diff --git a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
--- a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
+++ b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
@@ -27,12 +27,12 @@
   // In addition to normal types arithmetic instructions can support cooperative
   // matrix.
   let arguments = (ins
-    SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<type>:$operand1,
-    SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<type>:$operand2
+    SPV_ScalarOrVectorOrCoopMatrixOf<type>:$operand1,
+    SPV_ScalarOrVectorOrCoopMatrixOf<type>:$operand2
   );
 
   let results = (outs
-    SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<type>:$result
+    SPV_ScalarOrVectorOrCoopMatrixOf<type>:$result
   );
   let assemblyFormat = "operands attr-dict `:` type($result)";
 }
diff --git a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVBase.td b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVBase.td
--- a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVBase.td
+++ b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVBase.td
@@ -4106,14 +4106,6 @@
     AnyTypeOf<[type, VectorOfLengthAndType<[2, 3, 4, 8, 16], [type]>,
                SPV_CoopMatrixOfType<[type]>]>;
 
-class SPV_ScalarOrVectorOrJointMatrixOf<Type type> :
-    AnyTypeOf<[type, VectorOfLengthAndType<[2, 3, 4, 8, 16], [type]>,
-               SPV_JointMatrixOfType<[type]>]>;
-
-class SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<Type type> :
-    AnyTypeOf<[type, VectorOfLengthAndType<[2, 3, 4, 8, 16], [type]>,
-               SPV_CoopMatrixOfType<[type]>, SPV_JointMatrixOfType<[type]> ]>;
-
 def SPV_ScalarOrVector : AnyTypeOf<[SPV_Scalar, SPV_Vector]>;
 def SPV_ScalarOrVectorOrPtr : AnyTypeOf<[SPV_ScalarOrVector, SPV_AnyPtr]>;
 
diff --git a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVCastOps.td b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVCastOps.td
--- a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVCastOps.td
+++ b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVCastOps.td
@@ -23,11 +23,11 @@
              !listconcat(traits,
                          [NoSideEffect, SameOperandsAndResultShape])> {
   let arguments = (ins
-    SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<operandType>:$operand
+    SPV_ScalarOrVectorOrCoopMatrixOf<operandType>:$operand
   );
 
   let results = (outs
-    SPV_ScalarOrVectorOrCoopMatrixOfOrJointMatrixOf<resultType>:$result
+    SPV_ScalarOrVectorOrCoopMatrixOf<resultType>:$result
   );
   let assemblyFormat = [{
     $operand attr-dict `:` type($operand) `to` type($result)
diff --git a/mlir/lib/Dialect/SPIRV/IR/SPIRVOps.cpp b/mlir/lib/Dialect/SPIRV/IR/SPIRVOps.cpp
--- a/mlir/lib/Dialect/SPIRV/IR/SPIRVOps.cpp
+++ b/mlir/lib/Dialect/SPIRV/IR/SPIRVOps.cpp
@@ -3921,7 +3921,9 @@
   spirv::StorageClass storage =
       pointer.cast<spirv::PointerType>().getStorageClass();
   if (storage != spirv::StorageClass::Workgroup &&
-      storage != spirv::StorageClass::CrossWorkgroup)
+      storage != spirv::StorageClass::CrossWorkgroup &&
+      storage != spirv::StorageClass::UniformConstant &&
+      storage != spirv::StorageClass::Generic)
     return op->emitError("Pointer storage class must be Workgroup or "
                          "CrossWorkgroup but provided ")
            << stringifyStorageClass(storage);
diff --git a/mlir/test/Dialect/SPIRV/IR/joint-matrix-ops.mlir b/mlir/test/Dialect/SPIRV/IR/joint-matrix-ops.mlir
--- a/mlir/test/Dialect/SPIRV/IR/joint-matrix-ops.mlir
+++ b/mlir/test/Dialect/SPIRV/IR/joint-matrix-ops.mlir
@@ -50,65 +50,6 @@
   spv.Return
 }
 
-// CHECK-LABEL: @joint_matrix_add
-spv.func @joint_matrix_add(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.IAdd {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  %r = spv.IAdd %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_sub
-spv.func @joint_matrix_sub(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.ISub {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  %r = spv.ISub %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_sdiv
-spv.func @joint_matrix_sdiv(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.SDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  %r = spv.SDiv %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_udiv
-spv.func @joint_matrix_udiv(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.UDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  %r = spv.UDiv %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_fadd
-spv.func @joint_matrix_fadd(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.FAdd {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  %r = spv.FAdd %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_fsub
-spv.func @joint_matrix_fsub(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.FSub {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  %r = spv.FSub %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// CHECK-LABEL: @joint_matrix_fdiv
-spv.func @joint_matrix_fdiv(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-  // CHECK: {{%.*}} = spv.FDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  %r = spv.FDiv %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-  spv.Return
-}
-
-// -----
-
-// CHECK-LABEL: @joint_matrix_access_chain
-spv.func @joint_matrix_access_chain(%a : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>) -> !spv.ptr<f32, Function> "None" {
-  %0 = spv.Constant 0: i32
-  // CHECK: {{%.*}} = spv.AccessChain {{%.*}}[{{%.*}}] : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>, i32
-  %1 = spv.AccessChain %a[%0] : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>, i32
-  spv.ReturnValue %1 : !spv.ptr<f32, Function>
-}
-
 // -----
 
 spv.func @joint_matrix_muladd(%a : !spv.jointmatrix<16x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<16x8xi32, RowMajor, Subgroup>, %c : !spv.jointmatrix<8x8xi32, RowMajor, Subgroup>) "None" {
diff --git a/mlir/test/Target/SPIRV/joint-matrix-ops.mlir b/mlir/test/Target/SPIRV/joint-matrix-ops.mlir
--- a/mlir/test/Target/SPIRV/joint-matrix-ops.mlir
+++ b/mlir/test/Target/SPIRV/joint-matrix-ops.mlir
@@ -42,61 +42,4 @@
     %r = spv.JointMatrixMadINTEL <Subgroup> %a, %b, %c : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, !spv.jointmatrix<16x8xi32, RowMajor, Subgroup> -> !spv.jointmatrix<8x8xi32, RowMajor, Subgroup>
     spv.Return
   }
-
-  // CHECK-LABEL: @joint_matrix_add
-  spv.func @joint_matrix_add(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.IAdd {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    %r = spv.IAdd %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_sub
-  spv.func @joint_matrix_sub(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.ISub {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    %r = spv.ISub %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_sdiv
-  spv.func @joint_matrix_sdiv(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.SDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    %r = spv.SDiv %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_udiv
-  spv.func @joint_matrix_udiv(%a : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.UDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    %r = spv.UDiv %a, %b : !spv.jointmatrix<8x16xi32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_fadd
-  spv.func @joint_matrix_fadd(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.FAdd {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    %r = spv.FAdd %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_fsub
-  spv.func @joint_matrix_fsub(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.FSub {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    %r = spv.FSub %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_fdiv
-  spv.func @joint_matrix_fdiv(%a : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>) "None" {
-    // CHECK: {{%.*}} = spv.FDiv {{%.*}}, {{%.*}} : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    %r = spv.FDiv %a, %b : !spv.jointmatrix<8x16xf32, RowMajor, Subgroup>
-    spv.Return
-  }
-
-  // CHECK-LABEL: @joint_matrix_access_chain
-  spv.func @joint_matrix_access_chain(%a : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>) -> !spv.ptr<f32, Function> "None" {
-    %0 = spv.Constant 0: i32
-    // CHECK: {{%.*}} = spv.AccessChain {{%.*}}[{{%.*}}] : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>, i32
-    %1 = spv.AccessChain %a[%0] : !spv.ptr<!spv.jointmatrix<8x16xf32, RowMajor, Subgroup>, Function>, i32
-    spv.ReturnValue %1 : !spv.ptr<f32, Function>
-  }
 }