diff --git a/mlir/test/Integration/Dialect/Linalg/CPU/mmt4d.mlir b/mlir/test/Integration/Dialect/Linalg/CPU/mmt4d.mlir
new file mode 100644
index 00000000000000..8ee4e1fb48fef1
--- /dev/null
+++ b/mlir/test/Integration/Dialect/Linalg/CPU/mmt4d.mlir
@@ -0,0 +1,121 @@
+// DEFINE: %{compile} =  mlir-opt %s \
+// DEFINE:    -transform-interpreter -test-transform-dialect-erase-schedule \
+// DEFINE:    -one-shot-bufferize -func-bufferize -cse -canonicalize -convert-vector-to-scf -test-lower-to-llvm -o %t
+// DEFINE: %{entry_point} = mmt4d
+// DEFINE: %{run} = mlir-cpu-runner %t -e %{entry_point} -entry-point-result=void \
+// DEFINE:    -shared-libs=%mlir_runner_utils,%mlir_c_runner_utils
+
+// RUN: %{compile}
+
+// RUN: %{run} | FileCheck %s
+
+func.func @mmt4d() {
+  // Allocate the matrices
+  %A_alloc = tensor.empty() : tensor<2x2x3x1xi32>
+  %B_alloc = tensor.empty() : tensor<2x2x3x1xi32>
+  %C_alloc = tensor.empty() : tensor<2x2x3x3xi32>
+  %C_in = arith.constant dense<[
+    [[[ 1, 2, 3],
+     [ 4, 5, 6],
+     [ 7, 8, 9]],
+    [[ 11, 12, 13],
+     [ 14, 15, 16],
+     [ 17, 18, 19]]],
+    [[[ 21, 22, 23],
+     [ 24, 25, 26],
+     [ 27, 28, 29]],
+    [[ 31, 32, 33],
+     [ 34, 35, 36],
+     [ 37, 38, 39]]]
+  ]> : tensor<2x2x3x3xi32>
+
+  // Initialise the matrices
+  %three = arith.constant 3 : i32
+  %four = arith.constant 4 : i32
+  %A = linalg.fill ins(%three : i32) outs(%A_alloc : tensor<2x2x3x1xi32>) -> tensor<2x2x3x1xi32>
+  %B = linalg.fill ins(%four : i32) outs(%B_alloc : tensor<2x2x3x1xi32>) -> tensor<2x2x3x1xi32>
+
+  // Matmul
+  %C_out = linalg.mmt4d ins(%A, %B: tensor<2x2x3x1xi32>, tensor<2x2x3x1xi32>) outs(%C_in: tensor<2x2x3x3xi32>) -> tensor<2x2x3x3xi32>
+
+  // Print and verify the output
+  // CHECK:  Unranked Memref {{.*}} rank = 4 offset = 0 sizes = [2, 2, 3, 3] strides = [18, 9, 3, 1] data =
+  // C[0, 0]
+  // CHECK-NEXT: [25,  26, 27]
+  // CHECK-NEXT: [28,  29, 30]
+  // CHECK-NEXT: [31,  32, 33]
+  // C[0, 1]
+  // CHECK-NEXT: [35,  36, 37]
+  // CHECK-NEXT: [38,  39, 40]
+  // CHECK-NEXT: [41,  42, 43]
+  // C[1, 0]
+  // CHECK-NEXT: [45,  46, 47]
+  // CHECK-NEXT: [48,  49, 50]
+  // CHECK-NEXT: [51,  52, 53]
+  // C[1, 1]
+  // CHECK-NEXT: [55,  56, 57]
+  // CHECK-NEXT: [58,  59, 60]
+  // CHECK-NEXT: [61,  62, 63]
+
+  %xf = tensor.cast %C_out : tensor<2x2x3x3xi32> to tensor<*xi32>
+  call @printMemrefI32(%xf) : (tensor<*xi32>) -> ()
+
+  return
+}
+
+module @transforms attributes { transform.with_named_sequence } {
+  transform.named_sequence @__transform_main(%module: !transform.any_op {transform.readonly}) {
+   %mmt4d = transform.collect_matching @match_mmt4d in %module : (!transform.any_op) -> (!transform.any_op)
+   %func = transform.get_parent_op %mmt4d {isolated_from_above} : (!transform.any_op) -> !transform.op<"func.func">
+
+   // Step 1: Tile
+   // Tile parallel dims
+   %tiled_linalg_op_p, %loops:4 = transform.structured.tile_using_for %mmt4d[1, 1, 0, 3, 3, 0]
+     : (!transform.any_op) -> (!transform.any_op, !transform.any_op, !transform.any_op, !transform.any_op, !transform.any_op)
+   // Tile reduction dims
+   %tiled_linalg_op_r, %loops2:2 = transform.structured.tile_using_for %tiled_linalg_op_p[0, 0, 1, 0, 0, 1]
+     : (!transform.any_op) -> (!transform.any_op, !transform.any_op, !transform.any_op)
+
+   // Step 2: Vectorize
+   transform.structured.vectorize %tiled_linalg_op_r : !transform.any_op
+
+   // Step 3: Simplify
+   // vector.multi_reduction --> vector.contract
+   // Generates a 6-dim vector.contract with the dim matching the original MMT4D Op
+   // and with the following split into parallel and reduction dims:
+   //    * parallel, parallel, reduction, parallel, parallel, reduction
+   transform.apply_patterns to %func {
+     transform.apply_patterns.vector.reduction_to_contract
+     // Reduce the rank of xfer ops. This transforms vector.contract to be
+     // more matmul-like and to enable the lowering to outer product Ops.
+     transform.apply_patterns.vector.transfer_permutation_patterns
+   } : !transform.op<"func.func">
+
+   // Hoisting and LICM - not strictly required
+   %func_h = transform.structured.hoist_redundant_vector_transfers %func
+     : (!transform.op<"func.func">) -> !transform.op<"func.func">
+   %all_loops = transform.structured.match interface{LoopLikeInterface} in %func_h
+     : (!transform.op<"func.func">) -> !transform.any_op
+   transform.apply_licm to %all_loops : !transform.any_op
+   transform.loop.hoist_loop_invariant_subsets %all_loops : !transform.any_op
+
+   // Simplify the 6-dim vector.contract into a 3-dim matmul-like
+   // vector.contract with the following split into parallel and reduction
+   // dims:
+   //    * parallel, parallel, reduction
+   transform.apply_patterns to %func_h {
+     transform.apply_patterns.vector.reduction_to_contract
+     transform.apply_patterns.vector.cast_away_vector_leading_one_dim
+     transform.apply_patterns.canonicalization
+   } : !transform.op<"func.func">
+    transform.yield
+  }
+
+  transform.named_sequence @match_mmt4d(
+      %entry: !transform.any_op {transform.readonly}) -> !transform.any_op {
+    transform.match.operation_name %entry ["linalg.mmt4d"] : !transform.any_op
+    transform.yield %entry : !transform.any_op
+  }
+}
+
+func.func private @printMemrefI32(%ptr : tensor<*xi32>)