diff --git a/Eigen/src/Core/arch/AVX512/GemmKernel.h b/Eigen/src/Core/arch/AVX512/GemmKernel.h
index e06b83c91c4134ff8de104b8b2bbe285ab526b9f..483e14937e87d9eb700b35856963f487b8fd7e21 100644
--- a/Eigen/src/Core/arch/AVX512/GemmKernel.h
+++ b/Eigen/src/Core/arch/AVX512/GemmKernel.h
@@ -35,6 +35,8 @@
 namespace Eigen {
 namespace internal {
 
+#if EIGEN_USE_AVX512_GEMM_KERNELS
+
 template <typename Scalar, bool is_unit_inc>
 class gemm_class {
   using vec = typename packet_traits<Scalar>::type;
@@ -947,7 +949,6 @@ EIGEN_DONT_INLINE void gemm_kern_avx512(Index m, Index n, Index k, Scalar *alpha
 }
 
 // Template specializations of GEBP kernels with nr = 8.
-#if EIGEN_USE_AVX512_GEMM_KERNELS
 template <bool ConjLhs_, bool ConjRhs_, int PacketSize_>
 class gebp_traits<float, float, ConjLhs_, ConjRhs_, Architecture::Target, PacketSize_>
     : public gebp_traits<float, float, ConjLhs_, ConjRhs_, Architecture::Generic, PacketSize_> {
diff --git a/Eigen/src/Core/arch/AVX512/TrsmKernel.h b/Eigen/src/Core/arch/AVX512/TrsmKernel.h
index c763b5fe3244d7e8b74556ba4558aa98cbd33173..cb72152472fbd3c1dfcb2a75aba8673b6a121e98 100644
--- a/Eigen/src/Core/arch/AVX512/TrsmKernel.h
+++ b/Eigen/src/Core/arch/AVX512/TrsmKernel.h
@@ -44,6 +44,8 @@
 namespace Eigen {
 namespace internal {
 
+#if (EIGEN_USE_AVX512_TRSM_KERNELS) && (EIGEN_COMP_CLANG != 0)
+
 #define EIGEN_AVX_MAX_NUM_ACC (int64_t(24))
 #define EIGEN_AVX_MAX_NUM_ROW (int64_t(8))  // Denoted L in code.
 #define EIGEN_AVX_MAX_K_UNROL (int64_t(4))
@@ -58,7 +60,6 @@ typedef Packet4d vecHalfDouble;
 // Note: this depends on macros and typedefs above.
 #include "TrsmUnrolls.inc"
 
-#if (EIGEN_USE_AVX512_TRSM_KERNELS) && (EIGEN_COMP_CLANG != 0)
 /**
  * For smaller problem sizes, and certain compilers, using the optimized kernels trsmKernelL/R directly
  * is faster than the packed versions in TriangularSolverMatrix.h.
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix.h b/Eigen/src/Core/products/TriangularSolverMatrix.h
index 8244758bd30962f00de7c73179451645d9bf5270..c09fec4f68144d00b0179abd5c411150b07589ba 100644
--- a/Eigen/src/Core/products/TriangularSolverMatrix.h
+++ b/Eigen/src/Core/products/TriangularSolverMatrix.h
@@ -141,7 +141,8 @@ EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar, Index, OnTheLeft, Mode, C
   std::ptrdiff_t l1, l2, l3;
   manage_caching_sizes(GetAction, &l1, &l2, &l3);
 
-#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_L_KERNELS && EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS
+#if defined(EIGEN_VECTORIZE_AVX512) && defined(EIGEN_USE_AVX512_TRSM_L_KERNELS) && EIGEN_USE_AVX512_TRSM_L_KERNELS && \
+    EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS
   EIGEN_IF_CONSTEXPR(
       (OtherInnerStride == 1 && (std::is_same<Scalar, float>::value || std::is_same<Scalar, double>::value))) {
     // Very rough cutoffs to determine when to call trsm w/o packing
@@ -209,7 +210,7 @@ EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar, Index, OnTheLeft, Mode, C
         // tr solve
         {
           Index i = IsLower ? k2 + k1 : k2 - k1;
-#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_L_KERNELS
+#if defined(EIGEN_VECTORIZE_AVX512) && defined(EIGEN_USE_AVX512_TRSM_L_KERNELS) && EIGEN_USE_AVX512_TRSM_L_KERNELS
           EIGEN_IF_CONSTEXPR(
               (OtherInnerStride == 1 && (std::is_same<Scalar, float>::value || std::is_same<Scalar, double>::value))) {
             i = IsLower ? k2 + k1 : k2 - k1 - actualPanelWidth;
@@ -273,7 +274,8 @@ EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar, Index, OnTheRight, Mode,
                                                                       level3_blocking<Scalar, Scalar>& blocking) {
   Index rows = otherSize;
 
-#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_R_KERNELS && EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS
+#if defined(EIGEN_VECTORIZE_AVX512) && defined(EIGEN_USE_AVX512_TRSM_R_KERNELS) && EIGEN_USE_AVX512_TRSM_R_KERNELS && \
+    EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS
   EIGEN_IF_CONSTEXPR(
       (OtherInnerStride == 1 && (std::is_same<Scalar, float>::value || std::is_same<Scalar, double>::value))) {
     // TODO: Investigate better heuristics for cutoffs.
diff --git a/ci/build.linux.gitlab-ci.yml b/ci/build.linux.gitlab-ci.yml
index 9e6303488024e2150d2bd0162fd9102c6edb7d87..04573f2ccf318f2cec730aaef2bd41e5e35e2ace 100644
--- a/ci/build.linux.gitlab-ci.yml
+++ b/ci/build.linux.gitlab-ci.yml
@@ -97,6 +97,18 @@ build:linux:cross:x86-64:clang-12:avx512dq:
   variables:
     EIGEN_CI_ADDITIONAL_ARGS: "-DEIGEN_TEST_AVX512DQ=on"
 
+# Generic vector extension backend.
+build:linux:cross:x86-64:clang-19:generic:avx512dq:
+  image: ubuntu:24.04
+  extends: build:linux:cross:x86-64:clang-12:default
+  variables:
+    EIGEN_CI_INSTALL: clang-19
+    EIGEN_CI_C_COMPILER: clang-19
+    EIGEN_CI_CXX_COMPILER: clang++-19
+    EIGEN_CI_CROSS_INSTALL: g++-14-x86-64-linux-gnu clang-19
+    EIGEN_CI_ADDITIONAL_ARGS: >
+      -DEIGEN_TEST_CUSTOM_CXX_FLAGS=-mfma;-mavx512dq;-DEIGEN_VECTORIZE_GENERIC=1
+
 build:linux:docs:
   extends: .build:linux:cross
   variables:
diff --git a/ci/test.linux.gitlab-ci.yml b/ci/test.linux.gitlab-ci.yml
index 17c7ee0e21832357b942c728f3a31e67f554e94e..6712337cc287d46e9a662700f82b279355d30d01 100644
--- a/ci/test.linux.gitlab-ci.yml
+++ b/ci/test.linux.gitlab-ci.yml
@@ -197,6 +197,29 @@ test:linux:x86-64:clang-12:avx512dq:unsupported:
   variables:
     EIGEN_CI_CTEST_LABEL: Unsupported
 
+# Generic vector extension backend.
+.test:linux:x86-64:clang-19:generic:avx512dq:
+  image: ubuntu:24.04
+  extends: .test:linux:x86-64
+  needs: [ build:linux:cross:x86-64:clang-19:generic:avx512dq ]
+  variables:
+    EIGEN_CI_INSTALL: clang-19
+  tags:
+    - eigen-runner
+    - linux
+    - x86-64
+    - avx512
+
+test:linux:x86-64:clang-19:generic:avx512dq:official:
+  extends: .test:linux:x86-64:clang-19:generic:avx512dq
+  variables:
+    EIGEN_CI_CTEST_LABEL: Official
+
+test:linux:x86-64:clang-19:generic:avx512dq:unsupported:
+  extends: .test:linux:x86-64:clang-19:generic:avx512dq
+  variables:
+    EIGEN_CI_CTEST_LABEL: Unsupported
+
 ##### CUDA #####################################################################
 .test:linux:cuda:
   extends: .test:linux