-7afa-83ab-aeb81687a57f_totalLabel_en-US" xlink:label="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total (in shares)</link:label>
    <link:label id="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares_label_en-US" xlink:label="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Participating Securities, Including Common Stock, Shares</link:label>
    <link:label id="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares_documentation_en-US" xlink:label="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Participating Securities, Including Common Stock, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:href="vate-20260630.xsd#vate_ParticipatingSecuritiesIncludingCommonStockShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:to="lab_vate_ParticipatingSecuritiesIncludingCommonStockShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedIncomeTaxes_019e46d7-b3d9-76fa-a9bf-4dd58c13892a_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued income taxes</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Income Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedIncomeTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxes" xlink:to="lab_us-gaap_AccruedIncomeTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerNetAssetLiability_019e46d7-b342-7b59-9f65-51aabb8ce0d0_totalLabel_en-US" xlink:label="lab_vate_ContractWithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net contract assets (liabilities)</link:label>
    <link:label id="lab_vate_ContractWithCustomerNetAssetLiability_label_en-US" xlink:label="lab_vate_ContractWithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Net Asset (Liability)</link:label>
    <link:label id="lab_vate_ContractWithCustomerNetAssetLiability_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerNetAssetLiability" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerNetAssetLiability" xlink:to="lab_vate_ContractWithCustomerNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_019e46d7-b341-7424-932b-d715e993e2bc_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAbstract" xlink:to="lab_us-gaap_TemporaryEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock_019e46d7-b342-7a48-86f3-dede2b3715a4_terseLabel_en-US" xlink:label="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Costs and Recognized Earnings in Excess of Billings and Billings in Excess of Costs and Recognized Earnings on Uncompleted Contracts</link:label>
    <link:label id="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock_label_en-US" xlink:label="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs And Recognized Earnings In Excess Of Billings And Billings In Excess Of Costs And Recognized Earnings On Uncompleted Contracts [Table Text Block]</link:label>
    <link:label id="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock_documentation_en-US" xlink:label="lab_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Costs And Recognized Earnings In Excess Of Billings And Billings In Excess Of Costs And Recognized Earnings On Uncompleted Contracts [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock" xlink:href="vate-20260630.xsd#vate_CostsAndRecognizedEarningsInExcessOfBillingsAndBillingsInExcessOfCostsAndRecognizedEarningsOnUncompletedContractsTableTextBlock"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_019f91c5-8d4e-7c1e-9249-7e3ac81b3b4d_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock_019e46d7-b3d9-79c7-bf4c-52050baee085_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets, Noncurrent [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherAssetsNoncurrentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019e46d7-b27a-7e0f-ad65-b511423fe4f2_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_BuildingAndLeaseholdImprovementsMember_019e46d7-b46d-7dc3-95d1-fc939e48afb3_terseLabel_en-US" xlink:label="lab_vate_BuildingAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and leasehold improvements</link:label>
    <link:label id="lab_vate_BuildingAndLeaseholdImprovementsMember_label_en-US" xlink:label="lab_vate_BuildingAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building And Leasehold Improvements [Member]</link:label>
    <link:label id="lab_vate_BuildingAndLeaseholdImprovementsMember_documentation_en-US" xlink:label="lab_vate_BuildingAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Building And Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_BuildingAndLeaseholdImprovementsMember" xlink:href="vate-20260630.xsd#vate_BuildingAndLeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_BuildingAndLeaseholdImprovementsMember" xlink:to="lab_vate_BuildingAndLeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e46d7-b27a-7988-a6cd-3a7a05a5565f_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_019e46d7-b342-7622-af76-cd4cf4216a90_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining performance obligation period</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount_019e46d7-b342-7760-9d6e-e4756694216d_terseLabel_en-US" xlink:label="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Daily VWAP, threshold amount (in dollars per share)</link:label>
    <link:label id="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount_label_en-US" xlink:label="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Daily Volume Weighted-Average Price, Threshold Amount</link:label>
    <link:label id="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount_documentation_en-US" xlink:label="lab_vate_DailyVolumeWeightedAveragePriceThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Daily Volume Weighted-Average Price, Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DailyVolumeWeightedAveragePriceThresholdAmount" xlink:href="vate-20260630.xsd#vate_DailyVolumeWeightedAveragePriceThresholdAmount"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019e46d7-b3d9-7e93-986b-35868396a9c2_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Shares</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MajorCustomersAxis_019e46d7-b3d9-74ad-8f74-d480f4098d53_terseLabel_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:label id="lab_srt_MajorCustomersAxis_label_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MajorCustomersAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MajorCustomersAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MajorCustomersAxis" xlink:to="lab_srt_MajorCustomersAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019e46d7-b342-7660-a735-11c5a15909b5_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.001 par value Shares authorized: 250,000,000; Shares issued: 13,818,904; Shares outstanding: 13,641,866 and 13,655,062, respectively</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019e46d7-b342-7e20-97d7-8b3a2e4dea76_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019fa9b6-6c8c-7c7c-90f7-ce0b059850ea_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair value, Debt Obligation</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis_019e46d7-b3d9-72d5-8519-8fff3f911e2d_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PerformanceBondsMember_019e46d7-b3d9-7d82-8522-735d270e7c59_terseLabel_en-US" xlink:label="lab_vate_PerformanceBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Bonds</link:label>
    <link:label id="lab_vate_PerformanceBondsMember_label_en-US" xlink:label="lab_vate_PerformanceBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Bonds [Member]</link:label>
    <link:label id="lab_vate_PerformanceBondsMember_documentation_en-US" xlink:label="lab_vate_PerformanceBondsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Bonds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PerformanceBondsMember" xlink:href="vate-20260630.xsd#vate_PerformanceBondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PerformanceBondsMember" xlink:to="lab_vate_PerformanceBondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent_019e46d7-b46d-7ed5-8a49-d2c700744204_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Miscellaneous, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsMiscellaneousNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:to="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_019e46d7-b3d9-7f05-8a25-8f194ceab4d6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Requisite service period (in years)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold_019e46d7-b27a-7863-bb2a-4b7a81cee21d_terseLabel_en-US" xlink:label="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt covenant, mandatory prepayment, proceeds from certain asset sales, amount threshold</link:label>
    <link:label id="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold_label_en-US" xlink:label="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Mandatory Prepayment, Proceeds From Certain Asset Sales, Amount Threshold</link:label>
    <link:label id="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold_documentation_en-US" xlink:label="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Mandatory Prepayment, Proceeds From Certain Asset Sales, Amount Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:href="vate-20260630.xsd#vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:to="lab_vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_019e46d7-b46d-79c3-8424-d893fd640186_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UnsecuredNoteDue2026Member_019e46d7-b27a-747b-a4d5-8686cecd84a0_terseLabel_en-US" xlink:label="lab_vate_UnsecuredNoteDue2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Note due 2026</link:label>
    <link:label id="lab_vate_UnsecuredNoteDue2026Member_label_en-US" xlink:label="lab_vate_UnsecuredNoteDue2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Note due 2026 [Member]</link:label>
    <link:label id="lab_vate_UnsecuredNoteDue2026Member_documentation_en-US" xlink:label="lab_vate_UnsecuredNoteDue2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Note due 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UnsecuredNoteDue2026Member" xlink:href="vate-20260630.xsd#vate_UnsecuredNoteDue2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UnsecuredNoteDue2026Member" xlink:to="lab_vate_UnsecuredNoteDue2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_019e46d7-b3d9-73c7-b275-e32347a1a747_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total outstanding principal</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_019e46d7-b3d9-7192-ac50-1cf39765d23b_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total aggregate finance lease and debt principal payments</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_019e46d7-b3d9-7514-8dd4-1e065d1d8062_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total aggregate finance lease and debt principal payments</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation, Including Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019e46d7-b46d-7571-b36e-a140c22a280d_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillLineItems_019e46d7-b3d9-7397-b33f-20f3de84b4a5_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_019e46d7-b3d9-7375-92f3-f47a57889241_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_019eab0d-d6ab-7eec-bf7d-cca30d78f096_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_019e46d7-b341-788e-b8b5-6da3357bbcc6_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing cash flows for finance leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_019e46d7-b27a-7266-a676-e0ef17e68d0c_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaid_019fa9ac-9f27-7610-aee1-0603ba2b2b70_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
    <link:label id="lab_us-gaap_InterestPaid_label_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Including Capitalized Interest, Operating and Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaid" xlink:to="lab_us-gaap_InterestPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTextBlock_019e46d7-b341-778c-989a-9fda9ad0a6e5_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTextBlock" xlink:to="lab_us-gaap_InvestmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_GenovelOrthopedicsIncMember_019e46d7-b3d9-7818-a8d1-6f5d338896c9_terseLabel_en-US" xlink:label="lab_vate_GenovelOrthopedicsIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Genoval Orthopedics inc.</link:label>
    <link:label id="lab_vate_GenovelOrthopedicsIncMember_label_en-US" xlink:label="lab_vate_GenovelOrthopedicsIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Genovel Orthopedics, Inc [Member]</link:label>
    <link:label id="lab_vate_GenovelOrthopedicsIncMember_documentation_en-US" xlink:label="lab_vate_GenovelOrthopedicsIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to the acquiree entity.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_GenovelOrthopedicsIncMember" xlink:href="vate-20260630.xsd#vate_GenovelOrthopedicsIncMember"/>
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    <link:label id="lab_us-gaap_LossContingenciesTable_019e46d7-b27a-7cf4-aa8d-dd854e9329a4_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember_019f446b-978a-7f73-9b78-d2770d81f2c4_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Held-for-Sale, Not Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember_label_en-US" xlink:label="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Held-for-Sale, Not Discontinued Operations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:to="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_R2TechnologiesMember_019e46d7-b342-7103-9112-653c411d7a1e_terseLabel_en-US" xlink:label="lab_vate_R2TechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">R2 Technologies</link:label>
    <link:label id="lab_vate_R2TechnologiesMember_label_en-US" xlink:label="lab_vate_R2TechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">R2 Technologies [Member]</link:label>
    <link:label id="lab_vate_R2TechnologiesMember_documentation_en-US" xlink:label="lab_vate_R2TechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">R2 Technologies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_R2TechnologiesMember" xlink:href="vate-20260630.xsd#vate_R2TechnologiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_R2TechnologiesMember" xlink:to="lab_vate_R2TechnologiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest_019e46d7-b341-75a1-b997-dd68d3c74908_verboseLabel_en-US" xlink:label="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income</link:label>
    <link:label id="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest_label_en-US" xlink:label="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Including Portion Attributable to Noncontrolling Interest and Redeemable Noncontrolling Interest</link:label>
    <link:label id="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest_documentation_en-US" xlink:label="lab_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Including Portion Attributable to Noncontrolling Interest and Redeemable Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest" xlink:href="vate-20260630.xsd#vate_OtherComprehensiveIncomeLossIncludingPortionAttributabletoNoncontrollingInterestandRedeemableNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_019e46d7-b3d8-7a1f-ae11-184ee585b55a_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019e46d7-b341-7b53-9c88-1db99929ca40_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019e46d7-b342-78d7-8cfb-1f6925b34cdc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment, net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019e46d7-b341-7619-a9c2-9448684862ea_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets_019e46d7-b46d-7c27-853f-50dd0949dd93_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital cash expenditures</link:label>
    <link:label id="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets_label_en-US" xlink:label="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Long-Lived Asset, Expenditure for Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentExpenditureAdditionToLongLivedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:to="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e46d7-b3d9-7936-976f-e12823b2ad5d_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e46d7-b3d9-7804-92c8-3c835527e9d4_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding - basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_019e46d7-b3d8-7c50-ba1d-a362dcdf21f6_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNetCurrent"/>
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    <link:label id="lab_vate_NetIncomeLossAttributableToCommonAndParticipatingPreferredStockholders_019fd2d1-097c-7064-8ba9-9cfcaa063a10_totalLabel_en-US" xlink:label="lab_vate_NetIncomeLossAttributableToCommonAndParticipatingPreferredStockholders" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders and participating preferred stockholders</link:label>
    <link:label id="lab_vate_NetIncomeLossAttributableToCommonAndParticipatingPreferredStockholders_label_en-US" xlink:label="lab_vate_NetIncomeLossAttributableToCommonAndParticipatingPreferredStockholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income Loss Attributable To Common And Participating Preferred Stockholders</link:label>
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    <link:label id="lab_us-gaap_LossContingenciesLineItems_019e46d7-b27a-75f8-bf9c-7f46805c2b4c_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019e46d7-b3d9-703e-a662-a5c1dd9c94e2_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure_019e46d7-b341-761d-9586-2a3594ba2fb0_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:to="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_019e46d7-b3d9-764b-8124-8e29d2375ae8_terseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Net</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
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    <link:label id="lab_dei_DocumentInformationLineItems_019e46d7-b3d9-77cb-8f89-313d3206abed_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_019eaa85-badd-731b-bb3d-33657450d5b6_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_019eaaaa-c3ed-7e48-9708-0179e0fac8a4_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_019fb551-82d7-7f8d-8b42-78e5db25335a_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total assets, held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019e46d7-b342-765b-b45e-eae1a276cf2c_negatedLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LeisureRevenueMember_019e46d7-b342-775d-a226-0491c8304321_terseLabel_en-US" xlink:label="lab_vate_LeisureRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leisure</link:label>
    <link:label id="lab_vate_LeisureRevenueMember_019faeaa-80a5-7e2d-ba65-b8f07823d5e1_verboseLabel_en-US" xlink:label="lab_vate_LeisureRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Leisure</link:label>
    <link:label id="lab_vate_LeisureRevenueMember_label_en-US" xlink:label="lab_vate_LeisureRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leisure Revenue [Member]</link:label>
    <link:label id="lab_vate_LeisureRevenueMember_documentation_en-US" xlink:label="lab_vate_LeisureRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leisure Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LeisureRevenueMember" xlink:href="vate-20260630.xsd#vate_LeisureRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LeisureRevenueMember" xlink:to="lab_vate_LeisureRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019e46d7-b342-7d76-a52a-f856c9f80afd_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019e46d7-b3d9-700d-98ab-e274fded15c2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CustomerBMember_019e46d7-b3d9-7020-9c20-cb2f46092ce3_terseLabel_en-US" xlink:label="lab_vate_CustomerBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer B</link:label>
    <link:label id="lab_vate_CustomerBMember_label_en-US" xlink:label="lab_vate_CustomerBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer B [Member]</link:label>
    <link:label id="lab_vate_CustomerBMember_documentation_en-US" xlink:label="lab_vate_CustomerBMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CustomerBMember" xlink:href="vate-20260630.xsd#vate_CustomerBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CustomerBMember" xlink:to="lab_vate_CustomerBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_019e46d7-b46d-7779-8079-7387221515bf_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsGross" xlink:to="lab_us-gaap_DeferredFinanceCostsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease_019e46d7-b3d9-7bb5-93d2-b064ca918cc3_terseLabel_en-US" xlink:label="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Surrender fees payments received for lease termination</link:label>
    <link:label id="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease_label_en-US" xlink:label="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surrender Fees Payments Received For Termination Of Lease</link:label>
    <link:label id="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease_documentation_en-US" xlink:label="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surrender Fees Payments Received For Termination Of Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:href="vate-20260630.xsd#vate_SurrenderFeesPaymentsReceivedForTerminationOfLease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:to="lab_vate_SurrenderFeesPaymentsReceivedForTerminationOfLease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e46d7-b342-721d-9645-0361d5bc31fb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Increase in net loss attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e46d7-b342-797a-a828-0b93741c33d4_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders - basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableGross_019e46d7-b342-7685-a2f8-492a9f152216_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade receivables</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableGross_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableGross" xlink:to="lab_us-gaap_AccountsReceivableGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019e46d7-b342-71d3-a7e8-f822dd8463df_negatedLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_019e46d7-b46d-7bba-8a0c-d824705cd28b_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019e46d7-b27a-78c1-b65f-1504b3c7ca89_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit, maximum amount</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotes1145Member_019e46d7-b27a-7924-ad04-c9d8c9c74ed1_terseLabel_en-US" xlink:label="lab_vate_SeniorNotes1145Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">11.45% Notes</link:label>
    <link:label id="lab_vate_SeniorNotes1145Member_label_en-US" xlink:label="lab_vate_SeniorNotes1145Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes,11.45% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotes1145Member_documentation_en-US" xlink:label="lab_vate_SeniorNotes1145Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes,11.45%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotes1145Member" xlink:href="vate-20260630.xsd#vate_SeniorNotes1145Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotes1145Member" xlink:to="lab_vate_SeniorNotes1145Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019e46d7-b27a-78c6-899c-5417fa5783ac_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019e46d7-b27a-731b-ad29-d37ad255a89d_negatedLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: current portion of debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019e46d7-b27a-7427-8d8d-71837cbfeab8_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Current portion of debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_GainLossOnStepUpOfEquityMethodInvestment_019e46d7-b27a-7bab-b84b-15c0c26d9b47_terseLabel_en-US" xlink:label="lab_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on step-up of equity method investment</link:label>
    <link:label id="lab_vate_GainLossOnStepUpOfEquityMethodInvestment_label_en-US" xlink:label="lab_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Step-up Of Equity Method Investment</link:label>
    <link:label id="lab_vate_GainLossOnStepUpOfEquityMethodInvestment_documentation_en-US" xlink:label="lab_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Step-up Of Equity Method Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:href="vate-20260630.xsd#vate_GainLossOnStepUpOfEquityMethodInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:to="lab_vate_GainLossOnStepUpOfEquityMethodInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentConversionDenominationMultiple_019e46d7-b3d9-7f28-bf84-a25c05ae6ace_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentConversionDenominationMultiple" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion denomination multiple</link:label>
    <link:label id="lab_vate_DebtInstrumentConversionDenominationMultiple_label_en-US" xlink:label="lab_vate_DebtInstrumentConversionDenominationMultiple" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Conversion Denomination Multiple</link:label>
    <link:label id="lab_vate_DebtInstrumentConversionDenominationMultiple_documentation_en-US" xlink:label="lab_vate_DebtInstrumentConversionDenominationMultiple" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Conversion Denomination Multiple</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentConversionDenominationMultiple" xlink:href="vate-20260630.xsd#vate_DebtInstrumentConversionDenominationMultiple"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentConversionDenominationMultiple" xlink:to="lab_vate_DebtInstrumentConversionDenominationMultiple" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019e46d7-b3d9-7fba-aa71-6046a24c5937_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_019e46d7-b3d9-7288-bf88-6f1945a34e22_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment included in accounts payable or accrued expenses</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_019e46d7-b3d9-7250-96d1-47ae73435b2c_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_019e46d7-b342-7255-95b5-19b8ae060079_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_019e46d7-b46d-7245-a99f-f48018bf5075_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Controlling Interests</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019e46d7-b3d9-7411-ae92-80fb9301e1bb_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LeaseCostNonCurrent_019e46d7-b3d9-7836-bab1-49565929bb67_totalLabel_en-US" xlink:label="lab_vate_LeaseCostNonCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-current lease cost</link:label>
    <link:label id="lab_vate_LeaseCostNonCurrent_label_en-US" xlink:label="lab_vate_LeaseCostNonCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Cost, Non Current</link:label>
    <link:label id="lab_vate_LeaseCostNonCurrent_documentation_en-US" xlink:label="lab_vate_LeaseCostNonCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Cost, Non Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LeaseCostNonCurrent" xlink:href="vate-20260630.xsd#vate_LeaseCostNonCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LeaseCostNonCurrent" xlink:to="lab_vate_LeaseCostNonCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_MinorityHoldersMember_019e46d7-b342-7562-ae95-19375429bf87_terseLabel_en-US" xlink:label="lab_vate_MinorityHoldersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minority Holders</link:label>
    <link:label id="lab_vate_MinorityHoldersMember_label_en-US" xlink:label="lab_vate_MinorityHoldersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minority Holders [Member]</link:label>
    <link:label id="lab_vate_MinorityHoldersMember_documentation_en-US" xlink:label="lab_vate_MinorityHoldersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Minority Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_MinorityHoldersMember" xlink:href="vate-20260630.xsd#vate_MinorityHoldersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_MinorityHoldersMember" xlink:to="lab_vate_MinorityHoldersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_019e46d7-b27a-7cae-a8cc-2316f6d06182_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CommonStockParValue0001PerShareMember_019e46d7-b342-7e67-86b7-f10f110f53c8_terseLabel_en-US" xlink:label="lab_vate_CommonStockParValue0001PerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock, par value $0.001 per share</link:label>
    <link:label id="lab_vate_CommonStockParValue0001PerShareMember_label_en-US" xlink:label="lab_vate_CommonStockParValue0001PerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, par value $0.001 per share [Member]</link:label>
    <link:label id="lab_vate_CommonStockParValue0001PerShareMember_documentation_en-US" xlink:label="lab_vate_CommonStockParValue0001PerShareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, par value $0.001 per share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CommonStockParValue0001PerShareMember" xlink:href="vate-20260630.xsd#vate_CommonStockParValue0001PerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CommonStockParValue0001PerShareMember" xlink:to="lab_vate_CommonStockParValue0001PerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019e46d7-b3d9-7923-9e76-dddb7370a77c_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019e46d7-b342-7bff-b38c-53d9628064c3_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise price of warrants (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_019e46d7-b342-7620-aa0e-99174bdf3beb_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019e46d7-b27a-71ae-8349-ee454fd27c20_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivablesInterestRateStatedPercentage_019f64d1-ce81-7dd1-ba84-76ed8c8d58cc_terseLabel_en-US" xlink:label="lab_vate_NotesReceivablesInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_vate_NotesReceivablesInterestRateStatedPercentage_label_en-US" xlink:label="lab_vate_NotesReceivablesInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivables, Interest Rate, Stated Percentage</link:label>
    <link:label id="lab_vate_NotesReceivablesInterestRateStatedPercentage_documentation_en-US" xlink:label="lab_vate_NotesReceivablesInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivables, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivablesInterestRateStatedPercentage" xlink:href="vate-20260630.xsd#vate_NotesReceivablesInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivablesInterestRateStatedPercentage" xlink:to="lab_vate_NotesReceivablesInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e46d7-b342-7d40-9f78-a44c3c00750f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_019e46d7-b342-7a62-971e-ca3eb79921ae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_AssetsExcludingAssetsHeldForSale_019fb54e-7c56-750e-86d9-c0535349b5de_terseLabel_en-US" xlink:label="lab_vate_AssetsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_vate_AssetsExcludingAssetsHeldForSale_label_en-US" xlink:label="lab_vate_AssetsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Excluding Assets Held for Sale</link:label>
    <link:label id="lab_vate_AssetsExcludingAssetsHeldForSale_documentation_en-US" xlink:label="lab_vate_AssetsExcludingAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Excluding Assets Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_AssetsExcludingAssetsHeldForSale" xlink:href="vate-20260630.xsd#vate_AssetsExcludingAssetsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_AssetsExcludingAssetsHeldForSale" xlink:to="lab_vate_AssetsExcludingAssetsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019e46d7-b27a-70f1-ae85-346e258782ca_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019e46d7-b342-7fa7-a445-56cf21970950_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders_019faf68-1cad-7cdb-904f-3f9d5a31c7a3_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants held by lenders (in shares)</link:label>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders_label_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Milestone Requirement, Warrants Held by Lenders</link:label>
    <link:label id="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders_documentation_en-US" xlink:label="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Milestone Requirement, Warrants Held by Lenders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:href="vate-20260630.xsd#vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:to="lab_vate_DebtInstrumentMilestoneRequirementWarrantsHeldByLenders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestPeriodIncreaseDecrease_019e46d7-b27a-7e98-a4ef-9c465f724afd_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transactions with non-controlling interests and redeemable non-controlling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterestPeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_MinorityInterestPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestPeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestPeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestPeriodIncreaseDecrease" xlink:to="lab_us-gaap_MinorityInterestPeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_019eab0e-6436-7738-8447-089268141f48_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_019e46d7-b3d9-76bc-b804-e1b42d0472f4_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire marketable securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireMarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:to="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019e46d7-b342-7f51-b93e-8801937b611b_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities not accounted for at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage_019e46d7-b3d9-7b7e-b186-5ccd569b3e21_terseLabel_en-US" xlink:label="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt covenant, asset sale prepayment requirement threshold percentage</link:label>
    <link:label id="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage_label_en-US" xlink:label="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Asset Sale Prepayment Requirement Threshold Percentage</link:label>
    <link:label id="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage_documentation_en-US" xlink:label="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Asset Sale Prepayment Requirement Threshold Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:href="vate-20260630.xsd#vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:to="lab_vate_DebtCovenantAssetSalePrepaymentRequirementThresholdPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_019e46d7-b27a-7472-bda3-d4614e343b94_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_019e46d7-b27a-784b-9724-40ea5428519d_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Property, Plant, and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019e46d7-b341-7e86-89f0-c6e8d43e9564_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare_019e46d7-b3d9-7eee-95d7-0b7ceda87d04_terseLabel_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued value per share (in usd per share)</link:label>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare_label_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock Conversion Price Accrued Value Per Share</link:label>
    <link:label id="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare_documentation_en-US" xlink:label="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock Conversion Price Accrued Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:href="vate-20260630.xsd#vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:to="lab_vate_ConvertiblePreferredStockConversionPriceAccruedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_019e46d7-b341-7b9c-bdfc-55103d65f6fd_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from marketable securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:to="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays_019e46d7-b27a-73d0-bd22-a528db7d8341_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Default grace period for payment days</link:label>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays_label_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Default Grace Period For Payment, Days</link:label>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays_documentation_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Default Grace Period For Payment, Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:href="vate-20260630.xsd#vate_DebtInstrumentDefaultGracePeriodForPaymentDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:to="lab_vate_DebtInstrumentDefaultGracePeriodForPaymentDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion_019e46d7-b342-7162-896d-422f3ee9adfd_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares to be issued upon conversion of preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock, Shares Issued upon Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:to="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_019e46d7-b342-7f48-a8bb-69f2a966f064_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-lived intangible assets</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, Indefinite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_019e46d7-b342-71cc-bab9-8696ef3f7866_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation expense unrecognized</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_019e46d7-b342-7e3c-be81-d54dba7de95a_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred financing costs and debt discount</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:to="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_019e46d7-b27a-7657-8eb5-40dc994202a6_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash investing and financing activities:</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019e46d7-b341-730c-9230-a03168ce0117_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Controlling interest (approximately)</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019fafdf-54fe-7482-b5a7-94d05c12ac8c_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019fa9b8-9622-71c4-be79-43d06632998a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_019e46d7-b342-79cf-989d-56e7a48f2683_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_TripleRingTechnologiesIncMember_019e46d7-b341-79a9-8437-a47460ac4bca_terseLabel_en-US" xlink:label="lab_vate_TripleRingTechnologiesIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Triple Ring</link:label>
    <link:label id="lab_vate_TripleRingTechnologiesIncMember_label_en-US" xlink:label="lab_vate_TripleRingTechnologiesIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Triple Ring Technologies, Inc [Member]</link:label>
    <link:label id="lab_vate_TripleRingTechnologiesIncMember_documentation_en-US" xlink:label="lab_vate_TripleRingTechnologiesIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Triple Ring Technologies, Inc [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_TripleRingTechnologiesIncMember" xlink:href="vate-20260630.xsd#vate_TripleRingTechnologiesIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_TripleRingTechnologiesIncMember" xlink:to="lab_vate_TripleRingTechnologiesIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e46d7-b342-7814-a27e-c6b8ff67d222_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e46d7-b342-761e-be5f-5cca4e404431_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding - diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_019e46d7-b342-7512-bc22-60365ef59dcf_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019e46d7-b342-7cae-8a45-6220e462686a_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019e46d7-b3d9-7861-bdc7-2fcb9796bb9c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_019e46d7-b3d9-70d3-960b-e1058f75b62e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from lines of credit, net of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_019e46d7-b342-7c10-bf24-ccceddfaf7a6_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_019e46d7-b342-725a-b496-981d78ed1f0e_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, after Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock_019e46d7-b3d9-76aa-91a2-97072e7419fc_terseLabel_en-US" xlink:label="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lease Right-of-use Assets and Liabilities</link:label>
    <link:label id="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Assets And Liabilities [Table Text Block]</link:label>
    <link:label id="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock_documentation_en-US" xlink:label="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Assets And Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:href="vate-20260630.xsd#vate_LesseeAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_vate_LesseeAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays_019e46d7-b27a-78d9-810a-22cb937b230e_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Default grace period for covenant breach days</link:label>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays_label_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Default Grace Period For Covenant Breach, Days</link:label>
    <link:label id="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays_documentation_en-US" xlink:label="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Default Grace Period For Covenant Breach, Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:href="vate-20260630.xsd#vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:to="lab_vate_DebtInstrumentDefaultGracePeriodForCovenantBreachDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019e46d7-b27a-7dbc-bb51-58b1aa499da0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: amounts representing interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermBorrowings_019e46d7-b3d9-7f5f-ae9c-221aa8bfdba1_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term debt</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowings_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermBorrowings" xlink:to="lab_us-gaap_ShortTermBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_019e46d7-b27a-720c-b71b-1efa7e8b328b_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_019e46d7-b3d9-78ff-94e6-ffa7a466bb9b_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivables_019e46d7-b341-7451-8ee0-96fa55e303c7_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other receivables</link:label>
    <link:label id="lab_us-gaap_OtherReceivables_label_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivables" xlink:to="lab_us-gaap_OtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract_019e46d7-b3d9-7c3c-ad5e-9c185a8cd5c6_terseLabel_en-US" xlink:label="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator for earnings (loss) per share:</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract_label_en-US" xlink:label="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Available to Common Shareholders, Basic And Diluted [Abstract]</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract_documentation_en-US" xlink:label="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Available to Common Shareholders, Basic And Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:href="vate-20260630.xsd#vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:to="lab_vate_UndistributedEarningsLossAvailableToCommonShareholdersBasicAndDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_019e46d7-b342-7925-9cf7-8d06b1555afc_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury Stock</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_019e46d7-b342-7ace-8723-82dfa4db0cd9_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_019e46d7-b27a-7b99-9a3f-eefbc3d6db1e_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of credit outstanding</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtAndCapitalLeaseObligations_019e46d7-b341-79e5-b52b-848abb8b0860_terseLabel_en-US" xlink:label="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_DebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_DebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_019e46d7-b341-78d1-8aee-e14fa51b4b90_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019e46d7-b342-7a95-b5b3-e2f6e4fcb680_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future minimum lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRate_019e46d7-b46d-7b23-9d61-25c7e0ec52ec_terseLabel_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividend rate</link:label>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRate_label_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Accreting Dividends Accruing Rate</link:label>
    <link:label id="lab_vate_PreferredStockAccretingDividendsAccruingRate_documentation_en-US" xlink:label="lab_vate_PreferredStockAccretingDividendsAccruingRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the preferred stock accreting dividends accruing rate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockAccretingDividendsAccruingRate" xlink:href="vate-20260630.xsd#vate_PreferredStockAccretingDividendsAccruingRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockAccretingDividendsAccruingRate" xlink:to="lab_vate_PreferredStockAccretingDividendsAccruingRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019e46d7-b342-74ec-a10f-5cbfb4b0eee8_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested at beginning of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019e46d7-b342-7d3e-b7f9-8735daa692eb_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested at ending of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue20279.50Member_019e46d7-b3d9-70b0-a3c8-0f4db585f00a_terseLabel_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">9.50% Convertible Senior Notes</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue20279.50Member_label_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2027, 9.50% [Member]</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue20279.50Member_documentation_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2027, 9.50%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:href="vate-20260630.xsd#vate_ConvertibleSeniorNotesDue20279.50Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:to="lab_vate_ConvertibleSeniorNotesDue20279.50Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019e46d7-b342-70cd-94d4-55de0bea7728_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Net Income (Loss) to Net Income (Loss) Used in Basic and Diluted EPS Calculations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_019e46d7-b3d9-771b-9531-acb68e4b8601_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019e46d7-b342-7033-a22f-520986a919ab_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments and Related Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019e46d7-b3d9-7f25-af21-36f76d5a8ad4_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CustomerAMember_019e46d7-b342-7c35-8605-e468392ec2f7_terseLabel_en-US" xlink:label="lab_vate_CustomerAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer A</link:label>
    <link:label id="lab_vate_CustomerAMember_label_en-US" xlink:label="lab_vate_CustomerAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer A [Member]</link:label>
    <link:label id="lab_vate_CustomerAMember_documentation_en-US" xlink:label="lab_vate_CustomerAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CustomerAMember" xlink:href="vate-20260630.xsd#vate_CustomerAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CustomerAMember" xlink:to="lab_vate_CustomerAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_019e46d7-b27a-770d-96eb-b9b7076ed74a_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract_019fa905-503b-7346-984f-214503bcea5d_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) allocable to common shares:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding Reconciliation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_019e46d7-b3d9-74e2-b93a-b4ae4f9e04e3_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average remaining life of option outstanding</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted-Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets_019eaa85-badd-7693-b540-faeedd709e04_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current assets</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019e46d7-b341-75cd-b249-428eb5328d27_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_VolumeWeightedAveragePriceThresholdPercentage_019e46d7-b3d9-70d8-96d9-d08e87997e59_terseLabel_en-US" xlink:label="lab_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Volume weighted average price threshold percentage</link:label>
    <link:label id="lab_vate_VolumeWeightedAveragePriceThresholdPercentage_label_en-US" xlink:label="lab_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Volume Weighted Average Price Threshold Percentage</link:label>
    <link:label id="lab_vate_VolumeWeightedAveragePriceThresholdPercentage_documentation_en-US" xlink:label="lab_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the percentage threshold of volume weighted average price.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:href="vate-20260630.xsd#vate_VolumeWeightedAveragePriceThresholdPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:to="lab_vate_VolumeWeightedAveragePriceThresholdPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CreditAndSecurityAgreementsMember_019e46d7-b3d9-7b5e-b2ad-0d4bdd782d89_terseLabel_en-US" xlink:label="lab_vate_CreditAndSecurityAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit and Security Agreements</link:label>
    <link:label id="lab_vate_CreditAndSecurityAgreementsMember_label_en-US" xlink:label="lab_vate_CreditAndSecurityAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit And Security Agreements [Member]</link:label>
    <link:label id="lab_vate_CreditAndSecurityAgreementsMember_documentation_en-US" xlink:label="lab_vate_CreditAndSecurityAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit And Security Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CreditAndSecurityAgreementsMember" xlink:href="vate-20260630.xsd#vate_CreditAndSecurityAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CreditAndSecurityAgreementsMember" xlink:to="lab_vate_CreditAndSecurityAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_019e46d7-b3d9-79dd-bdd0-2cfbef532bee_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Stock Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock Unit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_019e46d7-b27a-7417-9bce-fbb6e3925dae_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable_019e46d7-b3d9-79b7-be96-0eeae214de82_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets, reclassified to receivables</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Reclassified to Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetReclassifiedToReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:to="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019e46d7-b342-7793-ab5c-692615df690c_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019e46d7-b3d9-73c2-bdac-384cbec9ff61_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien_019e46d7-b342-7eb0-8737-eabbc3105cf9_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, number of real estate parcels, first priority lien</link:label>
    <link:label id="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien_label_en-US" xlink:label="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Number Of Real Estate Parcels, First Priority Lien</link:label>
    <link:label id="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien_documentation_en-US" xlink:label="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Number Of Real Estate Parcels, First Priority Lien</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:href="vate-20260630.xsd#vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:to="lab_vate_DebtInstrumentNumberOfRealEstateParcelsFirstPriorityLien" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_019e46d7-b27a-726d-a8e6-182b67373dda_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityAxis" xlink:to="lab_us-gaap_LineOfCreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_MediBeaconIncMember_019e46d7-b341-79e2-8d81-7e6764c7aa92_terseLabel_en-US" xlink:label="lab_vate_MediBeaconIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MediBeacon Inc.</link:label>
    <link:label id="lab_vate_MediBeaconIncMember_label_en-US" xlink:label="lab_vate_MediBeaconIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MediBeacon Inc. [Member]</link:label>
    <link:label id="lab_vate_MediBeaconIncMember_documentation_en-US" xlink:label="lab_vate_MediBeaconIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">MediBeacon Inc. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_MediBeaconIncMember" xlink:href="vate-20260630.xsd#vate_MediBeaconIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_MediBeaconIncMember" xlink:to="lab_vate_MediBeaconIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019e46d7-b3d9-7b62-8fca-a6c35074d778_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effects of exchange rate changes on cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNet_019e46d7-b342-730a-abf8-32abc80ca280_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related receivables from this subsidiary</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeriesA3AndA4PreferredStockMember_019e46d7-b3d9-7fc3-893c-8bbb2efa8fbb_terseLabel_en-US" xlink:label="lab_vate_SeriesA3AndA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3 and A-4 Preferred Stock</link:label>
    <link:label id="lab_vate_SeriesA3AndA4PreferredStockMember_label_en-US" xlink:label="lab_vate_SeriesA3AndA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-3 And A-4 Preferred Stock [Member]</link:label>
    <link:label id="lab_vate_SeriesA3AndA4PreferredStockMember_documentation_en-US" xlink:label="lab_vate_SeriesA3AndA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-3 And A-4 Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeriesA3AndA4PreferredStockMember" xlink:href="vate-20260630.xsd#vate_SeriesA3AndA4PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeriesA3AndA4PreferredStockMember" xlink:to="lab_vate_SeriesA3AndA4PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale_019f452f-9e62-702b-8242-ea8ee5dcdcae_terseLabel_en-US" xlink:label="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in cash and cash equivalents from assets held for sale</link:label>
    <link:label id="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale_label_en-US" xlink:label="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided By (Used In) Cash And Cash Equivalents From Assets Held For Sale</link:label>
    <link:label id="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale_documentation_en-US" xlink:label="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash Provided By (Used In) Cash And Cash Equivalents From Assets Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:href="vate-20260630.xsd#vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:to="lab_vate_CashProvidedByUsedInCashAndCashEquivalentsFromAssetsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock_019e46d7-b342-77f4-bf06-7bb156be73f2_terseLabel_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible notes and accrued interest converted to stock</link:label>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock_label_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Notes And Accrued Interest Converted To Stock</link:label>
    <link:label id="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock_documentation_en-US" xlink:label="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Notes And Accrued Interest Converted To Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:href="vate-20260630.xsd#vate_ConvertibleNotesAndAccruedInterestConvertedToStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:to="lab_vate_ConvertibleNotesAndAccruedInterestConvertedToStock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsGross_019e46d7-b3d9-7e42-b972-a245431ca32e_totalLabel_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Contract revenue earned on uncompleted contracts</link:label>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsGross_label_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost Earned On Uncompleted Contracts, Gross</link:label>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsGross_documentation_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cost Earned On Uncompleted Contracts, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CostEarnedOnUncompletedContractsGross" xlink:href="vate-20260630.xsd#vate_CostEarnedOnUncompletedContractsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CostEarnedOnUncompletedContractsGross" xlink:to="lab_vate_CostEarnedOnUncompletedContractsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019e46d7-b342-7f1f-8210-ac2ee6ee36ef_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest and exit fees</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_019faeb5-e11f-75fe-9b44-289163b62ec2_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio_019f4578-f3d3-7def-8abc-ad5402653e24_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued and capitalized interest, ratio</link:label>
    <link:label id="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio_label_en-US" xlink:label="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debt Covenant, Including Accrued And Capitalized Interest, Ratio</link:label>
    <link:label id="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio_documentation_en-US" xlink:label="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debt Covenant, Including Accrued And Capitalized Interest, Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:href="vate-20260630.xsd#vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:to="lab_vate_DebtInstrumentDebtCovenantIncludingAccruedAndCapitalizedInterestRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_019e46d7-b27a-744d-8d23-985b8415e148_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized premium net of unamortized deferred financing costs</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_019e46d7-b27a-7441-88e2-fa21796327e2_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unamortized issuance discount, issuance premium, and deferred financing costs</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_019e46d7-b342-7d1c-a277-a2b3c970e29e_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_019e46d7-b342-75e1-b412-fe6460fa799d_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019e46d7-b27a-7c56-a47e-a9f2b9fe0f59_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_InvestmentInSubsidiaryConvertibleNote_019e46d7-b341-7061-8ff9-7ce75bbe9d9f_terseLabel_en-US" xlink:label="lab_vate_InvestmentInSubsidiaryConvertibleNote" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment in subsidiary, convertible note</link:label>
    <link:label id="lab_vate_InvestmentInSubsidiaryConvertibleNote_label_en-US" xlink:label="lab_vate_InvestmentInSubsidiaryConvertibleNote" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment In Subsidiary, Convertible Note</link:label>
    <link:label id="lab_vate_InvestmentInSubsidiaryConvertibleNote_documentation_en-US" xlink:label="lab_vate_InvestmentInSubsidiaryConvertibleNote" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment In Subsidiary, Convertible Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_InvestmentInSubsidiaryConvertibleNote" xlink:href="vate-20260630.xsd#vate_InvestmentInSubsidiaryConvertibleNote"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_InvestmentInSubsidiaryConvertibleNote" xlink:to="lab_vate_InvestmentInSubsidiaryConvertibleNote" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableGrossCurrent_019e46d7-b3d9-7de5-8da4-be890352d3b4_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total accounts receivable with customers</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableGrossCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableGrossCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableGrossCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableGrossCurrent" xlink:to="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock_019e46d7-b3d9-7655-8c41-2e4c4ace3923_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Income, Net</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Nonoperating Income (Expense) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_019f4577-3542-7f36-8342-de745d92ff78_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate purchase price, amount</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019e46d7-b3d9-7672-8538-016bbb3a58bc_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_019f446e-4d96-7776-981c-e6fdd0288d0c_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangibles, net</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Intangible Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance_019e46d7-b3d9-7763-a1e2-e9c7c19fe4ff_terseLabel_en-US" xlink:label="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized loss, equity issuance</link:label>
    <link:label id="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance_label_en-US" xlink:label="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Loss, Equity Method Investments, Equity Issuance</link:label>
    <link:label id="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance_documentation_en-US" xlink:label="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized Loss, Equity Method Investments, Equity Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:href="vate-20260630.xsd#vate_RealizedLossEquityMethodInvestmentsEquityIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:to="lab_vate_RealizedLossEquityMethodInvestmentsEquityIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019e46d7-b3d9-7010-890a-08c4f0a2819b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019e46d7-b3d9-7ad3-820e-cb560686bccf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total lease liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019e46d7-b3d9-7f17-9a23-4bdb83a6792d_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding at beginning of period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019e46d7-b3d9-7aa9-9a64-9c08d5e2fc08_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding at ending of period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_019e46d7-b3d9-7c99-a7db-73f31e387b76_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total lease liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_019e46d7-b3d9-7aa4-9173-9604f4e149c7_netLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Obligations under finance leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_019e46d7-b3d9-792e-a0be-f6288a60487b_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total aggregate finance lease and debt principal payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_019e46d7-b3d9-7fe5-8ad0-cc4d6c7f74ed_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other financing activities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payment for) Other Financing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_019e46d7-b3d9-737c-b810-31fa6332f408_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_019e46d7-b3d9-74ee-a9d6-62f768aa906a_verboseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative expenses</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract_019e46d7-b3d9-715d-9985-c84ee244b691_terseLabel_en-US" xlink:label="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of the consolidated segment income from operations to consolidated income (loss) from operations before income taxes:</link:label>
    <link:label id="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract_label_en-US" xlink:label="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation Of The Consolidated Segment Income (Loss) From Operations To Consolidated (Loss) From Operations Before Income Taxes [Abstract]</link:label>
    <link:label id="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract_documentation_en-US" xlink:label="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reconciliation Of The Consolidated Segment Income (Loss) From Operations To Consolidated (Loss) From Operations Before Income Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:href="vate-20260630.xsd#vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:to="lab_vate_ReconciliationOfTheConsolidatedSegmentIncomeLossFromOperationsToConsolidatedLossFromOperationsBeforeIncomeTaxesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage_019e46d7-b341-7c3f-8ef5-c1f0536de4b9_terseLabel_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock (as percent)</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage_label_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Common Stock, Allocation Percentage</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage_documentation_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Common Stock, Allocation Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:href="vate-20260630.xsd#vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:to="lab_vate_UndistributedEarningsLossAllocatedToCommonStockAllocationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_019fb199-fb02-7b56-8953-c86a4ca0c804_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets held for sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_019fb198-e593-71c4-a1be-154e1725e0bb_verboseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other assets held for sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Prepaid and Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019e46d7-b3d9-7f22-9f59-4aed181c65f5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotesDue2026850Member_019e46d7-b27a-7956-8fc4-4dda58022446_terseLabel_en-US" xlink:label="lab_vate_SeniorNotesDue2026850Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.50% Senior Secured Notes</link:label>
    <link:label id="lab_vate_SeniorNotesDue2026850Member_label_en-US" xlink:label="lab_vate_SeniorNotesDue2026850Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes Due 2026, 8.50% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotesDue2026850Member_documentation_en-US" xlink:label="lab_vate_SeniorNotesDue2026850Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes Due 2026, 8.50% [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotesDue2026850Member" xlink:href="vate-20260630.xsd#vate_SeniorNotesDue2026850Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotesDue2026850Member" xlink:to="lab_vate_SeniorNotesDue2026850Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019e46d7-b3d9-79dc-89ee-b930b1267b8e_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ComponentsOfFinanceLeaseCostAbstract_019e46d7-b46d-7b2a-9ab3-9ffec6099187_terseLabel_en-US" xlink:label="lab_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease cost:</link:label>
    <link:label id="lab_vate_ComponentsOfFinanceLeaseCostAbstract_label_en-US" xlink:label="lab_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components Of Finance Lease Cost [Abstract]</link:label>
    <link:label id="lab_vate_ComponentsOfFinanceLeaseCostAbstract_documentation_en-US" xlink:label="lab_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Components Of Finance Lease Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:href="vate-20260630.xsd#vate_ComponentsOfFinanceLeaseCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:to="lab_vate_ComponentsOfFinanceLeaseCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressGross_019e46d7-b46d-7fcd-b599-92178f175845_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contracts in progress</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressGross_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionInProgressGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConstructionInProgressGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressGross" xlink:to="lab_us-gaap_ConstructionInProgressGross" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ScaledCellSolutionsMember_019e46d7-b342-7869-a1fd-4f3b73ec49a2_terseLabel_en-US" xlink:label="lab_vate_ScaledCellSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scaled Cell</link:label>
    <link:label id="lab_vate_ScaledCellSolutionsMember_label_en-US" xlink:label="lab_vate_ScaledCellSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scaled Cell Solutions [Member]</link:label>
    <link:label id="lab_vate_ScaledCellSolutionsMember_documentation_en-US" xlink:label="lab_vate_ScaledCellSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scaled Cell Solutions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ScaledCellSolutionsMember" xlink:href="vate-20260630.xsd#vate_ScaledCellSolutionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ScaledCellSolutionsMember" xlink:to="lab_vate_ScaledCellSolutionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued_019e46d7-b46d-77b5-b985-8a16ff721798_terseLabel_en-US" xlink:label="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt conversion, maximum number of shares to be issued</link:label>
    <link:label id="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued_label_en-US" xlink:label="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Covenant, Maximum Number Of Shares To Be Issued</link:label>
    <link:label id="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued_documentation_en-US" xlink:label="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Conversion, Covenant, Maximum Number Of Shares To Be Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:href="vate-20260630.xsd#vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:to="lab_vate_DebtConversionCovenantMaximumNumberOfSharesToBeIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivablesConvertibleConversionPrice_019f64d1-ce81-7368-bfe1-86847a78ebb6_terseLabel_en-US" xlink:label="lab_vate_NotesReceivablesConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible notes receivable, conversion price</link:label>
    <link:label id="lab_vate_NotesReceivablesConvertibleConversionPrice_label_en-US" xlink:label="lab_vate_NotesReceivablesConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivables, Convertible, Conversion Price</link:label>
    <link:label id="lab_vate_NotesReceivablesConvertibleConversionPrice_documentation_en-US" xlink:label="lab_vate_NotesReceivablesConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivables, Convertible, Conversion Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivablesConvertibleConversionPrice" xlink:href="vate-20260630.xsd#vate_NotesReceivablesConvertibleConversionPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivablesConvertibleConversionPrice" xlink:to="lab_vate_NotesReceivablesConvertibleConversionPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019e46d7-b27a-7f46-82f4-7751281e7692_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Operating Corporate</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019e46d7-b3d9-761d-a1c2-4ca984ae219e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_019f446d-2721-70db-ac0e-e189e38b8c5b_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Property, Plant, and Equipment, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e46d7-b3d9-7460-b73f-7c3ab3db856c_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableMember_019e46d7-b342-7b2e-a6b3-ded262047376_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableMember_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableMember" xlink:to="lab_us-gaap_AccountsReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock_019f4577-3542-7a7d-95eb-c82ab4f62369_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of conversion shares of common stock</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Percentage of Conversion Shares of Common Stock</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Percentage of Conversion Shares of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationPercentageOfConversionSharesOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease_019f7f49-dcc3-73c9-8964-6af30e132f61_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transactions with non-controlling interests and redeemable non-controlling interests</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease" xlink:to="lab_us-gaap_TemporaryEquityIssuePeriodIncreaseOrDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_019e46d7-b3d9-7db5-a33c-e9fc89e1d21d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DBMGlobalCreditFacilitiesMember_019e46d7-b3d9-7bc6-bfc2-191dc335f5f7_terseLabel_en-US" xlink:label="lab_vate_DBMGlobalCreditFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DBM Global Credit Facilities</link:label>
    <link:label id="lab_vate_DBMGlobalCreditFacilitiesMember_label_en-US" xlink:label="lab_vate_DBMGlobalCreditFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DBM Global Credit Facilities [Member]</link:label>
    <link:label id="lab_vate_DBMGlobalCreditFacilitiesMember_documentation_en-US" xlink:label="lab_vate_DBMGlobalCreditFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DBM Global Credit Facilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DBMGlobalCreditFacilitiesMember" xlink:href="vate-20260630.xsd#vate_DBMGlobalCreditFacilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DBMGlobalCreditFacilitiesMember" xlink:to="lab_vate_DBMGlobalCreditFacilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019e46d7-b27a-727a-9d9c-edf9ae92655b_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_019e46d7-b342-7fa3-ab34-61f9cd8af031_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019e46d7-b342-754e-b61e-7f6e33c0a395_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_IndustrialRevenueMember_019e46d7-b341-7d54-beeb-110aae231d53_terseLabel_en-US" xlink:label="lab_vate_IndustrialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrial</link:label>
    <link:label id="lab_vate_IndustrialRevenueMember_019e46d7-b341-7d52-bd89-819e16292615_verboseLabel_en-US" xlink:label="lab_vate_IndustrialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Industrial</link:label>
    <link:label id="lab_vate_IndustrialRevenueMember_label_en-US" xlink:label="lab_vate_IndustrialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrial Revenue [Member]</link:label>
    <link:label id="lab_vate_IndustrialRevenueMember_documentation_en-US" xlink:label="lab_vate_IndustrialRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Industrial Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_IndustrialRevenueMember" xlink:href="vate-20260630.xsd#vate_IndustrialRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_IndustrialRevenueMember" xlink:to="lab_vate_IndustrialRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_019e46d7-b3d9-7f14-94ac-5a160db23e9a_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets Subject to Amortization</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019e46d7-b46d-728c-8b2a-d5b4ee5eb9c5_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization_019e46d7-b342-7bb2-9016-6507ec9fab88_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant, and equipment and finance lease right-of-use asset, gross</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, before Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019e46d7-b342-79a7-bb38-c2e661b502ac_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019e46d7-b341-792e-9c2e-de9d5412cd9e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_019fa9b8-9622-7e0a-89dc-f996b1c3299d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019e46d7-b342-7643-b79e-cdb976368f24_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Grant Date Fair Value</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract_019e46d7-b341-736e-b81f-fe69d45f9a2c_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The above is included in the accompanying Condensed Consolidated Balance Sheets under the following line items:</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract" xlink:to="lab_us-gaap_ContractWithCustomerAssetAndLiabilityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019e46d7-b342-708f-8ed8-0126746be290_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_019e46d7-b46d-717a-ab5e-cc67464aba05_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentPrepaymentBusinessDueDay_019e46d7-b341-7e0d-99d6-1d45b355de1c_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, prepayment business due day</link:label>
    <link:label id="lab_vate_DebtInstrumentPrepaymentBusinessDueDay_label_en-US" xlink:label="lab_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prepayment Business Due Day</link:label>
    <link:label id="lab_vate_DebtInstrumentPrepaymentBusinessDueDay_documentation_en-US" xlink:label="lab_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prepayment Business Due Day</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:href="vate-20260630.xsd#vate_DebtInstrumentPrepaymentBusinessDueDay"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:to="lab_vate_DebtInstrumentPrepaymentBusinessDueDay" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LiquidityAndGoingConcernPolicyTextBlock_019e46d7-b3d9-7c75-b2a9-213c47b5f9f8_terseLabel_en-US" xlink:label="lab_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidity and Going Concern</link:label>
    <link:label id="lab_vate_LiquidityAndGoingConcernPolicyTextBlock_label_en-US" xlink:label="lab_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liquidity and Going Concern [Policy Text Block]</link:label>
    <link:label id="lab_vate_LiquidityAndGoingConcernPolicyTextBlock_documentation_en-US" xlink:label="lab_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liquidity and Going Concern</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:href="vate-20260630.xsd#vate_LiquidityAndGoingConcernPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:to="lab_vate_LiquidityAndGoingConcernPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects_019e46d7-b342-711c-ba88-a5984ce345c3_terseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets, increase due to new projects</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects_label_en-US" xlink:label="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Asset, Increase Due to New Projects</link:label>
    <link:label id="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Asset, Increase Due to New Projects</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerAssetIncreaseDueToNewProjects"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:to="lab_vate_ContractWithCustomerAssetIncreaseDueToNewProjects" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromConvertibleDebt_019e46d7-b46d-7dbd-be8a-3e9e7c055871_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from convertible debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromConvertibleDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Convertible Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromConvertibleDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromConvertibleDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromConvertibleDebt" xlink:to="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_019e46d7-b342-7c4c-88f0-3528944531a4_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Other Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:to="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NatureOfOperations_019e46d7-b3d8-752c-82ec-664b6d4f5d26_terseLabel_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization and Business</link:label>
    <link:label id="lab_us-gaap_NatureOfOperations_label_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NatureOfOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NatureOfOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NatureOfOperations" xlink:to="lab_us-gaap_NatureOfOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019e46d7-b3d9-7bfa-afa9-a7d870464024_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock, net of forfeitures (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019e46d7-b3d9-74ae-a7c4-e163d1ed0086_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CustomerCMember_019e46d7-b3d9-762c-8831-bbfd4d673f2d_terseLabel_en-US" xlink:label="lab_vate_CustomerCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer C</link:label>
    <link:label id="lab_vate_CustomerCMember_label_en-US" xlink:label="lab_vate_CustomerCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer C [Member]</link:label>
    <link:label id="lab_vate_CustomerCMember_documentation_en-US" xlink:label="lab_vate_CustomerCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer C</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CustomerCMember" xlink:href="vate-20260630.xsd#vate_CustomerCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CustomerCMember" xlink:to="lab_vate_CustomerCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019e46d7-b3d9-7e6f-b2b6-9cdc1611c7dc_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <link:label id="lab_us-gaap_TemporaryEquityAccretionOfDividends_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAccretionOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Accretion of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAccretionOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityAccretionOfDividends"/>
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    <link:label id="lab_us-gaap_Investments_019e46d7-b342-7ce9-8caf-483e216280da_netLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_Investments_019e46d7-b342-7d4c-82ac-e84046a7a0cb_totalLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_Investments_019e46d7-b342-7751-b7e3-de74dc8eda21_terseLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_019e46d7-b27a-70a6-ab10-5ebab8e342a9_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A shares issued and outstanding</link:label>
    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Preferred Stock [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesAPreferredStockMember" xlink:to="lab_us-gaap_SeriesAPreferredStockMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_019f91d3-77bc-744d-aa69-9f99d8fbb1a4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs paid to third parties</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019e46d7-b342-749e-a97e-40c6b4163ca8_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e46d7-b27a-7b77-a705-dd3a6ed73991_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash used in financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities_019eaa85-badd-74d3-92d2-10c49dfff53c_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Current</link:label>
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    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_019e46d7-b342-7a92-b89f-f41bed636113_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares withheld to satisfy tax withholdings</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_019e46d7-b3d9-70d9-96c7-828fb882b19a_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract"/>
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    <link:label id="lab_vate_SystemsAndConsumablesRevenueMember_label_en-US" xlink:label="lab_vate_SystemsAndConsumablesRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Systems And Consumables Revenue [Member]</link:label>
    <link:label id="lab_vate_SystemsAndConsumablesRevenueMember_documentation_en-US" xlink:label="lab_vate_SystemsAndConsumablesRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Systems And Consumables Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SystemsAndConsumablesRevenueMember" xlink:href="vate-20260630.xsd#vate_SystemsAndConsumablesRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SystemsAndConsumablesRevenueMember" xlink:to="lab_vate_SystemsAndConsumablesRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_019e46d7-b3d9-7d81-a73a-7e642c577846_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock_019e46d7-b3d9-7f55-88c1-080f22714b60_terseLabel_en-US" xlink:label="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt and Finance Lease Obligations</link:label>
    <link:label id="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock_label_en-US" xlink:label="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Debt And Finance Lease Obligations [Table Text Block]</link:label>
    <link:label id="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock_documentation_en-US" xlink:label="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Debt And Finance Lease Obligations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:href="vate-20260630.xsd#vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:to="lab_vate_ScheduleOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019e46d7-b3d9-7fbd-a583-3150bba56974_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DBMGlobalIncMember_019e46d7-b3d9-7500-81f7-287f82c7e19f_terseLabel_en-US" xlink:label="lab_vate_DBMGlobalIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DBMG</link:label>
    <link:label id="lab_vate_DBMGlobalIncMember_label_en-US" xlink:label="lab_vate_DBMGlobalIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DBM Global Inc [Member]</link:label>
    <link:label id="lab_vate_DBMGlobalIncMember_documentation_en-US" xlink:label="lab_vate_DBMGlobalIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DBM Global Inc. (&#8220;DBMG&#8221;) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DBMGlobalIncMember" xlink:href="vate-20260630.xsd#vate_DBMGlobalIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DBMGlobalIncMember" xlink:to="lab_vate_DBMGlobalIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_019e46d7-b342-7781-a21a-3cd39a57617c_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureTextBlock" xlink:to="lab_us-gaap_InventoryDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_019e46d7-b342-70f4-918b-edcfaf653731_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_019e46d7-b27a-7370-8e49-9cf61381263e_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Intangibles, Net</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset and Goodwill [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019e46d7-b3d9-7a0f-b564-7302b9bd0d3b_negatedLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (income) loss attributable to non-controlling interests and redeemable non-controlling interests</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019e46d7-b342-7642-a918-9383c27183f3_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_019e46d7-b342-7063-901c-a4f083c9a8ab_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue and Contracts in Process</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherEntitiesMember_019e46d7-b3d9-70c0-a0a9-686388b673f4_terseLabel_en-US" xlink:label="lab_vate_OtherEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Entities</link:label>
    <link:label id="lab_vate_OtherEntitiesMember_label_en-US" xlink:label="lab_vate_OtherEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Entities [Member]</link:label>
    <link:label id="lab_vate_OtherEntitiesMember_documentation_en-US" xlink:label="lab_vate_OtherEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherEntitiesMember" xlink:href="vate-20260630.xsd#vate_OtherEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherEntitiesMember" xlink:to="lab_vate_OtherEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_019e46d7-b3d9-79ba-b51e-e6e11d571649_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseCurrent" xlink:to="lab_us-gaap_PrepaidExpenseCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026750Member_019e46d7-b3d9-7019-988b-2baa92303a02_terseLabel_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026750Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">7.50% Convertible Senior Notes</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026750Member_label_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026750Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2026, 7.50% [Member]</link:label>
    <link:label id="lab_vate_ConvertibleSeniorNotesDue2026750Member_documentation_en-US" xlink:label="lab_vate_ConvertibleSeniorNotesDue2026750Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Senior Notes Due 2026, 7.50% [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ConvertibleSeniorNotesDue2026750Member" xlink:href="vate-20260630.xsd#vate_ConvertibleSeniorNotesDue2026750Member"/>
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    <link:label id="lab_vate_CGICPromissoryNoteMember_019e46d7-b342-7aea-b4de-72d99118e927_terseLabel_en-US" xlink:label="lab_vate_CGICPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CGIC Promissory Note</link:label>
    <link:label id="lab_vate_CGICPromissoryNoteMember_label_en-US" xlink:label="lab_vate_CGICPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CGIC Promissory Note [Member]</link:label>
    <link:label id="lab_vate_CGICPromissoryNoteMember_documentation_en-US" xlink:label="lab_vate_CGICPromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CGIC Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CGICPromissoryNoteMember" xlink:href="vate-20260630.xsd#vate_CGICPromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CGICPromissoryNoteMember" xlink:to="lab_vate_CGICPromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_019e46d7-b46d-70bb-8f0a-6aab0a65e094_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Inventories</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInventories" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInventories"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInventories" xlink:to="lab_us-gaap_IncreaseDecreaseInInventories" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_019e46d7-b27a-7fce-a3c4-ac9875dd2c37_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average discount rate - operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherLiabilitiesNoncurrentOther_019e46d7-b341-7c61-9e32-80e604c58c66_terseLabel_en-US" xlink:label="lab_vate_OtherLiabilitiesNoncurrentOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_vate_OtherLiabilitiesNoncurrentOther_label_en-US" xlink:label="lab_vate_OtherLiabilitiesNoncurrentOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent, Other</link:label>
    <link:label id="lab_vate_OtherLiabilitiesNoncurrentOther_documentation_en-US" xlink:label="lab_vate_OtherLiabilitiesNoncurrentOther" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherLiabilitiesNoncurrentOther" xlink:href="vate-20260630.xsd#vate_OtherLiabilitiesNoncurrentOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherLiabilitiesNoncurrentOther" xlink:to="lab_vate_OtherLiabilitiesNoncurrentOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019e46d7-b342-7699-8ed3-a9e6faf35296_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_019e46d7-b342-7d97-abac-bb966b74e5bb_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Net Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityNetIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityNetIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityNetIncome" xlink:to="lab_us-gaap_TemporaryEquityNetIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019e46d7-b342-7a91-b0ef-b2b7a7068551_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions, by Related Party [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RightOfUseAssetAbstract_019e46d7-b342-7d6c-8701-bee5aeb985c6_terseLabel_en-US" xlink:label="lab_vate_RightOfUseAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets:</link:label>
    <link:label id="lab_vate_RightOfUseAssetAbstract_label_en-US" xlink:label="lab_vate_RightOfUseAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset [Abstract]</link:label>
    <link:label id="lab_vate_RightOfUseAssetAbstract_documentation_en-US" xlink:label="lab_vate_RightOfUseAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RightOfUseAssetAbstract" xlink:href="vate-20260630.xsd#vate_RightOfUseAssetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RightOfUseAssetAbstract" xlink:to="lab_vate_RightOfUseAssetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts_019e46d7-b3d9-7617-875e-7f1cf32325ab_terseLabel_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities, revenue recognized</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts_label_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Revenue Recognized Including New Contracts</link:label>
    <link:label id="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts_documentation_en-US" xlink:label="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Revenue Recognized Including New Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:href="vate-20260630.xsd#vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:to="lab_vate_ContractWithCustomerLiabilityRevenueRecognizedIncludingNewContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_019e46d7-b3d9-7f6e-ae9d-823b3ba260c9_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Lease Expense</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_019e46d7-b46d-79df-9470-52374d0a6f5c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_019e46d7-b46d-7209-9ae0-73d68dce7153_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsCurrent" xlink:to="lab_us-gaap_OtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_InfrastructureSegmentMember_019e46d7-b27a-7716-81a8-12c8716181d4_terseLabel_en-US" xlink:label="lab_vate_InfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Infrastructure</link:label>
    <link:label id="lab_vate_InfrastructureSegmentMember_label_en-US" xlink:label="lab_vate_InfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Infrastructure Segment [Member]</link:label>
    <link:label id="lab_vate_InfrastructureSegmentMember_documentation_en-US" xlink:label="lab_vate_InfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Infrastructure Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_InfrastructureSegmentMember" xlink:href="vate-20260630.xsd#vate_InfrastructureSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_InfrastructureSegmentMember" xlink:to="lab_vate_InfrastructureSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_019e46d7-b27a-78d5-90db-485b79d50a76_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares_019f4577-3542-79cb-8b09-fe6ab1c6d579_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of stock, right to receive percentage of common shares</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Conversion of Stock, Right to Receive Percentage of Common Shares</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Conversion of Stock, Right to Receive Percentage of Common Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationConversionOfStockRightToReceivePercentageOfCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne_019e46d7-b342-7c1a-9a0d-6bf974b0a7b2_totalLabel_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne_label_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal In Year One</link:label>
    <link:label id="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne_documentation_en-US" xlink:label="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt And Lease Obligations, Maturities Repayments Of Principal In Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:href="vate-20260630.xsd#vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:to="lab_vate_LongTermDebtAndLeaseObligationsMaturitiesRepaymentsOfPrincipalInYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019e46d7-b3d9-72f7-b365-16a68e3eedc3_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_019e46d7-b3d9-7b8d-bf3f-65add4c402ac_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss, not subject to expiration</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_019eaa85-badd-73e6-bbfd-4db51b3628fd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019e46d7-b342-700b-9f13-68b7a9325497_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_019e46d7-b342-7c0b-986c-44aa12da2f39_terseLabel_en-US" xlink:label="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:label id="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:href="vate-20260630.xsd#vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_vate_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeniorNotesDue202520.00Member_019e46d7-b3d9-7bf3-9d96-b8c46b3c8a34_terseLabel_en-US" xlink:label="lab_vate_SeniorNotesDue202520.00Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes, Due 2025, 20.00%</link:label>
    <link:label id="lab_vate_SeniorNotesDue202520.00Member_label_en-US" xlink:label="lab_vate_SeniorNotesDue202520.00Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes, Due 2025, 20.00% [Member]</link:label>
    <link:label id="lab_vate_SeniorNotesDue202520.00Member_documentation_en-US" xlink:label="lab_vate_SeniorNotesDue202520.00Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes, Due 2025, 20.00%</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeniorNotesDue202520.00Member" xlink:href="vate-20260630.xsd#vate_SeniorNotesDue202520.00Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeniorNotesDue202520.00Member" xlink:to="lab_vate_SeniorNotesDue202520.00Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_019e46d7-b3d9-7b3a-8f4d-1c666a501913_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock Option Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019e46d7-b3d8-73e2-8f30-eaa32bcf4d4d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Exercise Price</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_019e46d7-b342-78d8-9313-fe31f057b1db_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of discount on investments, net</link:label>
    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_label_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Discount (Premium)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfDebtDiscountPremium" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfDebtDiscountPremium"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfDebtDiscountPremium" xlink:to="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis_019e46d7-b342-7c7f-b308-bb593976962c_terseLabel_en-US" xlink:label="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest, ownership percentage by parent, fully diluted basis</link:label>
    <link:label id="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis_label_en-US" xlink:label="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Ownership Percentage By Parent, Fully Diluted Basis</link:label>
    <link:label id="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis_documentation_en-US" xlink:label="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Ownership Percentage By Parent, Fully Diluted Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:href="vate-20260630.xsd#vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:to="lab_vate_NoncontrollingInterestOwnershipPercentageByParentFullyDilutedBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_HealthcareRevenueMember_019e46d7-b342-77f3-8ba7-d4f748172ac8_verboseLabel_en-US" xlink:label="lab_vate_HealthcareRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Healthcare</link:label>
    <link:label id="lab_vate_HealthcareRevenueMember_019e46d7-b342-7ae8-8220-820780bf64b4_terseLabel_en-US" xlink:label="lab_vate_HealthcareRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Healthcare</link:label>
    <link:label id="lab_vate_HealthcareRevenueMember_label_en-US" xlink:label="lab_vate_HealthcareRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Healthcare Revenue [Member]</link:label>
    <link:label id="lab_vate_HealthcareRevenueMember_documentation_en-US" xlink:label="lab_vate_HealthcareRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Healthcare Revenue [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_HealthcareRevenueMember" xlink:href="vate-20260630.xsd#vate_HealthcareRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_HealthcareRevenueMember" xlink:to="lab_vate_HealthcareRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e46d7-b46d-7b6b-aa5c-12643e58360a_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract_019ea6e6-2c34-7cb9-8491-0e4dd5bddb35_terseLabel_en-US" xlink:label="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (Loss) per share</link:label>
    <link:label id="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract_label_en-US" xlink:label="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Loss Per Share Attributable To Common Stock And Participating Preferred Stockholders [Abstract]</link:label>
    <link:label id="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract_documentation_en-US" xlink:label="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Loss Per Share Attributable To Common Stock And Participating Preferred Stockholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:href="vate-20260630.xsd#vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:to="lab_vate_EarningsLossPerShareAttributableToCommonStockAndParticipatingPreferredStockholdersAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019e46d7-b3d9-741a-a8f1-596bc40556ef_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019e46d7-b342-753d-928c-33484aad8943_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019e46d7-b3d9-7124-ac76-20c9b0f0608d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes, net of refunds</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DTVMember_019eaa6b-2a28-75c8-83ef-dd9d9fc5f614_terseLabel_en-US" xlink:label="lab_vate_DTVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DTV</link:label>
    <link:label id="lab_vate_DTVMember_label_en-US" xlink:label="lab_vate_DTVMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">DTV [Member]</link:label>
    <link:label id="lab_vate_DTVMember_documentation_en-US" xlink:label="lab_vate_DTVMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">DTV</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DTVMember" xlink:href="vate-20260630.xsd#vate_DTVMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DTVMember" xlink:to="lab_vate_DTVMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019e46d7-b3d9-78b0-95bc-52c40c57aece_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e46d7-b342-752c-987d-f1003fe267ee_negatedLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net (income) loss attributable to non-controlling interests and redeemable non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019e46d7-b342-782d-9e4d-eb5d6bb74de1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net (income) loss attributable to non-controlling interests and redeemable non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019e46d7-b342-7831-b2be-195371252b34_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019e46d7-b341-73b3-8a07-4783fc582fee_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss) attributable to INNOVATE Corp.</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_019e46d7-b27a-7d0a-960b-651949f43e88_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized discount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_019e46d7-b27a-7514-9dc3-e30a20f70a9b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares withheld to satisfy tax withholdings (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_019e46d7-b341-7f5c-8455-03846fbbcc93_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Original Useful Life</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired, Weighted-Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_019e46d7-b342-740f-be0a-ae163c4a270b_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions_019e46d7-b46d-7ba4-a4f9-11188cd0d505_negatedLabel_en-US" xlink:label="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchase of property, plant and equipment</link:label>
    <link:label id="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions_label_en-US" xlink:label="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Property, Plant And Equipment, Excluding Asset Acquisitions</link:label>
    <link:label id="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions_documentation_en-US" xlink:label="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Property, Plant And Equipment, Excluding Asset Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:href="vate-20260630.xsd#vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:to="lab_vate_PaymentsToAcquirePropertyPlantAndEquipmentExcludingAssetAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019e46d7-b27a-7d92-abca-2dd191899be9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019e46d7-b27a-72ee-a226-061fb9e76137_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_019e46d7-b342-727c-8c10-eb3798cf8e41_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019e46d7-b341-7103-9d38-1de36b538620_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019e46d7-b3d9-792f-b015-4026b34b735c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019e46d7-b3d9-7dd9-b0f0-f526f61e4866_verboseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019eac02-ea00-7964-90f8-7132dc48bbc7_netLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">(Gain) loss on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019e46d7-b3d9-7bbe-b26a-cb28b1a985a5_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain (loss) on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
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    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019e46d7-b342-718b-b1d4-aa3c68376074_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis_019e46d7-b342-741b-bcb7-2075078ad8b0_terseLabel_en-US" xlink:label="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership percentage, fully diluted basis</link:label>
    <link:label id="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis_label_en-US" xlink:label="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage, Fully Diluted Basis</link:label>
    <link:label id="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis_documentation_en-US" xlink:label="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage, Fully Diluted Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:href="vate-20260630.xsd#vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:to="lab_vate_EquityMethodInvestmentOwnershipPercentageFullyDilutedBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentAccruedInterestAndFee_019fc71b-ac4d-74db-a6e0-28cd95bb79b4_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentAccruedInterestAndFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest and exit fees</link:label>
    <link:label id="lab_vate_DebtInstrumentAccruedInterestAndFee_label_en-US" xlink:label="lab_vate_DebtInstrumentAccruedInterestAndFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Accrued Interest And Fee</link:label>
    <link:label id="lab_vate_DebtInstrumentAccruedInterestAndFee_documentation_en-US" xlink:label="lab_vate_DebtInstrumentAccruedInterestAndFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Accrued Interest And Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentAccruedInterestAndFee" xlink:href="vate-20260630.xsd#vate_DebtInstrumentAccruedInterestAndFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentAccruedInterestAndFee" xlink:to="lab_vate_DebtInstrumentAccruedInterestAndFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_019e46d7-b27a-7f90-b287-e93969bf2e50_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019e46d7-b3d9-70b8-bf4a-73a41c019a31_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019e46d7-b3d9-7078-be93-70461cf069d4_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member_019e46d7-b342-74ff-b495-c1df5535d1e4_verboseLabel_en-US" xlink:label="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Revolving Credit Facility</link:label>
    <link:label id="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member_label_en-US" xlink:label="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Revolving Credit Facility due 2030 [Member]</link:label>
    <link:label id="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member_documentation_en-US" xlink:label="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SOFR plus 2.75% Revolving Credit Facility due 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:href="vate-20260630.xsd#vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:to="lab_vate_SOFRPlus2.75RevolvingCreditFacilityDue2030Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_019e46d7-b342-79d6-b853-a26ed0a52888_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Work in process</link:label>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_label_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Work in Process, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryWorkInProcess" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryWorkInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryWorkInProcess" xlink:to="lab_us-gaap_InventoryWorkInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_019e46d7-b27a-7b7a-a77a-20fa7e4441b2_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplementary Financial Information</link:label>
    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Financial Information Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalFinancialInformationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:to="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_019eaa85-badd-7a01-a77d-46643134a9dd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Deferred Tax Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LancerCapitalMember_019e46d7-b3d9-7161-be47-388be73cbae9_terseLabel_en-US" xlink:label="lab_vate_LancerCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lancer Capital</link:label>
    <link:label id="lab_vate_LancerCapitalMember_label_en-US" xlink:label="lab_vate_LancerCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lancer Capital [Member]</link:label>
    <link:label id="lab_vate_LancerCapitalMember_documentation_en-US" xlink:label="lab_vate_LancerCapitalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lancer Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LancerCapitalMember" xlink:href="vate-20260630.xsd#vate_LancerCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LancerCapitalMember" xlink:to="lab_vate_LancerCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments_019e46d7-b3d9-7bf6-af57-3203084be94c_terseLabel_en-US" xlink:label="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable non-controlling interests</link:label>
    <link:label id="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments_019e46d7-b3d9-77ed-b6a1-196c96518e5e_negatedLabel_en-US" xlink:label="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Redeemable non-controlling interest</link:label>
    <link:label id="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments_label_en-US" xlink:label="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Common, Carrying Amount, Net Of Adjustments</link:label>
    <link:label id="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments_documentation_en-US" xlink:label="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Common, Carrying Amount, Net Of Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:href="vate-20260630.xsd#vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:to="lab_vate_RedeemableNoncontrollingInterestEquityCommonCarryingAmountNetOfAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_019e46d7-b342-7a31-88be-ba94e7521972_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third party legal costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Debt Extinguishment or Debt Prepayment Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e46d7-b3d9-7679-a4e5-e61098c28a0e_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from operations before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage_019fd2ca-9ca4-7436-b2b3-7d49acee7af9_terseLabel_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unvested restricted stock (as a percent)</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage_label_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Unvested Restricted Stock, Allocation Percentage</link:label>
    <link:label id="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage_documentation_en-US" xlink:label="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Unvested Restricted Stock, Allocation Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:href="vate-20260630.xsd#vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:to="lab_vate_UndistributedEarningsLossAllocatedToUnvestedRestrictedStockAllocationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019e46d7-b3d9-701c-af90-f7c3103855fb_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 14)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock_019e46d7-b342-7ae1-b3f7-07fc57055963_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncurrent Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncurrentLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OtherNoncurrentLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019e46d7-b342-7a3a-badb-c2e5fc482400_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_LeasesLeaseLiabilityAbstract_019e46d7-b342-77b8-9fe6-b169f6b79cab_terseLabel_en-US" xlink:label="lab_vate_LeasesLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities:</link:label>
    <link:label id="lab_vate_LeasesLeaseLiabilityAbstract_label_en-US" xlink:label="lab_vate_LeasesLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases, Lease Liability [Abstract]</link:label>
    <link:label id="lab_vate_LeasesLeaseLiabilityAbstract_documentation_en-US" xlink:label="lab_vate_LeasesLeaseLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leases, Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_LeasesLeaseLiabilityAbstract" xlink:href="vate-20260630.xsd#vate_LeasesLeaseLiabilityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_LeasesLeaseLiabilityAbstract" xlink:to="lab_vate_LeasesLeaseLiabilityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019e46d7-b342-7183-bffe-589582834acf_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019e46d7-b342-7da8-ab5e-01fe809fe982_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019e46d7-b27a-743a-8386-265022a0f187_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, temporary equity and stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_019e46d7-b27a-70b3-a366-e3cb3c22d240_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryNet_019e46d7-b27a-7df2-a44a-e1add102f69f_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total inventory</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeriesA4PreferredStockMember_019e46d7-b342-7ec6-a091-866c21f908ca_terseLabel_en-US" xlink:label="lab_vate_SeriesA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-4 Preferred Stock</link:label>
    <link:label id="lab_vate_SeriesA4PreferredStockMember_label_en-US" xlink:label="lab_vate_SeriesA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-4 Preferred Stock [Member]</link:label>
    <link:label id="lab_vate_SeriesA4PreferredStockMember_documentation_en-US" xlink:label="lab_vate_SeriesA4PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-4 Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeriesA4PreferredStockMember" xlink:href="vate-20260630.xsd#vate_SeriesA4PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeriesA4PreferredStockMember" xlink:to="lab_vate_SeriesA4PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019e46d7-b341-79cc-95a3-10465fb6c786_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019e46d7-b46d-7fce-a0ea-71d95d9b3fe9_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019e46d7-b3d9-7ef7-9949-ccd689e0fca1_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_019fd2ce-54bf-7300-b481-34d8ed979ee7_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_019fd2b9-186b-7bb7-b207-87bc7f6eec3a_netLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_019e46d7-b3d9-7bd7-ab0f-fffeb341eeda_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019e46d7-b342-76c3-9463-b396972a3ca7_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivableFaceAmount_019e46d7-b342-7405-9dfe-09fd2eab6c70_terseLabel_en-US" xlink:label="lab_vate_NotesReceivableFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes receivable, face amount</link:label>
    <link:label id="lab_vate_NotesReceivableFaceAmount_label_en-US" xlink:label="lab_vate_NotesReceivableFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable, Face Amount</link:label>
    <link:label id="lab_vate_NotesReceivableFaceAmount_documentation_en-US" xlink:label="lab_vate_NotesReceivableFaceAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivableFaceAmount" xlink:href="vate-20260630.xsd#vate_NotesReceivableFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivableFaceAmount" xlink:to="lab_vate_NotesReceivableFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019e46d7-b3d9-7d95-94cc-82426bebe6b8_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e46d7-b3d9-75be-8b0d-78bc1b1e003a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_019e46d7-b342-7dd3-b5ca-ff3c88ad472b_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019e46d7-b342-762d-91f0-311578f99e82_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_019e46d7-b342-7908-976f-5e38e74b17cd_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_019eaa6a-849c-7196-a536-dcf998284515_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_019e46d7-b342-7b5e-8436-908419ee5a13_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, amounts of transaction</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019e46d7-b3d9-70eb-88e5-84616ca0bc7d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_019e46d7-b342-77db-b4a0-26a503542e5b_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_019e46d7-b3d9-75d0-a95a-79d2e19bb19e_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term lease costs</link:label>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_label_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermLeaseCost" xlink:to="lab_us-gaap_ShortTermLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019e46d7-b46d-7cce-b776-90f83704b8c5_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019e46d7-b46d-7118-9bbc-b96ae86b28fd_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableMember_019e46d7-b341-7c57-be2b-337a07d6c46b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableMember_label_en-US" xlink:label="lab_us-gaap_AccountsPayableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableMember" xlink:to="lab_us-gaap_AccountsPayableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_019e46d7-b341-7265-80f0-9b526c61e476_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock Series A-3 and Preferred Stock Series A-4, $0.001 par value Shares authorized: 20,000,000; Shares issued and outstanding: 6,125 of Series A-3; 1,937 of Series A-4</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_label_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Preferred, Carrying Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount" xlink:to="lab_us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NumberOfPotentialExtensions_019f4577-3542-7634-a0f5-9d806b57e691_terseLabel_en-US" xlink:label="lab_vate_NumberOfPotentialExtensions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of potential extensions</link:label>
    <link:label id="lab_vate_NumberOfPotentialExtensions_label_en-US" xlink:label="lab_vate_NumberOfPotentialExtensions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Potential Extensions</link:label>
    <link:label id="lab_vate_NumberOfPotentialExtensions_documentation_en-US" xlink:label="lab_vate_NumberOfPotentialExtensions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Potential Extensions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NumberOfPotentialExtensions" xlink:href="vate-20260630.xsd#vate_NumberOfPotentialExtensions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NumberOfPotentialExtensions" xlink:to="lab_vate_NumberOfPotentialExtensions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_019e46d7-b342-7b30-8f88-ab07a1c26432_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unvested stock options (in shares)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Nonvested, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_VariousNonconsolidatedSubsidiariesMember_019e46d7-b3d9-7eab-a696-1fcccc5a3b70_terseLabel_en-US" xlink:label="lab_vate_VariousNonconsolidatedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Various Nonconsolidated Subsidiaries</link:label>
    <link:label id="lab_vate_VariousNonconsolidatedSubsidiariesMember_label_en-US" xlink:label="lab_vate_VariousNonconsolidatedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Various Nonconsolidated Subsidiaries [Member]</link:label>
    <link:label id="lab_vate_VariousNonconsolidatedSubsidiariesMember_documentation_en-US" xlink:label="lab_vate_VariousNonconsolidatedSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Various Nonconsolidated Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_VariousNonconsolidatedSubsidiariesMember" xlink:href="vate-20260630.xsd#vate_VariousNonconsolidatedSubsidiariesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_VariousNonconsolidatedSubsidiariesMember" xlink:to="lab_vate_VariousNonconsolidatedSubsidiariesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_019e46d7-b342-7dd7-8828-7393a60cb4b8_totalLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total temporary equity</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_019e46d7-b342-7e26-8648-7be73d4f4050_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_019e46d7-b342-7f05-a140-93ad16e68d8f_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Including Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019e46d7-b342-7448-ace2-8bdf2c63460b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CashFlowLesseeAbstract_019e46d7-b341-71b5-b253-f4d7dd307e59_terseLabel_en-US" xlink:label="lab_vate_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for amounts included in the measurement of lease liabilities:</link:label>
    <link:label id="lab_vate_CashFlowLesseeAbstract_label_en-US" xlink:label="lab_vate_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Lessee [Abstract]</link:label>
    <link:label id="lab_vate_CashFlowLesseeAbstract_documentation_en-US" xlink:label="lab_vate_CashFlowLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash Flow, Lessee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CashFlowLesseeAbstract" xlink:href="vate-20260630.xsd#vate_CashFlowLesseeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CashFlowLesseeAbstract" xlink:to="lab_vate_CashFlowLesseeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_019e46d7-b3d9-7dfa-a3a0-65d3af7d36f8_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from other debt obligations, net of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019e46d7-b342-777d-a9d7-f90ba3037a26_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock_019e46d7-b3d9-7d55-8cdf-8ccd62d101ed_terseLabel_en-US" xlink:label="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets, Accrued Liabilities and Other Liabilities</link:label>
    <link:label id="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Accrued Liabilities And Other Liabilities Disclosure [Text Block]</link:label>
    <link:label id="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock_documentation_en-US" xlink:label="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets, Accrued Liabilities And Other Liabilities Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:href="vate-20260630.xsd#vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:to="lab_vate_OtherAssetsAccruedLiabilitiesAndOtherLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_019f91ec-9779-738d-a837-fd63020aa9c5_totalLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-current assets</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CostsIncurredOnContractsInProgress_019e46d7-b342-7121-913b-c23c0985ecb6_terseLabel_en-US" xlink:label="lab_vate_CostsIncurredOnContractsInProgress" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Costs incurred on contracts in progress</link:label>
    <link:label id="lab_vate_CostsIncurredOnContractsInProgress_label_en-US" xlink:label="lab_vate_CostsIncurredOnContractsInProgress" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs Incurred On Contracts In Progress</link:label>
    <link:label id="lab_vate_CostsIncurredOnContractsInProgress_documentation_en-US" xlink:label="lab_vate_CostsIncurredOnContractsInProgress" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Costs Incurred On Contracts In Progress</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CostsIncurredOnContractsInProgress" xlink:href="vate-20260630.xsd#vate_CostsIncurredOnContractsInProgress"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CostsIncurredOnContractsInProgress" xlink:to="lab_vate_CostsIncurredOnContractsInProgress" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOther_019e46d7-b342-7424-b605-9b6ed0f46028_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOther_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOther" xlink:to="lab_us-gaap_InterestIncomeOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019e46d7-b342-7cc5-8786-2a93d818b4b4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Receivable, Net</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_019e46d7-b3d9-7795-b964-27ac6fb6fcad_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_019e46d7-b342-7ef9-b070-affcb55c5bdd_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureAbstract" xlink:to="lab_us-gaap_InventoryDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsNet_019e46d7-b27a-7152-9596-2cfead5c2e66_totalLabel_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net of cost earned on uncompleted contracts</link:label>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsNet_label_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost Earned On Uncompleted Contracts, Net</link:label>
    <link:label id="lab_vate_CostEarnedOnUncompletedContractsNet_documentation_en-US" xlink:label="lab_vate_CostEarnedOnUncompletedContractsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cost Earned On Uncompleted Contracts, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_CostEarnedOnUncompletedContractsNet" xlink:href="vate-20260630.xsd#vate_CostEarnedOnUncompletedContractsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_CostEarnedOnUncompletedContractsNet" xlink:to="lab_vate_CostEarnedOnUncompletedContractsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_BridgeLoanFacilityMember_019ea74d-5afb-7ff2-91f8-094d6d91b27e_terseLabel_en-US" xlink:label="lab_vate_BridgeLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bridge Loan Facility</link:label>
    <link:label id="lab_vate_BridgeLoanFacilityMember_label_en-US" xlink:label="lab_vate_BridgeLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bridge Loan Facility [Member]</link:label>
    <link:label id="lab_vate_BridgeLoanFacilityMember_documentation_en-US" xlink:label="lab_vate_BridgeLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bridge Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_BridgeLoanFacilityMember" xlink:href="vate-20260630.xsd#vate_BridgeLoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_BridgeLoanFacilityMember" xlink:to="lab_vate_BridgeLoanFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities_019e46d7-b341-77dc-8b72-bd490bd30651_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019e46d7-b3d9-7bbd-902e-e7cbc5a8a745_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019e46d7-b3d9-77a5-a94e-65916b5e1126_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019e46d7-b3d9-7a59-9a26-707173d44f22_totalLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_019e46d7-b3d9-72f6-90fe-084186a6052c_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total INNOVATE Stockholders' (Deficit) Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_GovernmentRevenueMember_019e46d7-b46d-741c-b89e-d0135ea1769b_terseLabel_en-US" xlink:label="lab_vate_GovernmentRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Government</link:label>
    <link:label id="lab_vate_GovernmentRevenueMember_label_en-US" xlink:label="lab_vate_GovernmentRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Government Revenue [Member]</link:label>
    <link:label id="lab_vate_GovernmentRevenueMember_documentation_en-US" xlink:label="lab_vate_GovernmentRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Government Revenue Member</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_GovernmentRevenueMember" xlink:href="vate-20260630.xsd#vate_GovernmentRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_GovernmentRevenueMember" xlink:to="lab_vate_GovernmentRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_019e46d7-b3d9-71e0-85f4-c3e95950e7ea_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_019e46d7-b3d9-7650-8c17-a0bfbaa2a39f_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchase of investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember_019e46d7-b3d9-75da-ac25-0aa66dfb9e9b_terseLabel_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Within One Year</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember_label_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period One [Member]</link:label>
    <link:label id="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember_documentation_en-US" xlink:label="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:href="vate-20260630.xsd#vate_RevenueRemainingPerformanceObligationPeriodOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:to="lab_vate_RevenueRemainingPerformanceObligationPeriodOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NotesReceivable_019e46d7-b342-79f7-938a-c14a647960c5_terseLabel_en-US" xlink:label="lab_vate_NotesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes receivable</link:label>
    <link:label id="lab_vate_NotesReceivable_label_en-US" xlink:label="lab_vate_NotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable</link:label>
    <link:label id="lab_vate_NotesReceivable_documentation_en-US" xlink:label="lab_vate_NotesReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NotesReceivable" xlink:href="vate-20260630.xsd#vate_NotesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NotesReceivable" xlink:to="lab_vate_NotesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019e46d7-b27a-7d55-bc9d-d3b0c26bcb36_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentExtensionFeePercentage_019e46d7-b342-7127-a4bc-841b32f2b8ba_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension fee percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeePercentage_label_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee Percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentExtensionFeePercentage_documentation_en-US" xlink:label="lab_vate_DebtInstrumentExtensionFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentExtensionFeePercentage" xlink:href="vate-20260630.xsd#vate_DebtInstrumentExtensionFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentExtensionFeePercentage" xlink:to="lab_vate_DebtInstrumentExtensionFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019e46d7-b3d9-7bd0-91b0-bd1520b69711_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019e46d7-b3d9-7619-8d1e-0c8637968c64_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_019eaa85-badd-7d0d-bfe5-6a5740351e90_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_019e46d7-b3d9-793f-ad31-89ecc99ad591_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SeriesATwoPreferredStockMember_019e46d7-b27a-716c-a6e2-d7d9623d1dc5_terseLabel_en-US" xlink:label="lab_vate_SeriesATwoPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-2 shares issued and outstanding</link:label>
    <link:label id="lab_vate_SeriesATwoPreferredStockMember_label_en-US" xlink:label="lab_vate_SeriesATwoPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A- Two Preferred Stock [Member]</link:label>
    <link:label id="lab_vate_SeriesATwoPreferredStockMember_documentation_en-US" xlink:label="lab_vate_SeriesATwoPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-1 convertible preferred stock that may be exchanged into common shares or other types of securities at the owner's option.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SeriesATwoPreferredStockMember" xlink:href="vate-20260630.xsd#vate_SeriesATwoPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SeriesATwoPreferredStockMember" xlink:to="lab_vate_SeriesATwoPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_019e46d7-b3d9-7431-96be-f44fb994c216_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019e46d7-b342-76e6-8769-83e96d8be064_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019e46d7-b341-7169-8602-f550098cc24a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other operating activities, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount_019e46d7-b46d-750c-9474-67e91c3bbe0d_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares exchanged for additional principal amount (in shares)</link:label>
    <link:label id="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount_label_en-US" xlink:label="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Shares Exchanged For Additional Principal Amount</link:label>
    <link:label id="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount_documentation_en-US" xlink:label="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Shares Exchanged For Additional Principal Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:href="vate-20260630.xsd#vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:to="lab_vate_DebtInstrumentSharesExchangedForAdditionalPrincipalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019e46d7-b3d9-7f0e-a69e-7437e8a192ca_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_PreferredStockPurchaseRightsMember_019e46d7-b342-7d8f-b3a7-40ba853bfec8_terseLabel_en-US" xlink:label="lab_vate_PreferredStockPurchaseRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock Purchase Rights</link:label>
    <link:label id="lab_vate_PreferredStockPurchaseRightsMember_label_en-US" xlink:label="lab_vate_PreferredStockPurchaseRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Purchase Rights [Member]</link:label>
    <link:label id="lab_vate_PreferredStockPurchaseRightsMember_documentation_en-US" xlink:label="lab_vate_PreferredStockPurchaseRightsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Purchase Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_PreferredStockPurchaseRightsMember" xlink:href="vate-20260630.xsd#vate_PreferredStockPurchaseRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_PreferredStockPurchaseRightsMember" xlink:to="lab_vate_PreferredStockPurchaseRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_EnergyRevenueMember_019e46d7-b27a-7325-a1b6-230b7eb1e02d_terseLabel_en-US" xlink:label="lab_vate_EnergyRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Energy</link:label>
    <link:label id="lab_vate_EnergyRevenueMember_019e46d7-b27a-7e9a-8f11-ba67c7b21dfc_verboseLabel_en-US" xlink:label="lab_vate_EnergyRevenueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Energy</link:label>
    <link:label id="lab_vate_EnergyRevenueMember_label_en-US" xlink:label="lab_vate_EnergyRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Energy Revenue [Member]</link:label>
    <link:label id="lab_vate_EnergyRevenueMember_documentation_en-US" xlink:label="lab_vate_EnergyRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Energy Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_EnergyRevenueMember" xlink:href="vate-20260630.xsd#vate_EnergyRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_EnergyRevenueMember" xlink:to="lab_vate_EnergyRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_SpectrumMergerMember_019eaa6a-849c-73be-92e5-617cde61bbc0_terseLabel_en-US" xlink:label="lab_vate_SpectrumMergerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spectrum Merger</link:label>
    <link:label id="lab_vate_SpectrumMergerMember_label_en-US" xlink:label="lab_vate_SpectrumMergerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Spectrum Merger [Member]</link:label>
    <link:label id="lab_vate_SpectrumMergerMember_documentation_en-US" xlink:label="lab_vate_SpectrumMergerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Spectrum Merger</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_SpectrumMergerMember" xlink:href="vate-20260630.xsd#vate_SpectrumMergerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_SpectrumMergerMember" xlink:to="lab_vate_SpectrumMergerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtByMaturityAbstract_019e46d7-b46d-7d22-b20d-5d39c0c310f4_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtByMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtByMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtByMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtByMaturityAbstract" xlink:to="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_019e46d7-b3d9-71a3-94d2-666126c5caea_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:to="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019e46d7-b3d9-7757-b7b3-e3ee8894375c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_019e46d7-b3d9-7b88-bad9-5b04acdb2743_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_HC2BroadcastingHoldingsIncMember_019e46d7-b27a-7cb7-8ac5-93f60af8be09_terseLabel_en-US" xlink:label="lab_vate_HC2BroadcastingHoldingsIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HC2 Broadcasting Holdings, Inc</link:label>
    <link:label id="lab_vate_HC2BroadcastingHoldingsIncMember_label_en-US" xlink:label="lab_vate_HC2BroadcastingHoldingsIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">HC2 Broadcasting Holdings, Inc [Member]</link:label>
    <link:label id="lab_vate_HC2BroadcastingHoldingsIncMember_documentation_en-US" xlink:label="lab_vate_HC2BroadcastingHoldingsIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">HC2 Broadcasting Holdings, Inc [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_HC2BroadcastingHoldingsIncMember" xlink:href="vate-20260630.xsd#vate_HC2BroadcastingHoldingsIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_HC2BroadcastingHoldingsIncMember" xlink:to="lab_vate_HC2BroadcastingHoldingsIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage_019f4577-3542-729a-9354-d6ab0c74a0c6_terseLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right to acquire equity interests, percentage</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Right to Acquire Equity Interests, Percentage</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Right to Acquire Equity Interests, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationRightToAcquireEquityInterestsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_019e46d7-b342-7066-b3d9-a63f68952872_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_HuadongMember_019e46d7-b3d9-7f1e-b7ea-4085caf44ba7_terseLabel_en-US" xlink:label="lab_vate_HuadongMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Huadong</link:label>
    <link:label id="lab_vate_HuadongMember_label_en-US" xlink:label="lab_vate_HuadongMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Huadong [Member]</link:label>
    <link:label id="lab_vate_HuadongMember_documentation_en-US" xlink:label="lab_vate_HuadongMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Huadong</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_HuadongMember" xlink:href="vate-20260630.xsd#vate_HuadongMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_HuadongMember" xlink:to="lab_vate_HuadongMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_019eab0a-67d5-78a9-897a-46e12ae8d580_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_019e46d7-b27a-7989-bdef-16deee2dc341_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019e46d7-b3d9-7c27-a0cb-fb5ef3173d97_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_019e46d7-b27a-7304-94d1-0faca3425d90_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019e46d7-b27a-72fc-8564-5c1d2fa9512a_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019e46d7-b27a-77b7-b1f5-157fab7c3746_netLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_019e46d7-b342-7019-97b2-d60363053d6b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents_019e46d7-b3d9-7a9a-a330-4e1ccf0772a1_periodStartLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Restricted cash classified in Assets held for sale, beginning of period</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents_019e46d7-b3d9-7835-8bf9-ab2aacb10b0f_periodEndLabel_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Restricted cash classified in Assets held for sale, end of period</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Restricted Cash and Cash Equivalents</link:label>
    <link:label id="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents_documentation_en-US" xlink:label="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Restricted Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:href="vate-20260630.xsd#vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:to="lab_vate_DisposalGroupIncludingDiscontinuedOperationRestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage_019e46d7-b342-7d1d-aacf-8ad8602990ed_terseLabel_en-US" xlink:label="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fundamental change repurchase price percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage_label_en-US" xlink:label="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fundamental Change Repurchase Price Percentage</link:label>
    <link:label id="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage_documentation_en-US" xlink:label="lab_vate_DebtInstrumentFundamentalChangeRepurchasePricePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fundamental Change Repurchase Price Percentage</link:label>
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    <link:label id="lab_us-gaap_SeniorNotesMember_019e46d7-b27a-7702-bda4-a8026504c9fc_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_NonOperatingCorporateMember_019e46d7-b342-7070-b1a1-8f76aeda315c_terseLabel_en-US" xlink:label="lab_vate_NonOperatingCorporateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Operating Corporate</link:label>
    <link:label id="lab_vate_NonOperatingCorporateMember_label_en-US" xlink:label="lab_vate_NonOperatingCorporateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Operating Corporate [Member]</link:label>
    <link:label id="lab_vate_NonOperatingCorporateMember_documentation_en-US" xlink:label="lab_vate_NonOperatingCorporateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Operating Corporate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_NonOperatingCorporateMember" xlink:href="vate-20260630.xsd#vate_NonOperatingCorporateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_NonOperatingCorporateMember" xlink:to="lab_vate_NonOperatingCorporateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019e46d7-b27a-70a8-9b5e-af2ec376935b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_019e46d7-b342-7c02-a85e-f79d7ec253fc_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating leases</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019e46d7-b342-7773-8b0a-48f6f97a95e7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e46d7-b341-7616-a77b-0e77b8614991_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e46d7-b341-7e70-af3c-96afb182cf34_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSoldDepreciation_019e46d7-b3d8-706e-a3c3-b0d193bce679_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense within cost of revenue</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSoldDepreciation_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost, Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfGoodsAndServicesSoldDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSoldDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019e46d7-b3d9-7b42-9c0c-ae15d53a4041_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock_label_en-US" xlink:label="lab_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Maturities Of Debt And Finance Lease Obligations [Table Text Block]</link:label>
    <link:label id="lab_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock_documentation_en-US" xlink:label="lab_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Maturities Of Debt And Finance Lease Obligations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:href="vate-20260630.xsd#vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:to="lab_vate_ScheduleOfMaturitiesOfDebtAndFinanceLeaseObligationsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnamortizedDebtIssuanceExpense_019e46d7-b3d9-7809-9e55-304c2a02cace_terseLabel_en-US" xlink:label="lab_us-gaap_UnamortizedDebtIssuanceExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing fees</link:label>
    <link:label id="lab_us-gaap_UnamortizedDebtIssuanceExpense_label_en-US" xlink:label="lab_us-gaap_UnamortizedDebtIssuanceExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unamortized Debt Issuance Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnamortizedDebtIssuanceExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnamortizedDebtIssuanceExpense"/>
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    <link:label id="lab_us-gaap_StatementTable_019e46d7-b3d9-7125-b198-c14257160807_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019e46d7-b342-70cd-8836-14d09f1f62ef_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock_019e46d7-b342-7285-be89-69f08140c9e7_terseLabel_en-US" xlink:label="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unvested restricted stock (in shares)</link:label>
    <link:label id="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock_label_en-US" xlink:label="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Conversion of Restricted Stock</link:label>
    <link:label id="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock_documentation_en-US" xlink:label="lab_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Conversion of Restricted Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock" xlink:href="vate-20260630.xsd#vate_IncrementalCommonSharesAttributabletoDilutiveEffectofConversionofRestrictedStock"/>
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    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_019e46d7-b342-7655-b30c-6f19a4cdce00_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Contract with Customer, Asset and Liability</link:label>
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