diff --git a/paddle/operators/activation_op.cc b/paddle/operators/activation_op.cc
index 55f673c22df53027ccf1a39f8b70b766ea45d8f0..4188858a90daf8b2c10eb6960393de977d467371 100644
--- a/paddle/operators/activation_op.cc
+++ b/paddle/operators/activation_op.cc
@@ -22,8 +22,8 @@ class ActivationOp : public framework::OperatorWithKernel {
   using framework::OperatorWithKernel::OperatorWithKernel;
 
   void InferShape(framework::InferShapeContext *ctx) const override {
-    ctx->SetOutputDim("Y", ctx->GetInputDim("X"));
-    ctx->ShareLoD("X", /*->*/ "Y");
+    ctx->SetOutputDim("Out", ctx->GetInputDim("X"));
+    ctx->ShareLoD("X", /*->*/ "Out");
   }
 };
 
@@ -32,7 +32,7 @@ class ActivationOpGrad : public framework::OperatorWithKernel {
   using framework::OperatorWithKernel::OperatorWithKernel;
 
   void InferShape(framework::InferShapeContext *ctx) const override {
-    ctx->SetOutputDim(framework::GradVarName("X"), ctx->GetInputDim("Y"));
+    ctx->SetOutputDim(framework::GradVarName("X"), ctx->GetInputDim("Out"));
   }
 };
 
@@ -41,11 +41,11 @@ class SigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
   SigmoidOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Sigmoid operator");
-    AddOutput("Y", "Output of Sigmoid operator");
+    AddOutput("Out", "Output of Sigmoid operator");
     AddComment(R"DOC(
 Sigmoid Activation Operator
 
-$$y = \frac{1}{1 + e^{-x}}$$
+$$out = \frac{1}{1 + e^{-x}}$$
 
 )DOC");
   }
@@ -56,11 +56,11 @@ class LogSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
   LogSigmoidOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of LogSigmoid operator");
-    AddOutput("Y", "Output of LogSigmoid operator");
+    AddOutput("Out", "Output of LogSigmoid operator");
     AddComment(R"DOC(
 Logsigmoid Activation Operator
 
-$$y = \log \frac{1}{1 + e^{-x}}$$
+$$out = \log \frac{1}{1 + e^{-x}}$$
 
 )DOC");
   }
@@ -71,11 +71,11 @@ class ExpOpMaker : public framework::OpProtoAndCheckerMaker {
   ExpOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Exp operator");
-    AddOutput("Y", "Output of Exp operator");
+    AddOutput("Out", "Output of Exp operator");
     AddComment(R"DOC(
 Exp Activation Operator.
 
-$y = e^x$
+$out = e^x$
 
 )DOC");
   }
@@ -86,11 +86,11 @@ class ReluOpMaker : public framework::OpProtoAndCheckerMaker {
   ReluOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Relu operator");
-    AddOutput("Y", "Output of Relu operator");
+    AddOutput("Out", "Output of Relu operator");
     AddComment(R"DOC(
 Relu Activation Operator.
 
-$y = \max(x, 0)$
+$out = \max(x, 0)$
 
 )DOC");
   }
@@ -101,12 +101,12 @@ class LeakyReluOpMaker : public framework::OpProtoAndCheckerMaker {
   LeakyReluOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of LeakyRelu operator");
-    AddOutput("Y", "Output of LeakyRelu operator");
+    AddOutput("Out", "Output of LeakyRelu operator");
     AddAttr<float>("alpha", "The small negative slope").SetDefault(0.02f);
     AddComment(R"DOC(
 LeakyRelu Activation Operator.
 
-$y = \max(x, \alpha * x)$
+$out = \max(x, \alpha * x)$
 
 )DOC");
   }
@@ -117,13 +117,13 @@ class SoftShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
   SoftShrinkOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softshrink operator");
-    AddOutput("Y", "Output of Softshrink operator");
+    AddOutput("Out", "Output of Softshrink operator");
     AddAttr<float>("lambda", "non-negative offset").SetDefault(0.5f);
     AddComment(R"DOC(
 Softshrink Activation Operator.
 
 $$
-y = \begin{cases} 
+out = \begin{cases} 
     x - \lambda, \text{if } x > \lambda \\
     x + \lambda, \text{if } x < -\lambda \\
     0,  \text{otherwise}
@@ -139,11 +139,11 @@ class TanhOpMaker : public framework::OpProtoAndCheckerMaker {
   TanhOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Tanh operator");
-    AddOutput("Y", "Output of Tanh operator");
+    AddOutput("Out", "Output of Tanh operator");
     AddComment(R"DOC(
 Tanh Activation Operator.
 
-$$y = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
+$$out = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
 
 )DOC");
   }
@@ -154,11 +154,11 @@ class TanhShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
   TanhShrinkOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of TanhShrink operator");
-    AddOutput("Y", "Output of TanhShrink operator");
+    AddOutput("Out", "Output of TanhShrink operator");
     AddComment(R"DOC(
 TanhShrink Activation Operator.
 
-$$y = x - \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
+$$out = x - \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
 
 )DOC");
   }
@@ -169,14 +169,14 @@ class HardShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
   HardShrinkOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of HardShrink operator");
-    AddOutput("Y", "Output of HardShrink operator");
+    AddOutput("Out", "Output of HardShrink operator");
     AddAttr<float>("threshold", "The value of threshold for HardShrink")
         .SetDefault(0.5f);
     AddComment(R"DOC(
 HardShrink Activation Operator.
 
 $$
-y = \begin{cases} 
+out = \begin{cases} 
     x, \text{if } x > \lambda \\
     x, \text{if } x < -\lambda \\
     0,  \text{otherwise}
@@ -192,11 +192,11 @@ class SqrtOpMaker : public framework::OpProtoAndCheckerMaker {
   SqrtOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Sqrt operator");
-    AddOutput("Y", "Output of Sqrt operator");
+    AddOutput("Out", "Output of Sqrt operator");
     AddComment(R"DOC(
 Sqrt Activation Operator.
 
-$y = \sqrt{x}$
+$out = \sqrt{x}$
 
 )DOC");
   }
@@ -207,11 +207,11 @@ class AbsOpMaker : public framework::OpProtoAndCheckerMaker {
   AbsOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Abs operator");
-    AddOutput("Y", "Output of Abs operator");
+    AddOutput("Out", "Output of Abs operator");
     AddComment(R"DOC(
 Abs Activation Operator.
 
-$y = |x|$
+$out = |x|$
 
 )DOC");
   }
@@ -222,11 +222,11 @@ class CeilOpMaker : public framework::OpProtoAndCheckerMaker {
   CeilOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Ceil operator");
-    AddOutput("Y", "Output of Ceil operator");
+    AddOutput("Out", "Output of Ceil operator");
     AddComment(R"DOC(
 Ceil Activation Operator.
 
-$y = ceil(x)$
+$out = ceil(x)$
 
 )DOC");
   }
@@ -237,11 +237,11 @@ class FloorOpMaker : public framework::OpProtoAndCheckerMaker {
   FloorOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Floor operator");
-    AddOutput("Y", "Output of Floor operator");
+    AddOutput("Out", "Output of Floor operator");
     AddComment(R"DOC(
 Floor Activation Operator.
 
-$y = floor(x)$
+$out = floor(x)$
 
 )DOC");
   }
@@ -252,11 +252,11 @@ class RoundOpMaker : public framework::OpProtoAndCheckerMaker {
   RoundOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Round operator");
-    AddOutput("Y", "Output of Round operator");
+    AddOutput("Out", "Output of Round operator");
     AddComment(R"DOC(
 Round Activation Operator.
 
-$y = [x]$
+$out = [x]$
 
 )DOC");
   }
@@ -267,11 +267,11 @@ class ReciprocalOpMaker : public framework::OpProtoAndCheckerMaker {
   ReciprocalOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Reciprocal operator");
-    AddOutput("Y", "Output of Reciprocal operator");
+    AddOutput("Out", "Output of Reciprocal operator");
     AddComment(R"DOC(
 Reciprocal Activation Operator.
 
-$$y = \frac{1}{x}$$
+$$out = \frac{1}{x}$$
 
 )DOC");
   }
@@ -282,11 +282,11 @@ class LogOpMaker : public framework::OpProtoAndCheckerMaker {
   LogOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Log operator");
-    AddOutput("Y", "Output of Log operator");
+    AddOutput("Out", "Output of Log operator");
     AddComment(R"DOC(
 Log Activation Operator.
 
-$y = \ln(x)$
+$out = \ln(x)$
 
 Natural logarithm of x.
 
@@ -299,11 +299,11 @@ class SquareOpMaker : public framework::OpProtoAndCheckerMaker {
   SquareOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Square operator");
-    AddOutput("Y", "Output of Square operator");
+    AddOutput("Out", "Output of Square operator");
     AddComment(R"DOC(
 Square Activation Operator.
 
-$y = x^2$
+$out = x^2$
 
 )DOC");
   }
@@ -314,11 +314,11 @@ class SoftplusOpMaker : public framework::OpProtoAndCheckerMaker {
   SoftplusOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softplus operator");
-    AddOutput("Y", "Output of Softplus operator");
+    AddOutput("Out", "Output of Softplus operator");
     AddComment(R"DOC(
 Softplus Activation Operator.
 
-$y = \ln(1 + e^{x})$
+$out = \ln(1 + e^{x})$
 
 )DOC");
   }
@@ -329,11 +329,11 @@ class SoftsignOpMaker : public framework::OpProtoAndCheckerMaker {
   SoftsignOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softsign operator");
-    AddOutput("Y", "Output of Softsign operator");
+    AddOutput("Out", "Output of Softsign operator");
     AddComment(R"DOC(
 Softsign Activation Operator.
 
-$$y = \frac{x}{1 + |x|}$$
+$$out = \frac{x}{1 + |x|}$$
 
 )DOC");
   }
@@ -344,7 +344,7 @@ class BReluOpMaker : public framework::OpProtoAndCheckerMaker {
   BReluOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of BRelu operator");
-    AddOutput("Y", "Output of BRelu operator");
+    AddOutput("Out", "Output of BRelu operator");
     AddAttr<float>("t_min", "The min marginal value of BRelu")
         .SetDefault(static_cast<float>(0));
     AddAttr<float>("t_max", "The max marginal value of BRelu")
@@ -352,7 +352,7 @@ class BReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddComment(R"DOC(
 BRelu Activation Operator.
 
-$y = \max(\min(x, t_{min}), t_{max})$
+$out = \max(\min(x, t_{min}), t_{max})$
 
 )DOC");
   }
@@ -363,13 +363,13 @@ class SoftReluOpMaker : public framework::OpProtoAndCheckerMaker {
   SoftReluOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of SoftRelu operator");
-    AddOutput("Y", "Output of SoftRelu operator");
+    AddOutput("Out", "Output of SoftRelu operator");
     AddAttr<float>("threshold", "The threshold value of SoftRelu")
         .SetDefault(40.0f);
     AddComment(R"DOC(
 SoftRelu Activation Operator.
 
-$y = \ln(1 + \exp(\max(\min(x, threshold), threshold))$
+$out = \ln(1 + \exp(\max(\min(x, threshold), threshold))$
 
 )DOC");
   }
@@ -380,7 +380,7 @@ class ELUOpMaker : public framework::OpProtoAndCheckerMaker {
   ELUOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of ELU operator");
-    AddOutput("Y", "Output of ELU operator");
+    AddOutput("Out", "Output of ELU operator");
     AddAttr<float>("alpha", "The alpha value of ELU").SetDefault(1.0f);
     AddComment(R"DOC(
 ELU Activation Operator.
@@ -388,7 +388,7 @@ ELU Activation Operator.
 Applies the following element-wise computation on the input according to
 https://arxiv.org/abs/1511.07289.
 
-$y = \max(0, x) + \min(0, \alpha * (e^x - 1))$
+$out = \max(0, x) + \min(0, \alpha * (e^x - 1))$
 
 )DOC");
   }
@@ -399,13 +399,13 @@ class Relu6OpMaker : public framework::OpProtoAndCheckerMaker {
   Relu6OpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Relu6 operator");
-    AddOutput("Y", "Output of Relu6 operator");
+    AddOutput("Out", "Output of Relu6 operator");
     AddAttr<float>("threshold", "The threshold value of Relu6")
         .SetDefault(6.0f);
     AddComment(R"DOC(
 Relu6 Activation Operator.
 
-$y = \min(\max(0, x), 6)$
+$out = \min(\max(0, x), 6)$
 
 )DOC");
   }
@@ -416,12 +416,12 @@ class PowOpMaker : public framework::OpProtoAndCheckerMaker {
   PowOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Pow operator");
-    AddOutput("Y", "Output of Pow operator");
+    AddOutput("Out", "Output of Pow operator");
     AddAttr<float>("factor", "The exponential factor of Pow").SetDefault(1.0f);
     AddComment(R"DOC(
 Pow Activation Operator.
 
-$y = x^{factor}$
+$out = x^{factor}$
 
 )DOC");
   }
@@ -432,7 +432,7 @@ class STanhOpMaker : public framework::OpProtoAndCheckerMaker {
   STanhOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of STanh operator");
-    AddOutput("Y", "Output of STanh operator");
+    AddOutput("Out", "Output of STanh operator");
     AddAttr<float>("scale_a", "The scale parameter of a for the input")
         .SetDefault(2.0f / 3.0f);
     AddAttr<float>("scale_b", "The scale parameter of b for the input")
@@ -440,7 +440,7 @@ class STanhOpMaker : public framework::OpProtoAndCheckerMaker {
     AddComment(R"DOC(
 STanh Activation Operator.
 
-$$y = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}}$$
+$$out = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}}$$
 
 )DOC");
   }
@@ -451,14 +451,14 @@ class ThresholdedReluOpMaker : public framework::OpProtoAndCheckerMaker {
   ThresholdedReluOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of ThresholdedRelu operator");
-    AddOutput("Y", "Output of ThresholdedRelu operator");
+    AddOutput("Out", "Output of ThresholdedRelu operator");
     AddAttr<float>("threshold", "The threshold location of activation")
         .SetDefault(1.0f);
     AddComment(R"DOC(
 ThresholdedRelu Activation Operator.
 
 $$
-y = \begin{cases} 
+out = \begin{cases} 
     x, \text{if } x > threshold \\
     0,  \text{otherwise}
     \end{cases}
@@ -473,7 +473,7 @@ class HardSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
   HardSigmoidOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of HardSigmoid operator");
-    AddOutput("Y", "Output of HardSigmoid operator");
+    AddOutput("Out", "Output of HardSigmoid operator");
     AddAttr<float>("slope", "Slope for linear approximation of sigmoid")
         .SetDefault(0.2f);
     AddAttr<float>("offset", "Offset for linear approximation of sigmoid")
@@ -484,7 +484,7 @@ HardSigmoid Activation Operator.
 Segment-wise linear approximation of sigmoid(https://arxiv.org/abs/1603.00391), 
 which is much faster than sigmoid.
 
-$y = \max(0, \min(1, slope * x + shift))$
+$out = \max(0, \min(1, slope * x + shift))$
 
 The slope should be positive. The offset can be either positive or negative.
 The default slope and shift are set according to the above reference.
@@ -499,12 +499,12 @@ class SwishOpMaker : public framework::OpProtoAndCheckerMaker {
   SwishOpMaker(OpProto *proto, OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Swish operator");
-    AddOutput("Y", "Output of Swish operator");
+    AddOutput("Out", "Output of Swish operator");
     AddAttr<float>("beta", "Constant beta of swish operator").SetDefault(1.0f);
     AddComment(R"DOC(
 Swish Activation Operator.
 
-$$y = \frac{x}{1 + e^{- \beta x}}$$
+$$out = \frac{x}{1 + e^{- \beta x}}$$
 
 )DOC");
   }
diff --git a/paddle/operators/activation_op.h b/paddle/operators/activation_op.h
index 7b433df995afae7340ac97f721f962efdd2f07c0..0885f7c570b9b52dc51597347295734fd689da8d 100644
--- a/paddle/operators/activation_op.h
+++ b/paddle/operators/activation_op.h
@@ -27,11 +27,11 @@ class ActivationKernel
 
   void Compute(const framework::ExecutionContext& context) const override {
     auto* X = context.Input<framework::Tensor>("X");
-    auto* Y = context.Output<framework::Tensor>("Y");
-    Y->mutable_data<T>(context.GetPlace());
+    auto* Out = context.Output<framework::Tensor>("Out");
+    Out->mutable_data<T>(context.GetPlace());
 
     auto x = framework::EigenVector<T>::Flatten(*X);
-    auto y = framework::EigenVector<T>::Flatten(*Y);
+    auto out = framework::EigenVector<T>::Flatten(*Out);
     auto* place =
         context.template device_context<DeviceContext>().eigen_device();
     Functor functor;
@@ -40,7 +40,7 @@ class ActivationKernel
     for (auto& attr : attrs) {
       *attr.second = context.Attr<float>(attr.first);
     }
-    functor(*place, x, y);
+    functor(*place, x, out);
   }
 };
 
@@ -51,14 +51,15 @@ class ActivationGradKernel
   using T = typename Functor::ELEMENT_TYPE;
   void Compute(const framework::ExecutionContext& context) const override {
     auto* X = context.Input<framework::Tensor>("X");
-    auto* Y = context.Input<framework::Tensor>("Y");
-    auto* dY = context.Input<framework::Tensor>(framework::GradVarName("Y"));
+    auto* Out = context.Input<framework::Tensor>("Out");
+    auto* dOut =
+        context.Input<framework::Tensor>(framework::GradVarName("Out"));
     auto* dX = context.Output<framework::Tensor>(framework::GradVarName("X"));
     dX->mutable_data<T>(context.GetPlace());
 
-    auto dy = framework::EigenVector<T>::Flatten(*dY);
+    auto dout = framework::EigenVector<T>::Flatten(*dOut);
     auto x = framework::EigenVector<T>::Flatten(*X);
-    auto y = framework::EigenVector<T>::Flatten(*Y);
+    auto out = framework::EigenVector<T>::Flatten(*Out);
     auto dx = framework::EigenVector<T>::Flatten(*dX);
     auto* place =
         context.template device_context<DeviceContext>().eigen_device();
@@ -67,7 +68,7 @@ class ActivationGradKernel
     for (auto& attr : attrs) {
       *attr.second = context.Attr<float>(attr.first);
     }
-    functor(*place, x, y, dy, dx);
+    functor(*place, x, out, dout, dx);
   }
 };
 
@@ -83,17 +84,18 @@ struct BaseActivationFunctor {
 // sigmoid(x) = 1 / (1 + exp(-x))
 template <typename T>
 struct SigmoidFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = static_cast<T>(1) / (static_cast<T>(1) + (-x).exp());
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = static_cast<T>(1) / (static_cast<T>(1) + (-x).exp());
   }
 };
 
 template <typename T>
 struct SigmoidGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * y * (static_cast<T>(1) - y);
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * out * (static_cast<T>(1) - out);
   }
 };
 
@@ -101,7 +103,7 @@ struct SigmoidGradFunctor : public BaseActivationFunctor<T> {
 // For numerical stability, we can use the log-sum-exp trick:
 // https://hips.seas.harvard.edu/blog/2013/01/09/computing-log-sum-exp/
 // We can rewrite the above equation as:
-// y = -log( exp(0) + exp(-x)) [since exp(0) = 1]
+// out = -log( exp(0) + exp(-x)) [since exp(0) = 1]
 //   = -log( exp(max(-x, 0) - max(-x, 0)) + exp(-x + max(-x, 0) - max(-x, 0)))
 //   = -log( exp(max(-x, 0)) * exp(-max(-x, 0)) - exp(max(-x, 0)) * exp(-x -
 //           max(-x, 0)))
@@ -112,10 +114,10 @@ struct SigmoidGradFunctor : public BaseActivationFunctor<T> {
 // + exp(-x - max(-x, 0))))
 template <typename T>
 struct LogSigmoidFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto temp = (-x).cwiseMax(static_cast<T>(0));  // temp = max(-x, 0)
-    y.device(d) = -temp - (((-temp).exp() + (-x - temp).exp()).log());
+    out.device(d) = -temp - (((-temp).exp() + (-x - temp).exp()).log());
   }
 };
 
@@ -124,62 +126,66 @@ struct LogSigmoidFunctor : public BaseActivationFunctor<T> {
 // exp(-x - max(-x, 0)))
 template <typename T>
 struct LogSigmoidGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto temp = (-x).cwiseMax(static_cast<T>(0));  // temp = max(-x, 0)
     dx.device(d) =
-        dy * ((-x - temp).exp() / ((-temp).exp() + (-x - temp).exp()));
+        dout * ((-x - temp).exp() / ((-temp).exp() + (-x - temp).exp()));
   }
 };
 
 // exp(x) = e^x
 template <typename T>
 struct ExpFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.exp();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.exp();
   }
 };
 
 template <typename T>
 struct ExpGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * y;
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * out;
   }
 };
 
 // relu(x) = max(x, 0)
 template <typename T>
 struct ReluFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.cwiseMax(static_cast<T>(0));
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.cwiseMax(static_cast<T>(0));
   }
 };
 
 template <typename T>
 struct ReluGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * (x > static_cast<T>(0)).template cast<T>();
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (x > static_cast<T>(0)).template cast<T>();
   }
 };
 
 // tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
 template <typename T>
 struct TanhFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.tanh();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.tanh();
   }
 };
 
 template <typename T>
 struct TanhGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * (static_cast<T>(1) - y * y);
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (static_cast<T>(1) - out * out);
   }
 };
 
@@ -187,17 +193,18 @@ struct TanhGradFunctor : public BaseActivationFunctor<T> {
 // where tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
 template <typename T>
 struct TanhShrinkFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x - x.tanh();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x - x.tanh();
   }
 };
 
 template <typename T>
 struct TanhShrinkGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * (x.tanh() * x.tanh());
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (x.tanh() * x.tanh());
   }
 };
 
@@ -210,11 +217,11 @@ struct HardShrinkFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"threshold", &threshold}};
   }
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto temp1 = (x < static_cast<T>(threshold * -1)).template cast<T>().eval();
     auto temp2 = (x > static_cast<T>(threshold)).template cast<T>().eval();
-    y.device(d) = x * (temp1 + temp2);
+    out.device(d) = x * (temp1 + temp2);
   }
 };
 
@@ -226,11 +233,12 @@ struct HardShrinkGradFunctor : public BaseActivationFunctor<T> {
     return {{"threshold", &threshold}};
   }
 
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto temp1 = (x < static_cast<T>(threshold * -1)).template cast<T>().eval();
     auto temp2 = (x > static_cast<T>(threshold)).template cast<T>().eval();
-    dx.device(d) = dy * (temp1 + temp2).template cast<T>();
+    dx.device(d) = dout * (temp1 + temp2).template cast<T>();
   }
 };
 
@@ -243,12 +251,12 @@ struct SoftShrinkFunctor : public BaseActivationFunctor<T> {
     return {{"lambda", &lambda}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto lambdaT = static_cast<T>(lambda);
     auto temp1 = (x > lambdaT).template cast<T>().eval();
     auto temp2 = (x < -lambdaT).template cast<T>().eval();
-    y.device(d) = temp1 * (x - lambdaT) + temp2 * (x + lambdaT);
+    out.device(d) = temp1 * (x - lambdaT) + temp2 * (x + lambdaT);
   }
 };
 
@@ -258,46 +266,49 @@ struct SoftShrinkGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"lambda", &lambda}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto lambdaT = static_cast<T>(lambda);
     auto temp1 = (x > lambdaT).template cast<T>().eval();
     auto temp2 = (x < -lambdaT).template cast<T>().eval();
-    dx.device(d) = dy * (temp1 + temp2).template cast<T>();
+    dx.device(d) = dout * (temp1 + temp2).template cast<T>();
   }
 };
 
 // sqrt(x) = x^(1/2)
 template <typename T>
 struct SqrtFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.sqrt();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.sqrt();
   }
 };
 
 template <typename T>
 struct SqrtGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    const Y y_conj = Eigen::numext::conj(y);
-    dx.device(d) = static_cast<T>(0.5) * dy / y_conj;
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    const Out out_conj = Eigen::numext::conj(out);
+    dx.device(d) = static_cast<T>(0.5) * dout / out_conj;
   }
 };
 
 // ceil(x) = ceiling(x)
 template <typename T>
 struct CeilFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.ceil();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.ceil();
   }
 };
 
 template <typename T>
 struct ZeroGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     dx.device(d) = static_cast<T>(0) / x;
   }
 };
@@ -305,86 +316,90 @@ struct ZeroGradFunctor : public BaseActivationFunctor<T> {
 // floor(x) = flooring(x)
 template <typename T>
 struct FloorFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.ceil();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.ceil();
   }
 };
 
 // round(x) = [x]
 template <typename T>
 struct RoundFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.round();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.round();
   }
 };
 
 // abs(x) = |x|
 template <typename T>
 struct AbsFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.abs();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.abs();
   }
 };
 
 template <typename T>
 struct AbsGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * x.sign();
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * x.sign();
   }
 };
 
 // reciprocal(x) = 1 / x
 template <typename T>
 struct ReciprocalFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = static_cast<T>(1) / x;
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = static_cast<T>(1) / x;
   }
 };
 
 template <typename T>
 struct ReciprocalGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * static_cast<T>(-1) * y * y;
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * static_cast<T>(-1) * out * out;
   }
 };
 
 // log(x) = natural logarithm of x
 template <typename T>
 struct LogFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.log();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.log();
   }
 };
 
 template <typename T>
 struct LogGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * (static_cast<T>(1) / x);
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (static_cast<T>(1) / x);
   }
 };
 
 // square(x) = x^2
 template <typename T>
 struct SquareFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.square();
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.square();
   }
 };
 
 template <typename T>
 struct SquareGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * static_cast<T>(2) * x;
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * static_cast<T>(2) * x;
   }
 };
 
@@ -399,9 +414,9 @@ struct BReluFunctor : public BaseActivationFunctor<T> {
     return {{"t_min", &t_min}, {"t_max", &t_max}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) =
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) =
         x.cwiseMax(static_cast<T>(t_min)).cwiseMin(static_cast<T>(t_max));
   }
 };
@@ -413,9 +428,10 @@ struct BReluGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"t_min", &t_min}, {"t_max", &t_max}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy *
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout *
                    ((x > static_cast<T>(t_min)) * (x < static_cast<T>(t_max)))
                        .template cast<T>();
   }
@@ -430,9 +446,9 @@ struct Relu6Functor : public BaseActivationFunctor<T> {
     return {{"threshold", &threshold}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) =
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) =
         x.cwiseMax(static_cast<T>(0)).cwiseMin(static_cast<T>(threshold));
   }
 };
@@ -443,9 +459,10 @@ struct Relu6GradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"threshold", &threshold}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy *
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout *
                    ((x > static_cast<T>(0)) * (x < static_cast<T>(threshold)))
                        .template cast<T>();
   }
@@ -458,10 +475,10 @@ struct Relu6GradFunctor : public BaseActivationFunctor<T> {
 // Then: softplus(x) = max(x, 0) + log(exp(-max(x, 0)) + exp(x - max(x, 0)))
 template <typename T>
 struct SoftplusFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) {
     auto temp = x.cwiseMax(static_cast<T>(0));  // temp = max(x, 0)
-    y.device(d) = temp + (((-temp).exp() + (x - temp).exp()).log());
+    out.device(d) = temp + (((-temp).exp() + (x - temp).exp()).log());
   }
 };
 
@@ -471,19 +488,21 @@ struct SoftplusFunctor : public BaseActivationFunctor<T> {
 // exp(x - max(x, 0)))
 template <typename T>
 struct SoftplusGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) {
     auto temp = x.cwiseMax(static_cast<T>(0));  // temp = max(x, 0)
-    dx.device(d) = dy * ((x - temp).exp() / ((-temp).exp() + (x - temp).exp()));
+    dx.device(d) =
+        dout * ((x - temp).exp() / ((-temp).exp() + (x - temp).exp()));
   }
 };
 
 // softsign(x) = x / (1 + |x|)
 template <typename T>
 struct SoftsignFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) {
-    y.device(d) = x / (static_cast<T>(1) + x.abs());
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) {
+    out.device(d) = x / (static_cast<T>(1) + x.abs());
   }
 };
 
@@ -491,10 +510,11 @@ struct SoftsignFunctor : public BaseActivationFunctor<T> {
 // Taken from https://en.wikipedia.org/wiki/Activation_function
 template <typename T>
 struct SoftsignGradFunctor : public BaseActivationFunctor<T> {
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) {
     dx.device(d) =
-        dy * (static_cast<T>(1) / (static_cast<T>(1) + x.abs()).square());
+        dout * (static_cast<T>(1) / (static_cast<T>(1) + x.abs()).square());
   }
 };
 
@@ -505,11 +525,11 @@ struct SoftReluFunctor : public BaseActivationFunctor<T> {
     return {{"threshold", &threshold}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto tmp = static_cast<T>(threshold);
     auto temp = x.cwiseMax(-tmp).cwiseMin(tmp);
-    y.device(d) = (static_cast<T>(1) + temp.exp()).log();
+    out.device(d) = (static_cast<T>(1) + temp.exp()).log();
   }
 };
 
@@ -519,11 +539,12 @@ struct SoftReluGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"threshold", &threshold}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto tmp = static_cast<T>(threshold);
     auto temp = ((x > -tmp) * (x < tmp)).template cast<T>().eval();
-    dx.device(d) = dy * (static_cast<T>(1) - (-y).exp()) * temp;
+    dx.device(d) = dout * (static_cast<T>(1) - (-out).exp()) * temp;
   }
 };
 
@@ -534,9 +555,9 @@ struct LeakyReluFunctor : public BaseActivationFunctor<T> {
     return {{"alpha", &alpha}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.cwiseMax(static_cast<T>(alpha) * x);
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.cwiseMax(static_cast<T>(alpha) * x);
   }
 };
 
@@ -546,12 +567,13 @@ struct LeakyReluGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"alpha", &alpha}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto temp1 = static_cast<T>(alpha) *
                  (x < static_cast<T>(0)).template cast<T>().eval();
     auto temp2 = (x >= static_cast<T>(0)).template cast<T>().eval();
-    dx.device(d) = dy * (temp1 + temp2).template cast<T>();
+    dx.device(d) = dout * (temp1 + temp2).template cast<T>();
   }
 };
 
@@ -562,11 +584,11 @@ struct ELUFunctor : public BaseActivationFunctor<T> {
     return {{"alpha", &alpha}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.cwiseMax(static_cast<T>(0)) +
-                  (static_cast<T>(alpha) * (x.exp() - static_cast<T>(1)))
-                      .cwiseMin(static_cast<T>(0));
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.cwiseMax(static_cast<T>(0)) +
+                    (static_cast<T>(alpha) * (x.exp() - static_cast<T>(1)))
+                        .cwiseMin(static_cast<T>(0));
   }
 };
 
@@ -576,10 +598,11 @@ struct ELUGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"alpha", &alpha}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * (x > static_cast<T>(0)).template cast<T>() +
-                   dy * (y + static_cast<T>(alpha)) *
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * (x > static_cast<T>(0)).template cast<T>() +
+                   dout * (out + static_cast<T>(alpha)) *
                        (x < static_cast<T>(0)).template cast<T>();
   }
 };
@@ -591,9 +614,9 @@ struct PowFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"factor", &factor}};
   }
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x.pow(static_cast<T>(factor));
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x.pow(static_cast<T>(factor));
   }
 };
 
@@ -603,9 +626,10 @@ struct PowGradFunctor : public BaseActivationFunctor<T> {
   typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
     return {{"factor", &factor}};
   }
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) = dy * static_cast<T>(factor) *
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout * static_cast<T>(factor) *
                    x.pow(static_cast<T>(factor - static_cast<T>(1)));
   }
 };
@@ -618,9 +642,9 @@ struct STanhFunctor : public BaseActivationFunctor<T> {
     return {{"scale_a", &scale_a}, {"scale_b", &scale_b}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) =
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) =
         static_cast<T>(scale_b) * (static_cast<T>(scale_a) * x).tanh();
   }
 };
@@ -633,12 +657,13 @@ struct STanhGradFunctor : public BaseActivationFunctor<T> {
     return {{"scale_a", &scale_a}, {"scale_b", &scale_b}};
   }
 
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto a = static_cast<T>(scale_a);
     auto b = static_cast<T>(scale_b);
     auto temp = (a * x).tanh() * (a * x).tanh();
-    dx.device(d) = dy * a * b * (static_cast<T>(1) - temp);
+    dx.device(d) = dout * a * b * (static_cast<T>(1) - temp);
   }
 };
 
@@ -649,10 +674,10 @@ struct ThresholdedReluFunctor : public BaseActivationFunctor<T> {
     return {{"threshold", &threshold}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto th = static_cast<T>(threshold);
-    y.device(d) = (x > th).template cast<T>() * x;
+    out.device(d) = (x > th).template cast<T>() * x;
   }
 };
 
@@ -663,10 +688,11 @@ struct ThresholdedReluGradFunctor : public BaseActivationFunctor<T> {
     return {{"threshold", &threshold}};
   }
 
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto th = static_cast<T>(threshold);
-    dx.device(d) = dy * (x > th).template cast<T>();
+    dx.device(d) = dout * (x > th).template cast<T>();
   }
 };
 
@@ -678,10 +704,11 @@ struct HardSigmoidFunctor : public BaseActivationFunctor<T> {
     return {{"slope", &slope}, {"offset", &offset}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
     auto temp = x * static_cast<T>(slope) + static_cast<T>(offset);
-    y.device(d) = temp.cwiseMax(static_cast<T>(0)).cwiseMin(static_cast<T>(1));
+    out.device(d) =
+        temp.cwiseMax(static_cast<T>(0)).cwiseMin(static_cast<T>(1));
   }
 };
 
@@ -693,12 +720,13 @@ struct HardSigmoidGradFunctor : public BaseActivationFunctor<T> {
     return {{"slope", &slope}, {"offset", &offset}};
   }
 
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
-    dx.device(d) =
-        dy *
-        ((y > static_cast<T>(0)) * (y < static_cast<T>(1))).template cast<T>() *
-        static_cast<T>(slope);
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+    dx.device(d) = dout *
+                   ((out > static_cast<T>(0)) * (out < static_cast<T>(1)))
+                       .template cast<T>() *
+                   static_cast<T>(slope);
   }
 };
 
@@ -709,9 +737,9 @@ struct SwishFunctor : public BaseActivationFunctor<T> {
     return {{"beta", &beta}};
   }
 
-  template <typename Device, typename X, typename Y>
-  void operator()(Device d, X x, Y y) const {
-    y.device(d) = x / (static_cast<T>(1) + (static_cast<T>(-beta) * x).exp());
+  template <typename Device, typename X, typename Out>
+  void operator()(Device d, X x, Out out) const {
+    out.device(d) = x / (static_cast<T>(1) + (static_cast<T>(-beta) * x).exp());
   }
 };
 
@@ -722,12 +750,13 @@ struct SwishGradFunctor : public BaseActivationFunctor<T> {
     return {{"beta", &beta}};
   }
 
-  template <typename Device, typename X, typename Y, typename dY, typename dX>
-  void operator()(Device d, X x, Y y, dY dy, dX dx) const {
+  template <typename Device, typename X, typename Out, typename dOut,
+            typename dX>
+  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
     auto temp1 = static_cast<T>(1) /
                  (static_cast<T>(1) + (static_cast<T>(-beta) * x).exp());
-    auto temp2 = temp1 * (static_cast<T>(1) - (beta * y));
-    dx.device(d) = dy * ((beta * y) + temp2);
+    auto temp2 = temp1 * (static_cast<T>(1) - (beta * out));
+    dx.device(d) = dout * ((beta * out) + temp2);
   }
 };
 
diff --git a/paddle/operators/softmax_op.cc b/paddle/operators/softmax_op.cc
index 6b3f19bb46c45b7dd8ec6c23ee449521b36d759c..e7306bc5f13377813e0bd49846bc834d501602eb 100644
--- a/paddle/operators/softmax_op.cc
+++ b/paddle/operators/softmax_op.cc
@@ -24,13 +24,13 @@ class SoftmaxOp : public framework::OperatorWithKernel {
   void InferShape(framework::InferShapeContext* ctx) const override {
     PADDLE_ENFORCE(ctx->HasInput("X"),
                    "Input(X) of SoftmaxOp should not be null.");
-    PADDLE_ENFORCE(ctx->HasOutput("Y"),
-                   "Output(Y) of SoftmaxOp should not be null.");
+    PADDLE_ENFORCE(ctx->HasOutput("Out"),
+                   "Output(Out) of SoftmaxOp should not be null.");
 
     auto x_dims = ctx->GetInputDim("X");
     PADDLE_ENFORCE(x_dims.size() == 2UL,
                    "The input of softmax op must be a matrix.");
-    ctx->SetOutputDim("Y", x_dims);
+    ctx->SetOutputDim("Out", x_dims);
   }
 };
 
@@ -41,7 +41,7 @@ class SoftmaxOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X",
              "The input tensor of softmax. "
              "2-D with shape [batch_size, input_feature_dimensions].");
-    AddOutput("Y", "The normalized values with the same shape as X.");
+    AddOutput("Out", "The normalized values with the same shape as X.");
     AddComment(R"DOC(
 Softmax Operator.
 
@@ -59,7 +59,7 @@ exponential values of all the other dimensions is the output of the softmax
 operator.
 
 For each row $i$ and each column $j$ in Input(X), we have:
-    $$Y[i, j] = \frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])}$$
+    $$Out[i, j] = \frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])}$$
 
 )DOC");
   }
@@ -70,12 +70,12 @@ class SoftmaxOpGrad : public framework::OperatorWithKernel {
   using framework::OperatorWithKernel::OperatorWithKernel;
 
   void InferShape(framework::InferShapeContext* ctx) const override {
-    PADDLE_ENFORCE(ctx->HasInput("Y"), "Input(Y) should be not null.");
-    PADDLE_ENFORCE(ctx->HasInput(framework::GradVarName("Y")),
-                   "Input(Y@GRAD) should be not null.");
-    PADDLE_ENFORCE_EQ(ctx->GetInputDim("Y"),
-                      ctx->GetInputDim(framework::GradVarName("Y")),
-                      "Input(Y) and its gradients should have a same shape.");
+    PADDLE_ENFORCE(ctx->HasInput("Out"), "Input(Out) should be not null.");
+    PADDLE_ENFORCE(ctx->HasInput(framework::GradVarName("Out")),
+                   "Input(Out@GRAD) should be not null.");
+    PADDLE_ENFORCE_EQ(ctx->GetInputDim("Out"),
+                      ctx->GetInputDim(framework::GradVarName("Out")),
+                      "Input(Out) and its gradients should have a same shape.");
 
     ctx->SetOutputDim(framework::GradVarName("X"), ctx->GetInputDim("X"));
   }
diff --git a/paddle/operators/softmax_op.h b/paddle/operators/softmax_op.h
index 0f8998b99e93b5ed6c9b43ad7adabc2d515c1ff1..63e379a3b31a6c75aab0c56b4ce1b988fa7f0318 100644
--- a/paddle/operators/softmax_op.h
+++ b/paddle/operators/softmax_op.h
@@ -26,13 +26,13 @@ class SoftmaxKernel : public framework::OpKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& context) const override {
     auto* X = context.Input<Tensor>("X");
-    auto* Y = context.Output<Tensor>("Y");
+    auto* Out = context.Output<Tensor>("Out");
 
     // allocate memory on device.
-    Y->mutable_data<T>(context.GetPlace());
+    Out->mutable_data<T>(context.GetPlace());
 
     math::SoftmaxFunctor<DeviceContext, T>()(
-        context.template device_context<DeviceContext>(), X, Y);
+        context.template device_context<DeviceContext>(), X, Out);
   }
 };
 
@@ -40,15 +40,15 @@ template <typename DeviceContext, typename T>
 class SoftmaxGradKernel : public framework::OpKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& context) const override {
-    auto* Y = context.Input<Tensor>("Y");
-    auto* dY = context.Input<Tensor>(framework::GradVarName("Y"));
+    auto* Out = context.Input<Tensor>("Out");
+    auto* dOut = context.Input<Tensor>(framework::GradVarName("Out"));
     auto* dX = context.Output<Tensor>(framework::GradVarName("X"));
 
     // allocate memory on device.
     dX->mutable_data<T>(context.GetPlace());
 
     math::SoftmaxGradFunctor<DeviceContext, T>()(
-        context.template device_context<DeviceContext>(), Y, dY, dX);
+        context.template device_context<DeviceContext>(), Out, dOut, dX);
   }
 };
 
diff --git a/python/paddle/v2/fluid/layer_helper.py b/python/paddle/v2/fluid/layer_helper.py
index a076f26f7ff279812f762bd62f72195dc2376378..4469f7285efe1c31d0955c6dd4ba3ecac08070af 100644
--- a/python/paddle/v2/fluid/layer_helper.py
+++ b/python/paddle/v2/fluid/layer_helper.py
@@ -184,7 +184,7 @@ class LayerHelper(object):
         self.append_op(
             type=act_type,
             inputs={"X": [input_var]},
-            outputs={"Y": [tmp]},
+            outputs={"Out": [tmp]},
             attrs=act)
         return tmp
 
diff --git a/python/paddle/v2/fluid/layers/nn.py b/python/paddle/v2/fluid/layers/nn.py
index ee9d7554fb1f0cc3b9229f046f8bcdd4dbd7c35d..2a462ee6cb47496b17a8f584e56ac2c8934b319a 100644
--- a/python/paddle/v2/fluid/layers/nn.py
+++ b/python/paddle/v2/fluid/layers/nn.py
@@ -386,7 +386,8 @@ def square_error_cost(input, label, **kwargs):
 
     square_out = helper.create_tmp_variable(dtype=input.dtype)
     helper.append_op(
-        type='square', inputs={'X': [minus_out]}, outputs={'Y': [square_out]})
+        type='square', inputs={'X': [minus_out]},
+        outputs={'Out': [square_out]})
     return square_out
 
 
@@ -604,7 +605,7 @@ def sequence_pool(input, pool_type, **kwargs):
          sqrt   : out.data = [2.82, 6.93, 4.24], where 2.82=(1+3)/sqrt(2),
                     6.93=(2+4+6)/sqrt(3), 4.24=(5+1)/sqrt(2)
          max    : out.data = [3, 6, 5], where 3=max(1,3), 6=max(2,4,6), 5=max(5,1)
-         
+
     Args:
         input(variable): The input variable which is a LoDTensor.
         pool_type (string): The pooling type of sequence_pool. 
@@ -616,7 +617,7 @@ def sequence_pool(input, pool_type, **kwargs):
     Examples:
 
         .. code-block:: python
-             
+
              x = fluid.layers.data(name='x', shape=[7, 1], 
                               dtype='float32', lod_level=1)
              avg_x = fluid.layers.sequence_pool(input=x, pool_type='average')
@@ -654,7 +655,7 @@ def sequence_first_step(input, **kwargs):
          out.dim = [3, 1]
          with condition len(x.lod[-1]) - 1 == out.dims[0]
          out.data = [1, 2, 5], where 1=first(1,3), 2=first(2,4,6), 5=first(5,1)
-         
+
     Args:
         input(variable): The input variable which is a LoDTensor.
 
@@ -664,7 +665,7 @@ def sequence_first_step(input, **kwargs):
     Examples:
 
         .. code-block:: python
-             
+
              x = fluid.layers.data(name='x', shape=[7, 1], 
                               dtype='float32', lod_level=1)
              x_first_step = fluid.layers.sequence_first_step(input=x)
@@ -687,7 +688,7 @@ def sequence_last_step(input, **kwargs):
          out.dim = [3, 1]
          with condition len(x.lod[-1]) - 1 == out.dims[0]
          out.data = [3, 6, 1], where 3=last(1,3), 6=last(2,4,6), 1=last(5,1)
-         
+
     Args:
         input(variable): The input variable which is a LoDTensor.
 
@@ -697,7 +698,7 @@ def sequence_last_step(input, **kwargs):
     Examples:
 
         .. code-block:: python
-             
+
              x = fluid.layers.data(name='x', shape=[7, 1], 
                               dtype='float32', lod_level=1)
              x_last_step = fluid.layers.sequence_last_step(input=x)
@@ -1132,7 +1133,7 @@ def reduce_sum(input, dim=None, keep_dim=False):
 
     Returns:
         Variable: The reduced Tensor variable.
-    
+
     Examples:
         .. code-block:: python
 
@@ -1176,7 +1177,7 @@ def reduce_mean(input, dim=None, keep_dim=False):
 
     Returns:
         Variable: The reduced Tensor variable.
-    
+
     Examples:
         .. code-block:: python
 
diff --git a/python/paddle/v2/fluid/tests/test_activation_op.py b/python/paddle/v2/fluid/tests/test_activation_op.py
index b052374dc7ec3c5684d6adfda6b9d000c5e19fe0..03eb7deb9a35933e5a1676a262a371c69151e6d1 100644
--- a/python/paddle/v2/fluid/tests/test_activation_op.py
+++ b/python/paddle/v2/fluid/tests/test_activation_op.py
@@ -10,13 +10,13 @@ class TestExp(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.exp(self.inputs['X'])}
+        self.outputs = {'Out': np.exp(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestSigmoid(OpTest):
@@ -25,13 +25,13 @@ class TestSigmoid(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': 1 / (1 + np.exp(-self.inputs['X']))}
+        self.outputs = {'Out': 1 / (1 + np.exp(-self.inputs['X']))}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.008)
+        self.check_grad(['X'], 'Out', max_relative_error=0.008)
 
 
 class TestLogSigmoid(OpTest):
@@ -40,13 +40,13 @@ class TestLogSigmoid(OpTest):
         self.inputs = {
             'X': np.random.uniform(-1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.log(1 / (1 + np.exp(-self.inputs['X'])))}
+        self.outputs = {'Out': np.log(1 / (1 + np.exp(-self.inputs['X'])))}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.008)
+        self.check_grad(['X'], 'Out', max_relative_error=0.008)
 
 
 class TestTanh(OpTest):
@@ -55,13 +55,13 @@ class TestTanh(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.tanh(self.inputs['X'])}
+        self.outputs = {'Out': np.tanh(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestTanhShrink(OpTest):
@@ -70,13 +70,13 @@ class TestTanhShrink(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [10, 17]).astype("float32")
         }
-        self.outputs = {'Y': self.inputs['X'] - np.tanh(self.inputs['X'])}
+        self.outputs = {'Out': self.inputs['X'] - np.tanh(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.008)
+        self.check_grad(['X'], 'Out', max_relative_error=0.008)
 
 
 class TestHardShrink(OpTest):
@@ -90,13 +90,13 @@ class TestHardShrink(OpTest):
 
         t = np.copy(x)
         t[(t >= -threshold) & (t <= threshold)] = 0
-        self.outputs = {'Y': t}
+        self.outputs = {'Out': t}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.005)
+        self.check_grad(['X'], 'Out', max_relative_error=0.005)
 
 
 class TestSoftShrink(OpTest):
@@ -110,13 +110,13 @@ class TestSoftShrink(OpTest):
         y = np.copy(self.inputs['X'])
         y = (y < -lambda_val) * (y + lambda_val) + (y > lambda_val) * (
             y - lambda_val)
-        self.outputs = {'Y': y}
+        self.outputs = {'Out': y}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestSqrt(OpTest):
@@ -125,13 +125,13 @@ class TestSqrt(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.sqrt(self.inputs['X'])}
+        self.outputs = {'Out': np.sqrt(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestAbs(OpTest):
@@ -144,13 +144,13 @@ class TestAbs(OpTest):
         # we should avoid this
         x[np.abs(x) < 0.005] = 0.02
         self.inputs = {'X': x}
-        self.outputs = {'Y': np.abs(self.inputs['X'])}
+        self.outputs = {'Out': np.abs(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestCeil(OpTest):
@@ -158,13 +158,13 @@ class TestCeil(OpTest):
         self.op_type = "ceil"
         x = np.random.uniform(-1, 1, [4, 4]).astype("float32")
         self.inputs = {'X': x}
-        self.outputs = {'Y': np.ceil(self.inputs['X'])}
+        self.outputs = {'Out': np.ceil(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestFloor(OpTest):
@@ -173,13 +173,13 @@ class TestFloor(OpTest):
         x = np.random.uniform(-1, 1, [4, 4]).astype("float32")
         self.inputs = {'X': x}
         # numpy floor need +1
-        self.outputs = {'Y': np.floor(self.inputs['X']) + 1.0}
+        self.outputs = {'Out': np.floor(self.inputs['X']) + 1.0}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestRound(OpTest):
@@ -187,13 +187,13 @@ class TestRound(OpTest):
         self.op_type = "round"
         x = np.random.uniform(-1, 1, [4, 4]).astype("float32")
         self.inputs = {'X': x}
-        self.outputs = {'Y': np.round(self.inputs['X'])}
+        self.outputs = {'Out': np.round(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestRelu(OpTest):
@@ -203,13 +203,13 @@ class TestRelu(OpTest):
         # The same reason with TestAbs
         x[np.abs(x) < 0.005] = 0.02
         self.inputs = {'X': x}
-        self.outputs = {'Y': np.maximum(self.inputs['X'], 0)}
+        self.outputs = {'Out': np.maximum(self.inputs['X'], 0)}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestBRelu(OpTest):
@@ -227,13 +227,13 @@ class TestBRelu(OpTest):
         t = np.copy(x)
         t[t < t_min] = t_min
         t[t > t_max] = t_max
-        self.outputs = {'Y': t}
+        self.outputs = {'Out': t}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.02)
+        self.check_grad(['X'], 'Out', max_relative_error=0.02)
 
 
 class TestRelu6(OpTest):
@@ -248,14 +248,14 @@ class TestRelu6(OpTest):
         self.inputs = {'X': x}
         self.attrs = {'threshold': threshold}
         self.outputs = {
-            'Y': np.minimum(np.maximum(self.inputs['X'], 0), threshold)
+            'Out': np.minimum(np.maximum(self.inputs['X'], 0), threshold)
         }
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.02)
+        self.check_grad(['X'], 'Out', max_relative_error=0.02)
 
 
 class TestSoftRelu(OpTest):
@@ -271,13 +271,13 @@ class TestSoftRelu(OpTest):
         t = np.copy(x)
         t[t < -threshold] = -threshold
         t[t > threshold] = threshold
-        self.outputs = {'Y': np.log((np.exp(t) + 1))}
+        self.outputs = {'Out': np.log((np.exp(t) + 1))}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.02)
+        self.check_grad(['X'], 'Out', max_relative_error=0.02)
 
 
 class TestELU(OpTest):
@@ -290,27 +290,27 @@ class TestELU(OpTest):
         self.inputs = {'X': x}
         self.attrs = {'alpha': alpha}
         self.outputs = {
-            'Y': np.maximum(0, x) + np.minimum(0, alpha * (np.exp(x) - 1))
+            'Out': np.maximum(0, x) + np.minimum(0, alpha * (np.exp(x) - 1))
         }
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.02)
+        self.check_grad(['X'], 'Out', max_relative_error=0.02)
 
 
 class TestReciprocal(OpTest):
     def setUp(self):
         self.op_type = "reciprocal"
         self.inputs = {'X': np.random.uniform(1, 2, [11, 17]).astype("float32")}
-        self.outputs = {'Y': np.reciprocal(self.inputs['X'])}
+        self.outputs = {'Out': np.reciprocal(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.01)
+        self.check_grad(['X'], 'Out', max_relative_error=0.01)
 
 
 class TestLog(OpTest):
@@ -319,13 +319,13 @@ class TestLog(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.log(self.inputs['X'])}
+        self.outputs = {'Out': np.log(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestSquare(OpTest):
@@ -334,13 +334,13 @@ class TestSquare(OpTest):
         self.inputs = {
             'X': np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         }
-        self.outputs = {'Y': np.square(self.inputs['X'])}
+        self.outputs = {'Out': np.square(self.inputs['X'])}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestPow(OpTest):
@@ -348,13 +348,13 @@ class TestPow(OpTest):
         self.op_type = "pow"
         self.inputs = {'X': np.random.uniform(1, 2, [11, 17]).astype("float32")}
         self.attrs = {'factor': 3.0}
-        self.outputs = {'Y': np.power(self.inputs['X'], 3)}
+        self.outputs = {'Out': np.power(self.inputs['X'], 3)}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.02)
+        self.check_grad(['X'], 'Out', max_relative_error=0.02)
 
 
 class TestSTanh(OpTest):
@@ -366,13 +366,13 @@ class TestSTanh(OpTest):
         scale_a = 2.0 / 3.0
         scale_b = 1.7159
         self.attrs = {'scale_a': scale_a, 'scale_b': scale_b}
-        self.outputs = {'Y': scale_b * np.tanh(self.inputs['X'] * scale_a)}
+        self.outputs = {'Out': scale_b * np.tanh(self.inputs['X'] * scale_a)}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestSoftplus(OpTest):
@@ -381,13 +381,13 @@ class TestSoftplus(OpTest):
         self.inputs = {
             'X': np.random.uniform(-1, 1, [11, 17]).astype("float64")
         }
-        self.outputs = {'Y': np.log(1 + np.exp(self.inputs['X']))}
+        self.outputs = {'Out': np.log(1 + np.exp(self.inputs['X']))}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestSoftsign(OpTest):
@@ -397,14 +397,14 @@ class TestSoftsign(OpTest):
             'X': np.random.uniform(-1, 1, [11, 17]).astype("float32")
         }
         self.outputs = {
-            'Y': np.divide(self.inputs['X'], 1 + np.abs(self.inputs['X']))
+            'Out': np.divide(self.inputs['X'], 1 + np.abs(self.inputs['X']))
         }
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.007)
+        self.check_grad(['X'], 'Out', max_relative_error=0.007)
 
 
 class TestThresholdedRelu(OpTest):
@@ -419,13 +419,13 @@ class TestThresholdedRelu(OpTest):
 
         self.inputs = {'X': X}
         self.attrs = {'threshold': threshold}
-        self.outputs = {'Y': (X > threshold) * X}
+        self.outputs = {'Out': (X > threshold) * X}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=self.relative_error)
+        self.check_grad(['X'], 'Out', max_relative_error=self.relative_error)
 
 
 class TestHardSigmoid(OpTest):
@@ -447,13 +447,13 @@ class TestHardSigmoid(OpTest):
             upper_threshold - 0.2
 
         temp = X * slope + offset
-        self.outputs = {'Y': np.maximum(0.0, np.minimum(1.0, temp))}
+        self.outputs = {'Out': np.maximum(0.0, np.minimum(1.0, temp))}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.002)
+        self.check_grad(['X'], 'Out', max_relative_error=0.002)
 
 
 class TestSwish(OpTest):
@@ -462,13 +462,13 @@ class TestSwish(OpTest):
         X = np.random.uniform(0.1, 1, [11, 17]).astype("float32")
         self.inputs = {'X': X}
         self.attrs = {'beta': 2.3}
-        self.outputs = {'Y': X * expit(self.attrs['beta'] * X)}
+        self.outputs = {'Out': X * expit(self.attrs['beta'] * X)}
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y', max_relative_error=0.008)
+        self.check_grad(['X'], 'Out', max_relative_error=0.008)
 
 
 if __name__ == "__main__":
diff --git a/python/paddle/v2/fluid/tests/test_net.py b/python/paddle/v2/fluid/tests/test_net.py
index 318df08a9e73ac95cab73c34182bc6220ef6c681..d9fe55a8af5c750c5c926e875ddbb645f8abb1a0 100644
--- a/python/paddle/v2/fluid/tests/test_net.py
+++ b/python/paddle/v2/fluid/tests/test_net.py
@@ -7,7 +7,7 @@ def fc(X, W, Y):
     ret_v = core.Net.create()
 
     ret_v.append_op(Operator("mul", X="X", Y="W", Out="pre_activation"))
-    ret_v.append_op(Operator("sigmoid", X="pre_activation", Y=Y))
+    ret_v.append_op(Operator("sigmoid", X="pre_activation", Out=Y))
     ret_v.complete_add_op(True)
     return ret_v
 
@@ -30,7 +30,7 @@ Op(plain_net), inputs:{all[W, X, Y]}, outputs:{all[Out, fc.out, pre_activation]}
     Op(plain_net), inputs:{all[W, X]}, outputs:{all[fc.out, pre_activation]}.
         Op(plain_net), inputs:{all[W, X]}, outputs:{all[fc.out, pre_activation]}.
             Op(mul), inputs:{X[X], Y[W]}, outputs:{Out[pre_activation]}.
-            Op(sigmoid), inputs:{X[pre_activation]}, outputs:{Y[fc.out]}.
+            Op(sigmoid), inputs:{X[pre_activation]}, outputs:{Out[fc.out]}.
 '''
         self.assertEqual(expected, "\n" + str(net))
 
diff --git a/python/paddle/v2/fluid/tests/test_softmax_op.py b/python/paddle/v2/fluid/tests/test_softmax_op.py
index b41c810d9a6269c934a434b085748a86deccb475..136fc0283afd6acf1de4baae5e681789662295ce 100644
--- a/python/paddle/v2/fluid/tests/test_softmax_op.py
+++ b/python/paddle/v2/fluid/tests/test_softmax_op.py
@@ -17,14 +17,14 @@ class TestSoftmaxOp(OpTest):
             'X': np.random.uniform(0.1, 1, [10, 10]).astype("float32")
         }
         self.outputs = {
-            'Y': np.apply_along_axis(stable_softmax, 1, self.inputs['X'])
+            'Out': np.apply_along_axis(stable_softmax, 1, self.inputs['X'])
         }
 
     def test_check_output(self):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Y')
+        self.check_grad(['X'], 'Out')
 
 
 if __name__ == "__main__":