diff --git a/paddle/fluid/API.spec b/paddle/fluid/API.spec
index 6876f5423d9a1cbf1816b8d53874af7988778b05..ca12ec7cb73a37794b4facd8c2e175e9281cf4a2 100644
--- a/paddle/fluid/API.spec
+++ b/paddle/fluid/API.spec
@@ -124,7 +124,7 @@ paddle.fluid.layers.split ArgSpec(args=['input', 'num_or_sections', 'dim', 'name
 paddle.fluid.layers.ctc_greedy_decoder ArgSpec(args=['input', 'blank', 'name'], varargs=None, keywords=None, defaults=(None,))
 paddle.fluid.layers.edit_distance ArgSpec(args=['input', 'label', 'normalized', 'ignored_tokens'], varargs=None, keywords=None, defaults=(True, None))
 paddle.fluid.layers.l2_normalize ArgSpec(args=['x', 'axis', 'epsilon', 'name'], varargs=None, keywords=None, defaults=(1e-12, None))
-paddle.fluid.layers.matmul ArgSpec(args=['x', 'y', 'transpose_x', 'transpose_y', 'name'], varargs=None, keywords=None, defaults=(False, False, None))
+paddle.fluid.layers.matmul ArgSpec(args=['x', 'y', 'transpose_x', 'transpose_y', 'alpha', 'name'], varargs=None, keywords=None, defaults=(False, False, 1.0, None))
 paddle.fluid.layers.topk ArgSpec(args=['input', 'k', 'name'], varargs=None, keywords=None, defaults=(None,))
 paddle.fluid.layers.warpctc ArgSpec(args=['input', 'label', 'blank', 'norm_by_times'], varargs=None, keywords=None, defaults=(0, False))
 paddle.fluid.layers.sequence_reshape ArgSpec(args=['input', 'new_dim'], varargs=None, keywords=None, defaults=None)
diff --git a/paddle/fluid/framework/grad_op_desc_maker.h b/paddle/fluid/framework/grad_op_desc_maker.h
index b4d3fa25c35fbf25b3d2fdd9fa1045dda0f773ec..9bccb1a32bf63b30351ef4428594691b0eef0b6a 100644
--- a/paddle/fluid/framework/grad_op_desc_maker.h
+++ b/paddle/fluid/framework/grad_op_desc_maker.h
@@ -129,6 +129,9 @@ class GradOpDescMakerBase {
 
   std::string ForwardOpType() const { return this->fwd_op_.Type(); }
 
+ protected:
+  const OpDesc& ForwardOp() const { return fwd_op_; }
+
  private:
   const OpDesc& fwd_op_;
   const std::unordered_set<std::string>& no_grad_set_;
diff --git a/paddle/fluid/operators/elementwise_mul_op.cc b/paddle/fluid/operators/elementwise_mul_op.cc
index 7cd67e74de6b9c4fbc718f60b4f671ccab2f9956..86a8459a79135d1fbcba6886172acc5a2abdb88b 100644
--- a/paddle/fluid/operators/elementwise_mul_op.cc
+++ b/paddle/fluid/operators/elementwise_mul_op.cc
@@ -13,9 +13,45 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #include "paddle/fluid/operators/elementwise_mul_op.h"
+#include <string>
 #include "paddle/fluid/operators/elementwise_op.h"
+
+namespace paddle {
+namespace operators {
+
+class ElementwiseMulOpGradDescMaker : public framework::SingleGradOpDescMaker {
+ public:
+  using framework::SingleGradOpDescMaker::SingleGradOpDescMaker;
+
+ protected:
+  std::unique_ptr<framework::OpDesc> Apply() const override {
+    std::unique_ptr<framework::OpDesc> op(new framework::OpDesc());
+    op->SetType("elementwise_mul_grad");
+    op->SetInput("X", Input("X"));
+    op->SetInput("Y", Input("Y"));
+    op->SetInput(framework::GradVarName("Out"), OutputGrad("Out"));
+    op->SetAttrMap(Attrs());
+    op->SetOutput(framework::GradVarName("X"), InputGrad("X"));
+    op->SetOutput(framework::GradVarName("Y"), InputGrad("Y"));
+    return op;
+  }
+};
+
+class ElementwiseMulOpMaker : public ElementwiseOpMaker {
+ protected:
+  virtual std::string GetName() const { return "Mul"; }
+  virtual std::string GetEquation() const { return "Out = X \\\\odot Y"; }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
 namespace ops = paddle::operators;
-REGISTER_ELEMWISE_OP(elementwise_mul, "Mul", "Out = X \\\\odot Y");
+REGISTER_OPERATOR(elementwise_mul, ops::ElementwiseOp,
+                  ops::ElementwiseMulOpMaker, ops::ElementwiseOpInferVarType,
+                  ops::ElementwiseMulOpGradDescMaker);
+REGISTER_OPERATOR(elementwise_mul_grad, ops::ElementwiseOpGrad);
+
 REGISTER_OP_CPU_KERNEL(
     elementwise_mul,
     ops::ElementwiseMulKernel<paddle::platform::CPUDeviceContext, float>,
diff --git a/paddle/fluid/operators/elementwise_mul_op.h b/paddle/fluid/operators/elementwise_mul_op.h
index 4437da4d95f97b5cbbca1650badf9710c26b4380..b870d08a1a28fd3e678aeb7211f7e3ec8b2c4c65 100644
--- a/paddle/fluid/operators/elementwise_mul_op.h
+++ b/paddle/fluid/operators/elementwise_mul_op.h
@@ -93,8 +93,8 @@ class ElementwiseMulGradKernel : public ElemwiseGradKernel<T> {
 
     auto* x = ctx.Input<Tensor>("X");
     auto* y = ctx.Input<Tensor>("Y");
-    auto* out = ctx.Input<Tensor>("Out");
     auto* dout = ctx.Input<Tensor>(framework::GradVarName("Out"));
+    auto* out = dout;  // out is not necessary
     auto* dx = ctx.Output<Tensor>(framework::GradVarName("X"));
     auto* dy = ctx.Output<Tensor>(framework::GradVarName("Y"));
     int axis = ctx.Attr<int>("axis");
diff --git a/paddle/fluid/operators/matmul_op.cc b/paddle/fluid/operators/matmul_op.cc
index 7182149164854038bb67a9f06cdbec8a4a0f1fb2..242a1b9ae92ade0caf1b0f1fcb5458b8b7070d84 100644
--- a/paddle/fluid/operators/matmul_op.cc
+++ b/paddle/fluid/operators/matmul_op.cc
@@ -59,7 +59,8 @@ class MatMulKernel : public framework::OpKernel<T> {
         RowMatrixFromVector(x.dims()), 0, context.Attr<bool>("transpose_X"));
     auto mat_dim_b = math::CreateMatrixDescriptor(
         ColumnMatrixFromVector(y.dims()), 0, context.Attr<bool>("transpose_Y"));
-    blas.MatMul(x, mat_dim_a, y, mat_dim_b, T(1), out, T(0));
+    auto scale = static_cast<T>(context.Attr<float>("alpha"));
+    blas.MatMul(x, mat_dim_a, y, mat_dim_b, scale, out, T(0));
   }
 };
 
@@ -185,7 +186,8 @@ class MatMulGradKernel : public framework::OpKernel<T> {
     auto blas = math::GetBlas<DeviceContext, T>(context);
     auto mat_dim_a = math::CreateMatrixDescriptor(a.dims(), 0, trans_a);
     auto mat_dim_b = math::CreateMatrixDescriptor(b.dims(), 0, trans_b);
-    blas.MatMul(a, mat_dim_a, b, mat_dim_b, T(1), out, T(0));
+    blas.MatMul(a, mat_dim_a, b, mat_dim_b,
+                static_cast<T>(context.Attr<float>("alpha")), out, T(0));
   }
 
   void CalcInputGrad(const framework::ExecutionContext &context,
@@ -334,6 +336,7 @@ class MatMulOpMaker : public framework::OpProtoAndCheckerMaker {
                   R"DOC(If true, use the transpose of `Y`.
         )DOC")
         .SetDefault(false);
+    AddAttr<float>("alpha", "The scale of Out").SetDefault(1.0f);
     AddComment(R"DOC(
 MatMul Operator.
 
diff --git a/paddle/fluid/operators/mul_op.cc b/paddle/fluid/operators/mul_op.cc
index 2a8e4af516ce9341772d4668dc993215b4aae24d..363abfb0e0c96e8a4d82124dff168f28e339a9ae 100644
--- a/paddle/fluid/operators/mul_op.cc
+++ b/paddle/fluid/operators/mul_op.cc
@@ -156,12 +156,29 @@ class MulGradOp : public framework::OperatorWithKernel {
   }
 };
 
+class MulOpGradMaker : public framework::SingleGradOpDescMaker {
+ public:
+  using framework::SingleGradOpDescMaker::SingleGradOpDescMaker;
+
+ protected:
+  std::unique_ptr<framework::OpDesc> Apply() const override {
+    std::unique_ptr<framework::OpDesc> retv(new framework::OpDesc());
+    retv->SetType("mul_grad");
+    retv->SetInput("X", Input("X"));
+    retv->SetInput("Y", Input("Y"));
+    retv->SetInput(framework::GradVarName("Out"), OutputGrad("Out"));
+    retv->SetOutput(framework::GradVarName("X"), InputGrad("X"));
+    retv->SetOutput(framework::GradVarName("Y"), InputGrad("Y"));
+    retv->SetAttrMap(Attrs());
+    return retv;
+  }
+};
+
 }  // namespace operators
 }  // namespace paddle
 
 namespace ops = paddle::operators;
-REGISTER_OPERATOR(mul, ops::MulOp, ops::MulOpMaker,
-                  paddle::framework::DefaultGradOpDescMaker<true>);
+REGISTER_OPERATOR(mul, ops::MulOp, ops::MulOpMaker, ops::MulOpGradMaker);
 REGISTER_OPERATOR(mul_grad, ops::MulGradOp);
 REGISTER_OP_CPU_KERNEL(
     mul, ops::MulKernel<paddle::platform::CPUDeviceContext, float>,
diff --git a/paddle/fluid/operators/scale_op.cc b/paddle/fluid/operators/scale_op.cc
index c614de2eac143b3a545c60226aefa93dd72dea4f..13be6c65be58314a75124106eb09b1300305baf0 100644
--- a/paddle/fluid/operators/scale_op.cc
+++ b/paddle/fluid/operators/scale_op.cc
@@ -52,6 +52,12 @@ $$Out = scale*X$$
 )DOC");
     AddAttr<float>("scale", "The scaling factor of the scale operator.")
         .SetDefault(1.0);
+    AddAttr<float>("bias", "The bias of the scale operator.").SetDefault(0.0);
+    AddAttr<bool>(
+        "bias_after_scale",
+        "Apply bias addition after or before scaling. It is useful for "
+        "numeric stability in some circumstances.")
+        .SetDefault(true);
   }
 };
 
@@ -80,6 +86,8 @@ class ScaleGradMaker : public framework::SingleGradOpDescMaker {
     grad_op->SetInput("X", OutputGrad("Out"));
     grad_op->SetOutput("Out", InputGrad("X"));
     grad_op->SetAttr("scale", GetAttr("scale"));
+    grad_op->SetAttr("bias", 0.0f);
+    grad_op->SetAttr("bias_after_scale", true);
     return std::unique_ptr<framework::OpDesc>(grad_op);
   }
 };
diff --git a/paddle/fluid/operators/scale_op.h b/paddle/fluid/operators/scale_op.h
index fe035aba81dd74d21539974beed255275be3013b..d8a199bc2b860515645b4954b49d8eb59fbd02dc 100644
--- a/paddle/fluid/operators/scale_op.h
+++ b/paddle/fluid/operators/scale_op.h
@@ -34,6 +34,8 @@ class ScaleKernel : public framework::OpKernel<T> {
                       "in and out should have the same dim");
 
     auto scale = static_cast<T>(ctx.Attr<float>("scale"));
+    auto bias = static_cast<T>(ctx.Attr<float>("bias"));
+    auto bias_after_scale = ctx.Attr<bool>("bias_after_scale");
 
     if (in_var->IsType<framework::SelectedRows>() && in_var != out_var) {
       auto& in_slr = in_var->Get<framework::SelectedRows>();
@@ -45,7 +47,11 @@ class ScaleKernel : public framework::OpKernel<T> {
     auto eigen_out = framework::EigenVector<T>::Flatten(*out);
     auto eigen_in = framework::EigenVector<T>::Flatten(*in);
     auto& dev = *ctx.template device_context<DeviceContext>().eigen_device();
-    eigen_out.device(dev) = scale * eigen_in;
+    if (bias_after_scale) {
+      eigen_out.device(dev) = scale * eigen_in + bias;
+    } else {
+      eigen_out.device(dev) = scale * (eigen_in + bias);
+    }
   }
 };
 
diff --git a/python/paddle/fluid/layers/nn.py b/python/paddle/fluid/layers/nn.py
index e8a11e68b124eece029f8e8289069f8f22f43a7b..c7df815175c912d3e0e476a53c370d42cf45e5e0 100644
--- a/python/paddle/fluid/layers/nn.py
+++ b/python/paddle/fluid/layers/nn.py
@@ -3499,7 +3499,7 @@ def l2_normalize(x, axis, epsilon=1e-12, name=None):
     return out
 
 
-def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
+def matmul(x, y, transpose_x=False, transpose_y=False, alpha=1.0, name=None):
     """
     Applies matrix multiplication to two tensors.
 
@@ -3533,6 +3533,7 @@ def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
         y (Variable): The input variable which is a Tensor or LoDTensor.
         transpose_x (bool): Whether to transpose :math:`x` before multiplication.
         transpose_y (bool): Whether to transpose :math:`y` before multiplication.
+        alpha (float): The scale of output. Default 1.0.
         name(str|None): A name for this layer(optional). If set None, the layer
             will be named automatically.
 
@@ -3600,8 +3601,11 @@ def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
         inputs={'X': x,
                 'Y': y},
         outputs={'Out': out},
-        attrs={'transpose_X': transpose_x,
-               'transpose_Y': transpose_y})
+        attrs={
+            'transpose_X': transpose_x,
+            'transpose_Y': transpose_y,
+            'alpha': alpha,
+        })
     return out