diff --git a/paddle/fluid/operators/elementwise_add_mkldnn_op.cc b/paddle/fluid/operators/elementwise_add_mkldnn_op.cc
index c86cd57316078778e5930c9b524b931d523028d7..9ad82aec8182d6ba06b67391d71317a3d0df1833 100644
--- a/paddle/fluid/operators/elementwise_add_mkldnn_op.cc
+++ b/paddle/fluid/operators/elementwise_add_mkldnn_op.cc
@@ -137,9 +137,10 @@ class EltwiseAddMKLDNNKernel : public framework::OpKernel<T> {
 };
 
 template <typename T>
-class EltwiseAddMKLDNNGradKernel : public framework::OpKernel<T> {
+class EltwiseAddMKLDNNGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* dout = ctx.Input<Tensor>(framework::GradVarName("Out"));
diff --git a/paddle/fluid/operators/elementwise_add_op.h b/paddle/fluid/operators/elementwise_add_op.h
index 5356105e2e551c0528694091608fc7585dce66d2..c60cb1f92e99329d52f6ed39dccde406a5f83563 100644
--- a/paddle/fluid/operators/elementwise_add_op.h
+++ b/paddle/fluid/operators/elementwise_add_op.h
@@ -15,6 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/fluid/framework/eigen.h"
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
 #include "paddle/fluid/operators/math/blas.h"
 
@@ -136,9 +137,11 @@ elementwise_add_grad(const framework::ExecutionContext& ctx,
 }
 
 template <typename DeviceContext, typename T>
-class ElementwiseAddGradKernel : public framework::OpKernel<T> {
+class ElementwiseAddGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
+
     using Tensor = framework::Tensor;
 
     auto* dout = ctx.Input<Tensor>(framework::GradVarName("Out"));
diff --git a/paddle/fluid/operators/elementwise_div_op.h b/paddle/fluid/operators/elementwise_div_op.h
index 95649ac46e6bd41b9e1a865794cdec3ae1e6e247..41a7950bf0c598507c0fda48c6a43f2fd38c41d2 100644
--- a/paddle/fluid/operators/elementwise_div_op.h
+++ b/paddle/fluid/operators/elementwise_div_op.h
@@ -14,8 +14,8 @@ limitations under the License. */
 
 #pragma once
 
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
-
 namespace paddle {
 namespace operators {
 
@@ -53,9 +53,10 @@ struct DivGradDY {
 };
 
 template <typename DeviceContext, typename T>
-class ElementwiseDivGradKernel : public framework::OpKernel<T> {
+class ElementwiseDivGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* x = ctx.Input<Tensor>("X");
diff --git a/paddle/fluid/operators/elementwise_max_op.h b/paddle/fluid/operators/elementwise_max_op.h
index 527a18ee3ba88a158a13266a7fbcdafe59ec69d9..bfb5c931958b4ca890ea720af42dad91d5625abb 100644
--- a/paddle/fluid/operators/elementwise_max_op.h
+++ b/paddle/fluid/operators/elementwise_max_op.h
@@ -14,6 +14,7 @@ limitations under the License. */
 
 #pragma once
 
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
 
 namespace paddle {
@@ -55,9 +56,10 @@ struct MaxGradDy {
 };
 
 template <typename DeviceContext, typename T>
-class ElementwiseMaxGradKernel : public framework::OpKernel<T> {
+class ElementwiseMaxGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* x = ctx.Input<Tensor>("X");
diff --git a/paddle/fluid/operators/elementwise_min_op.h b/paddle/fluid/operators/elementwise_min_op.h
index d4e5831463f3e54c72789b6876ea696cf1b4ef4b..db035ffb52e619b337c8190af4ed0e155aaac48d 100644
--- a/paddle/fluid/operators/elementwise_min_op.h
+++ b/paddle/fluid/operators/elementwise_min_op.h
@@ -14,8 +14,8 @@ limitations under the License. */
 
 #pragma once
 
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
-
 namespace paddle {
 namespace operators {
 
@@ -55,9 +55,10 @@ struct MinGradDy {
 };
 
 template <typename DeviceContext, typename T>
-class ElementwiseMinGradKernel : public framework::OpKernel<T> {
+class ElementwiseMinGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* x = ctx.Input<Tensor>("X");
diff --git a/paddle/fluid/operators/elementwise_mul_op.h b/paddle/fluid/operators/elementwise_mul_op.h
index dc73cb6f23614504640283af01981d3f69e89126..82c5fa0472bcc3b4d2d12b7a80c3418da5d6dd7b 100644
--- a/paddle/fluid/operators/elementwise_mul_op.h
+++ b/paddle/fluid/operators/elementwise_mul_op.h
@@ -13,8 +13,8 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #pragma once
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
-
 namespace paddle {
 namespace operators {
 
@@ -50,9 +50,10 @@ struct MulGradDY {
 };
 
 template <typename DeviceContext, typename T>
-class ElementwiseMulGradKernel : public framework::OpKernel<T> {
+class ElementwiseMulGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* x = ctx.Input<Tensor>("X");
diff --git a/paddle/fluid/operators/elementwise_op.h b/paddle/fluid/operators/elementwise_op.h
index d8a12e800ad733800c1ec333f15d31d4dcd1a3a5..a79b900b9801e6b80e4433a9acdd4dab6c34859d 100644
--- a/paddle/fluid/operators/elementwise_op.h
+++ b/paddle/fluid/operators/elementwise_op.h
@@ -205,6 +205,20 @@ class ElementwiseOpExplicitGrad : public ElementwiseOpGrad {
   }
 };
 
+template <typename T>
+class ElemwiseGradKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    auto* dx =
+        context.Output<framework::LoDTensor>(framework::GradVarName("X"));
+    if (dx != nullptr) {
+      auto& dout =
+          *context.Input<framework::LoDTensor>(framework::GradVarName("Out"));
+      dx->set_lod(dout.lod());
+    }
+  }
+};
+
 }  // namespace operators
 }  // namespace paddle
 
diff --git a/paddle/fluid/operators/elementwise_sub_op.h b/paddle/fluid/operators/elementwise_sub_op.h
index 11c7e3fe628001f095836a788f2bcc7c4ee7ad4b..3385df0897700d37d60d8804a01db777ebc02a7e 100644
--- a/paddle/fluid/operators/elementwise_sub_op.h
+++ b/paddle/fluid/operators/elementwise_sub_op.h
@@ -13,6 +13,7 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #pragma once
+#include "paddle/fluid/operators/elementwise_op.h"
 #include "paddle/fluid/operators/elementwise_op_function.h"
 
 namespace paddle {
@@ -50,9 +51,10 @@ struct SubGradDY {
 };
 
 template <typename DeviceContext, typename T>
-class ElementwiseSubGradKernel : public framework::OpKernel<T> {
+class ElementwiseSubGradKernel : public ElemwiseGradKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    ElemwiseGradKernel<T>::Compute(ctx);
     using Tensor = framework::Tensor;
 
     auto* dout = ctx.Input<Tensor>(framework::GradVarName("Out"));
diff --git a/paddle/fluid/operators/mul_op.h b/paddle/fluid/operators/mul_op.h
index 15dd975e3bbf80b2e616e6628555e812d025f70a..f72824806ed6ee3a4490938403d441326f8a3d4a 100644
--- a/paddle/fluid/operators/mul_op.h
+++ b/paddle/fluid/operators/mul_op.h
@@ -62,23 +62,31 @@ class MulGradKernel : public framework::OpKernel<T> {
   void Compute(const framework::ExecutionContext& ctx) const override {
     int x_num_col_dims = ctx.template Attr<int>("x_num_col_dims");
     int y_num_col_dims = ctx.template Attr<int>("y_num_col_dims");
-    const Tensor* x = ctx.Input<Tensor>("X");
-    const Tensor* y = ctx.Input<Tensor>("Y");
-    const Tensor x_matrix = x->dims().size() > 2
-                                ? framework::ReshapeToMatrix(*x, x_num_col_dims)
-                                : *x;
-    const Tensor y_matrix = y->dims().size() > 2
-                                ? framework::ReshapeToMatrix(*y, y_num_col_dims)
-                                : *y;
-    const Tensor* dout = ctx.Input<Tensor>(framework::GradVarName("Out"));
+    auto* x = ctx.Input<framework::LoDTensor>("X");
+    auto* y = ctx.Input<framework::LoDTensor>("Y");
+    auto x_matrix = x->dims().size() > 2
+                        ? framework::ReshapeToMatrix(*x, x_num_col_dims)
+                        : static_cast<const Tensor&>(*x);
+    auto y_matrix = y->dims().size() > 2
+                        ? framework::ReshapeToMatrix(*y, y_num_col_dims)
+                        : static_cast<const Tensor&>(*y);
+    auto* dout = ctx.Input<framework::LoDTensor>(framework::GradVarName("Out"));
 
     Tensor dout_mat;
     dout_mat.ShareDataWith(*dout);
     dout_mat.Resize({framework::flatten_to_2d(x->dims(), x_num_col_dims)[0],
                      framework::flatten_to_2d(y->dims(), y_num_col_dims)[1]});
 
-    Tensor* dx = ctx.Output<Tensor>(framework::GradVarName("X"));
-    Tensor* dy = ctx.Output<Tensor>(framework::GradVarName("Y"));
+    auto* dx = ctx.Output<framework::LoDTensor>(framework::GradVarName("X"));
+    auto* dy = ctx.Output<framework::LoDTensor>(framework::GradVarName("Y"));
+
+    if (dx != nullptr) {
+      dx->set_lod(x->lod());
+    }
+    if (dy != nullptr) {
+      dy->set_lod(y->lod());
+    }
+
     auto& dev_ctx = ctx.template device_context<DeviceContext>();
     auto blas = math::GetBlas<DeviceContext, T>(dev_ctx);
     if (dx) {