diff --git a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
index 944833237..009ebee81 100644
--- a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
+++ b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
@@ -2,7 +2,7 @@ module MatrixAlgebraKitEnzymeExt
 
 using MatrixAlgebraKit
 using MatrixAlgebraKit: copy_input, initialize_output, zero!, has_equal_storage
-using MatrixAlgebraKit: diagview, inv_safe, truncate
+using MatrixAlgebraKit: diagview, inv_safe, truncate, TruncationStrategy
 using MatrixAlgebraKit: qr_pullback!, lq_pullback!
 using MatrixAlgebraKit: qr_pushforward!, lq_pushforward!
 using MatrixAlgebraKit: qr_null_pullback!, lq_null_pullback!
@@ -19,7 +19,7 @@ using Enzyme.EnzymeCore: EnzymeRules
 using LinearAlgebra
 
 @inline EnzymeRules.inactive_type(::Type{Alg}) where {Alg <: MatrixAlgebraKit.AbstractAlgorithm} = true
-@inline EnzymeRules.inactive_type(::Type{TS}) where {TS <: MatrixAlgebraKit.TruncationStrategy} = true
+@inline EnzymeRules.inactive_type(::Type{TS}) where {TS <: TruncationStrategy} = true
 @inline EnzymeRules.inactive(::typeof(MatrixAlgebraKit.select_algorithm), func::F, A::AbstractMatrix, alg::Alg) where {F, Alg} = true
 @inline EnzymeRules.inactive(::typeof(MatrixAlgebraKit.default_algorithm), func::F, A::AbstractMatrix) where {F} = true
 @inline EnzymeRules.inactive(::typeof(MatrixAlgebraKit.check_input), func::F, A::AbstractMatrix, alg::Alg) where {F, Alg} = true
@@ -552,4 +552,56 @@ function EnzymeRules.forward(
     end
 end
 
+function EnzymeRules.forward(
+        config::EnzymeRules.FwdConfigWidth{1},
+        func::Const{typeof(truncate)},
+        ::Type{RT},
+        f::Const{<:Union{typeof(eigh_trunc!), typeof(eig_trunc!)}},
+        DV::Annotation,
+        strategy::Annotation{<:TruncationStrategy},
+    ) where {RT}
+    D, V = DV.val
+    ind = MatrixAlgebraKit.findtruncated(diagview(D), strategy.val)
+    Dtrunc = Diagonal(diagview(D)[ind])
+    Vtrunc = V[:, ind]
+    dDtrunc = isa(DV, Const) ? nothing : Diagonal(diagview(DV.dval[1])[ind])
+    dVtrunc = isa(DV, Const) ? nothing : DV.dval[2][:, ind]
+    if EnzymeRules.needs_primal(config) && EnzymeRules.needs_shadow(config)
+        return Duplicated(((Dtrunc, Vtrunc), ind), ((dDtrunc, dVtrunc), make_zero(ind)))
+    elseif EnzymeRules.needs_primal(config)
+        return ((Dtrunc, Vtrunc), ind)
+    elseif EnzymeRules.needs_shadow(config)
+        return ((dDtrunc, dVtrunc), make_zero(ind))
+    else
+        return nothing
+    end
+end
+
+function EnzymeRules.forward(
+        config::EnzymeRules.FwdConfigWidth{1},
+        func::Const{typeof(truncate)},
+        ::Type{RT},
+        f::Const{typeof(svd_trunc!)},
+        USVᴴ::Annotation,
+        strategy::Annotation{<:TruncationStrategy},
+    ) where {RT}
+    U, S, Vᴴ = USVᴴ.val
+    ind = MatrixAlgebraKit.findtruncated_svd(diagview(S), strategy.val)
+    Utrunc = U[:, ind]
+    Strunc = Diagonal(diagview(S)[ind])
+    Vᴴtrunc = Vᴴ[ind, :]
+    dUtrunc = isa(USVᴴ, Const) ? nothing : USVᴴ.dval[1][:, ind]
+    dStrunc = isa(USVᴴ, Const) ? nothing : Diagonal(diagview(USVᴴ.dval[2])[ind])
+    dVᴴtrunc = isa(USVᴴ, Const) ? nothing : USVᴴ.dval[3][ind, :]
+    if EnzymeRules.needs_primal(config) && EnzymeRules.needs_shadow(config)
+        return Duplicated(((Utrunc, Strunc, Vᴴtrunc), ind), ((dUtrunc, dStrunc, dVᴴtrunc), make_zero(ind)))
+    elseif EnzymeRules.needs_primal(config)
+        return ((Utrunc, Strunc, Vᴴtrunc), ind)
+    elseif EnzymeRules.needs_shadow(config)
+        return ((dUtrunc, dStrunc, dVᴴtrunc), make_zero(ind))
+    else
+        return nothing
+    end
+end
+
 end
diff --git a/test/testsuite/enzyme/eig.jl b/test/testsuite/enzyme/eig.jl
index 1f11949eb..4eaf878f3 100644
--- a/test/testsuite/enzyme/eig.jl
+++ b/test/testsuite/enzyme/eig.jl
@@ -76,7 +76,9 @@ function test_enzyme_eig_trunc(
             A = make_eig_matrix(T, sz)
             DV, _, ΔDV, ΔDVtrunc = ad_eig_trunc_setup(A, truncalg)
             test_reverse(eig_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
-            test_reverse(call_and_zero!, RT, (eig_trunc_no_error!, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_reverse(call_and_zero!, RT, (eig_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_forward(eig_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, fdm)
+            test_forward(call_and_zero!, RT, (eig_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, fdm)
         end
         @testset "trunctol" begin
             A = make_eig_matrix(T, sz)
@@ -85,7 +87,9 @@ function test_enzyme_eig_trunc(
             truncalg = TruncatedAlgorithm(alg, trunc)
             DV, _, ΔDV, ΔDVtrunc = ad_eig_trunc_setup(A, truncalg)
             test_reverse(eig_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
-            test_reverse(call_and_zero!, RT, (eig_trunc_no_error!, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_reverse(call_and_zero!, RT, (eig_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_forward(eig_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
+            test_forward(call_and_zero!, RT, (eig_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
         end
     end
 end
diff --git a/test/testsuite/enzyme/eigh.jl b/test/testsuite/enzyme/eigh.jl
index 4e42d7b3c..8143678ec 100644
--- a/test/testsuite/enzyme/eigh.jl
+++ b/test/testsuite/enzyme/eigh.jl
@@ -76,7 +76,9 @@ function test_enzyme_eigh_trunc(
             A = make_eigh_matrix(T, sz)
             DV, _, ΔDV, ΔDVtrunc = ad_eigh_trunc_setup(A, truncalg)
             test_reverse(eigh_wrapper, RT, (eigh_trunc_no_error, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
-            test_reverse(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_reverse(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_forward(eigh_wrapper, RT, (eigh_trunc_no_error, Const), (A, TA), (truncalg, Const); atol, rtol, fdm)
+            test_forward(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, fdm)
         end
         @testset "trunctol" begin
             A = make_eigh_matrix(T, sz)
@@ -85,7 +87,9 @@ function test_enzyme_eigh_trunc(
             truncalg = TruncatedAlgorithm(alg, trunc)
             DV, _, ΔDV, ΔDVtrunc = ad_eigh_trunc_setup(A, truncalg)
             test_reverse(eigh_wrapper, RT, (eigh_trunc_no_error, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
-            test_reverse(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_reverse(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
+            test_forward(eigh_wrapper, RT, (eigh_trunc_no_error, Const), (A, TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
+            test_forward(eigh!_wrapper, RT, (eigh_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
         end
     end
 end
diff --git a/test/testsuite/enzyme/svd.jl b/test/testsuite/enzyme/svd.jl
index 07a35d6d4..cddd1b8ee 100644
--- a/test/testsuite/enzyme/svd.jl
+++ b/test/testsuite/enzyme/svd.jl
@@ -94,16 +94,20 @@ function test_enzyme_svd_trunc(
             trunc = truncrank(r)
             truncalg = TruncatedAlgorithm(alg, trunc)
             USVᴴ, _, ΔUSVᴴ, ΔUSVᴴtrunc = ad_svd_trunc_setup(A, truncalg)
-            test_reverse(svd_trunc_no_error, RT, (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
+            test_reverse(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
             test_reverse(call_and_zero!, RT, (svd_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
+            test_forward(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, fdm)
+            test_forward(call_and_zero!, RT, (svd_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, fdm)
         end
         @testset "trunctol" begin
             S = svd_vals(A, alg)
             trunc = trunctol(atol = maximum(S) / 2)
             truncalg = TruncatedAlgorithm(alg, trunc)
             USVᴴ, _, ΔUSVᴴ, ΔUSVᴴtrunc = ad_svd_trunc_setup(A, truncalg)
-            test_reverse(svd_trunc_no_error, RT, (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
+            test_reverse(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
             test_reverse(call_and_zero!, RT, (svd_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
+            test_forward(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
+            test_forward(call_and_zero!, RT, (svd_trunc_no_error!, Const), (copy(A), TA), (truncalg, Const); atol, rtol, fdm = EnzymeTestUtils.FiniteDifferences.central_fdm(5, 1, max_range = 1.0e-3))
         end
     end
 end