diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
@@ -26,7 +26,7 @@
 //===----------------------------------------------------------------------===//
 
 def SparseTensor_NewOp : SparseTensor_Op<"new", [Pure]>,
-    Arguments<(ins AnyType:$source)>,
+    Arguments<(ins AnyType:$source, UnitAttr:$expandSymmetry)>,
     Results<(outs AnySparseTensor:$result)> {
   string summary = "Materializes a new sparse tensor from given source";
   string description = [{
@@ -39,13 +39,22 @@
     code. The operation is provided as an anchor that materializes a properly
     typed sparse tensor with inital contents into a computation.
 
+    An optional attribute `expandSymmetry` can be used to extend this operation
+    to make symmetry in external formats explicit in the storage. That is, when
+    the attribute presents and a non-zero value is discovered at (i, j) where
+    i!=j, we add the same value to (j, i). This claims more storage than a pure
+    symmetric storage, and thus may cause a bad performance hit. True symmetric
+    storage is planned for the future.
+
     Example:
 
     ```mlir
     sparse_tensor.new %source : !Source to tensor<1024x1024xf64, #CSR>
     ```
   }];
-  let assemblyFormat = "$source attr-dict `:` type($source) `to` type($result)";
+  let assemblyFormat = "(`expand_symmetry` $expandSymmetry^)? $source attr-dict"
+                       "`:` type($source) `to` type($result)";
+  let hasVerifier = 1;
 }
 
 def SparseTensor_ConvertOp : SparseTensor_Op<"convert",
diff --git a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
--- a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
+++ b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
@@ -334,6 +334,13 @@
   return failure();
 }
 
+LogicalResult NewOp::verify() {
+  if (getExpandSymmetry() &&
+      getResult().getType().cast<RankedTensorType>().getRank() != 2)
+    return emitOpError("expand_symmetry can only be used for 2D tensors");
+  return success();
+}
+
 LogicalResult ConvertOp::verify() {
   if (auto tp1 = getSource().getType().dyn_cast<RankedTensorType>()) {
     if (auto tp2 = getDest().getType().dyn_cast<RankedTensorType>()) {
diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorRewriting.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorRewriting.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorRewriting.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorRewriting.cpp
@@ -915,8 +915,8 @@
                                {indexTp}, {reader}, EmitCInterface::Off)
                     .getResult(0);
     Value symmetric;
-    // We assume only rank 2 tensors may have the isSymmetric flag set.
-    if (rank == 2) {
+    // The verifier ensures only 2D tensors can have the expandSymmetry flag.
+    if (rank == 2 && op.getExpandSymmetry()) {
       symmetric =
           createFuncCall(rewriter, loc, "getSparseTensorReaderIsSymmetric",
                          {rewriter.getI1Type()}, {reader}, EmitCInterface::Off)
diff --git a/mlir/test/Dialect/SparseTensor/invalid.mlir b/mlir/test/Dialect/SparseTensor/invalid.mlir
--- a/mlir/test/Dialect/SparseTensor/invalid.mlir
+++ b/mlir/test/Dialect/SparseTensor/invalid.mlir
@@ -180,6 +180,16 @@
 
 // -----
 
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+func.func @sparse_new(%arg0: !llvm.ptr<i8>) {
+  // expected-error@+1 {{expand_symmetry can only be used for 2D tensors}}
+  %0 = sparse_tensor.new expand_symmetry %arg0 : !llvm.ptr<i8> to tensor<128xf64, #SparseVector>
+  return
+}
+
+// -----
+
 func.func @sparse_convert_unranked(%arg0: tensor<*xf32>) -> tensor<10xf32> {
   // expected-error@+1 {{unexpected type in convert}}
   %0 = sparse_tensor.convert %arg0 : tensor<*xf32> to tensor<10xf32>
diff --git a/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir b/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
--- a/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
+++ b/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
@@ -5,7 +5,7 @@
   dimLevelType = ["dense", "compressed"]
 }>
 
-// CHECK-LABEL:   func.func @sparse_new(
+// CHECK-LABEL:   func.func @sparse_new_symmetry(
 // CHECK-SAME:    %[[A:.*]]: !llvm.ptr<i8>) -> tensor<?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> {
 // CHECK-DAG:     %[[C2:.*]] = arith.constant 2 : index
 // CHECK-DAG:     %[[C0:.*]] = arith.constant 0 : index
@@ -39,6 +39,37 @@
 // CHECK:         %[[R:.*]] = sparse_tensor.convert %[[T5]]
 // CHECK:         bufferization.dealloc_tensor %[[T5]]
 // CHECK:         return %[[R]]
+func.func @sparse_new_symmetry(%arg0: !llvm.ptr<i8>) -> tensor<?x?xf32, #CSR> {
+  %0 = sparse_tensor.new expand_symmetry %arg0 : !llvm.ptr<i8> to tensor<?x?xf32, #CSR>
+  return %0 : tensor<?x?xf32, #CSR>
+}
+
+// CHECK-LABEL:   func.func @sparse_new(
+// CHECK-SAME:    %[[A:.*]]: !llvm.ptr<i8>) -> tensor<?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> {
+// CHECK-DAG:     %[[C2:.*]] = arith.constant 2 : index
+// CHECK-DAG:     %[[C0:.*]] = arith.constant 0 : index
+// CHECK-DAG:     %[[C1:.*]] = arith.constant 1 : index
+// CHECK:         %[[R:.*]] = call @createSparseTensorReader(%[[A]])
+// CHECK:         %[[DS:.*]] = memref.alloca(%[[C2]]) : memref<?xindex>
+// CHECK:         call @getSparseTensorReaderDimSizes(%[[R]], %[[DS]])
+// CHECK:         %[[D0:.*]] = memref.load %[[DS]]{{\[}}%[[C0]]]
+// CHECK:         %[[D1:.*]] = memref.load %[[DS]]{{\[}}%[[C1]]]
+// CHECK:         %[[T:.*]] = bufferization.alloc_tensor(%[[D0]], %[[D1]])
+// CHECK:         %[[N:.*]] = call @getSparseTensorReaderNNZ(%[[R]])
+// CHECK:         %[[VB:.*]] = memref.alloca()
+// CHECK:         %[[T2:.*]] = scf.for %{{.*}} = %[[C0]] to %[[N]] step %[[C1]] iter_args(%[[A2:.*]] = %[[T]])
+// CHECK:           func.call @getSparseTensorReaderNextF32(%[[R]], %[[DS]], %[[VB]])
+// CHECK:           %[[E0:.*]] = memref.load %[[DS]]{{\[}}%[[C0]]]
+// CHECK:           %[[E1:.*]] = memref.load %[[DS]]{{\[}}%[[C1]]]
+// CHECK:           %[[V:.*]] = memref.load %[[VB]][]
+// CHECK:           %[[T1:.*]] = sparse_tensor.insert %[[V]] into %[[A2]]{{\[}}%[[E0]], %[[E1]]]
+// CHECK:           scf.yield %[[T1]]
+// CHECK:         }
+// CHECK:         call @delSparseTensorReader(%[[R]])
+// CHECK:         %[[T4:.*]] = sparse_tensor.load %[[T2]] hasInserts
+// CHECK:         %[[R:.*]] = sparse_tensor.convert %[[T4]]
+// CHECK:         bufferization.dealloc_tensor %[[T4]]
+// CHECK:         return %[[R]]
 func.func @sparse_new(%arg0: !llvm.ptr<i8>) -> tensor<?x?xf32, #CSR> {
   %0 = sparse_tensor.new %arg0 : !llvm.ptr<i8> to tensor<?x?xf32, #CSR>
   return %0 : tensor<?x?xf32, #CSR>
diff --git a/mlir/test/Dialect/SparseTensor/roundtrip.mlir b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
--- a/mlir/test/Dialect/SparseTensor/roundtrip.mlir
+++ b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
@@ -13,6 +13,19 @@
 
 // -----
 
+#SparseMatrix = #sparse_tensor.encoding<{dimLevelType = ["compressed", "compressed"]}>
+
+// CHECK-LABEL: func @sparse_new_symmetry(
+// CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//       CHECK: %[[T:.*]] = sparse_tensor.new expand_symmetry %[[A]] : !llvm.ptr<i8> to tensor<?x?xf64, #{{.*}}>
+//       CHECK: return %[[T]] : tensor<?x?xf64, #{{.*}}>
+func.func @sparse_new_symmetry(%arg0: !llvm.ptr<i8>) -> tensor<?x?xf64, #SparseMatrix> {
+  %0 = sparse_tensor.new expand_symmetry %arg0 : !llvm.ptr<i8> to tensor<?x?xf64, #SparseMatrix>
+  return %0 : tensor<?x?xf64, #SparseMatrix>
+}
+
+// -----
+
 #SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
 
 // CHECK-LABEL: func @sparse_dealloc(
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum.mlir
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum.mlir
@@ -63,7 +63,7 @@
 
     // Read the sparse matrix from file, construct sparse storage.
     %fileName = call @getTensorFilename(%c0) : (index) -> (!Filename)
-    %a = sparse_tensor.new %fileName : !Filename to tensor<?x?xf64, #SparseMatrix>
+    %a = sparse_tensor.new expand_symmetry %fileName : !Filename to tensor<?x?xf64, #SparseMatrix>
 
     // Call the kernel.
     %0 = call @kernel_sum_reduce(%a, %x)
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum_c32.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum_c32.mlir
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum_c32.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sum_c32.mlir
@@ -66,7 +66,7 @@
 
     // Read the sparse matrix from file, construct sparse storage.
     %fileName = call @getTensorFilename(%c0) : (index) -> (!Filename)
-    %a = sparse_tensor.new %fileName : !Filename to tensor<?x?xcomplex<f64>, #SparseMatrix>
+    %a = sparse_tensor.new expand_symmetry %fileName : !Filename to tensor<?x?xcomplex<f64>, #SparseMatrix>
 
     // Call the kernel.
     %0 = call @kernel_sum_reduce(%a, %x)