diff --git a/paddle/operators/activation_op.cc b/paddle/operators/activation_op.cc
index 90f1535fcd387c34ea39d84d9c2ec78fcbc3c764..483f9888973edc9db6317723c136778d40cc7878 100644
--- a/paddle/operators/activation_op.cc
+++ b/paddle/operators/activation_op.cc
@@ -43,7 +43,12 @@ class SigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Sigmoid operator");
     AddOutput("Y", "Output of Sigmoid operator");
-    AddComment("Sigmoid activation operator, sigmoid = 1 / (1 + exp(-x))");
+    AddComment(R"DOC(
+Sigmoid activation operator.
+
+$y = 1 / (1 + e^{-x})$
+
+)DOC");
   }
 };
 
@@ -54,8 +59,12 @@ class LogSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of LogSigmoid operator");
     AddOutput("Y", "Output of LogSigmoid operator");
-    AddComment(
-        "Logsigmoid activation operator, logsigmoid = log (1 / (1 + exp(-x)))");
+    AddComment(R"DOC(
+Logsigmoid activation operator.
+
+$y = \log(1 / (1 + e^{-x}))$
+
+)DOC");
   }
 };
 
@@ -65,7 +74,12 @@ class ExpOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Exp operator");
     AddOutput("Y", "Output of Exp operator");
-    AddComment("Exp activation operator, exp(x) = e^x");
+    AddComment(R"DOC(
+Exp activation operator.
+
+$y = e^x$
+
+)DOC");
   }
 };
 
@@ -75,7 +89,12 @@ class ReluOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Relu operator");
     AddOutput("Y", "Output of Relu operator");
-    AddComment("Relu activation operator, relu(x) = max(x, 0)");
+    AddComment(R"DOC(
+Relu activation operator.
+
+$y = \max(x, 0)$
+
+)DOC");
   }
 };
 
@@ -87,11 +106,14 @@ class LeakyReluOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of LeakyRelu operator");
     AddOutput("Y", "Output of LeakyRelu operator");
-    AddComment(
-        "LeakyRelu activation operator, "
-        "leaky_relu = max(x, alpha * x)");
     AddAttr<AttrType>("alpha", "The small negative slope")
         .SetDefault(static_cast<AttrType>(0.02f));
+    AddComment(R"DOC(
+LeakyRelu activation operator.
+
+$y = \max(x, \alpha * x)$
+
+)DOC");
   }
 };
 
@@ -103,12 +125,20 @@ class SoftShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softshrink operator");
     AddOutput("Y", "Output of Softshrink operator");
-    AddComment(
-        "Softshrink activation operator, "
-        "softshrink = x - lambda, if x > lambda;"
-        " x + lambda, if x < lambda; 0 otherwise");
     AddAttr<AttrType>("lambda", "non-negative offset")
         .SetDefault(static_cast<AttrType>(0.5f));
+    AddComment(R"DOC(
+Softshrink activation operator.
+
+$$
+y = \begin{cases} 
+    x - \lambda, \text{if } x > \lambda \\
+    x + \lambda, \text{if } x < -\lambda \\
+    0,  \text{otherwise}
+    \end{cases}
+$$
+
+)DOC");
   }
 };
 
@@ -118,9 +148,12 @@ class TanhOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Tanh operator");
     AddOutput("Y", "Output of Tanh operator");
-    AddComment(
-        "Tanh activation operator, tanh = (exp(x) - exp(-x)) / (exp(x) + "
-        "exp(-x))");
+    AddComment(R"DOC(
+Tanh activation operator.
+
+$$y = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
+
+)DOC");
   }
 };
 
@@ -131,7 +164,12 @@ class TanhShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of TanhShrink operator");
     AddOutput("Y", "Output of TanhShrink operator");
-    AddComment("TanhShrink activation operator, tanhshrink(x) = x - tanh(x)");
+    AddComment(R"DOC(
+TanhShrink activation operator.
+
+$$y = x - \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
+
+)DOC");
   }
 };
 
@@ -143,13 +181,20 @@ class HardShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of HardShrink operator");
     AddOutput("Y", "Output of HardShrink operator");
-    AddComment(
-        "HardShrink activation operator, "
-        "hard_shrink(x) = x if x > lambda"
-        "hard_shrink(x) = x if x < -lambda"
-        "hard_shrink(x) = 0 otherwise");
     AddAttr<AttrType>("threshold", "The value of threshold for HardShrink")
         .SetDefault(static_cast<AttrType>(0.5));
+    AddComment(R"DOC(
+HardShrink activation operator.
+
+$$
+y = \begin{cases} 
+    x, \text{if } x > \lambda \\
+    x, \text{if } x < -\lambda \\
+    0,  \text{otherwise}
+    \end{cases}
+$$
+
+)DOC");
   }
 };
 
@@ -159,7 +204,12 @@ class SqrtOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Sqrt operator");
     AddOutput("Y", "Output of Sqrt operator");
-    AddComment("Sqrt activation operator, sqrt(x) = x^(1/2)");
+    AddComment(R"DOC(
+Sqrt activation operator.
+
+$y = \sqrt{x}$
+
+)DOC");
   }
 };
 
@@ -169,7 +219,12 @@ class AbsOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Abs operator");
     AddOutput("Y", "Output of Abs operator");
-    AddComment("Abs activation operator, abs(x) = |x|");
+    AddComment(R"DOC(
+Abs activation operator.
+
+$y = |x|$
+
+)DOC");
   }
 };
 
@@ -180,7 +235,12 @@ class ReciprocalOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Reciprocal operator");
     AddOutput("Y", "Output of Reciprocal operator");
-    AddComment("Reciprocal activation operator, reciprocal(x) = 1 / x");
+    AddComment(R"DOC(
+Reciprocal activation operator.
+
+$$y = \frac{1}{x}$$
+
+)DOC");
   }
 };
 
@@ -190,7 +250,14 @@ class LogOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Log operator");
     AddOutput("Y", "Output of Log operator");
-    AddComment("Log activation operator, log(x) = natural logarithm of x");
+    AddComment(R"DOC(
+Log activation operator.
+
+$y = \ln(x)$
+
+Natural logarithm of x.
+
+)DOC");
   }
 };
 
@@ -200,7 +267,12 @@ class SquareOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Square operator");
     AddOutput("Y", "Output of Square operator");
-    AddComment("Square activation operator, square(x) = x^2");
+    AddComment(R"DOC(
+Square activation operator.
+
+$y = x^2$
+
+)DOC");
   }
 };
 
@@ -211,7 +283,12 @@ class SoftplusOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softplus operator");
     AddOutput("Y", "Output of Softplus operator");
-    AddComment("Softplus activation operator, softplus(x) = log(1 + exp(x))");
+    AddComment(R"DOC(
+Softplus activation operator.
+
+$y = \ln(1 + e^{x})$
+
+)DOC");
   }
 };
 
@@ -222,7 +299,12 @@ class SoftsignOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Softsign operator");
     AddOutput("Y", "Output of Softsign operator");
-    AddComment("Softsign activation operator, softsign(x) = x / (1 + |x|)");
+    AddComment(R"DOC(
+Softsign activation operator.
+
+$$y = \frac{x}{1 + |x|}$$
+
+)DOC");
   }
 };
 
@@ -233,11 +315,16 @@ class BReluOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of BRelu operator");
     AddOutput("Y", "Output of BRelu operator");
-    AddComment("BRelu activation operator, brelu = max(min(x, t_min), t_max)");
     AddAttr<AttrType>("t_min", "The min marginal value of BRelu")
         .SetDefault(static_cast<AttrType>(0));
     AddAttr<AttrType>("t_max", "The max marginal value of BRelu")
         .SetDefault(static_cast<AttrType>(24));
+    AddComment(R"DOC(
+BRelu activation operator.
+
+$y = \max(\min(x, t_{min}), t_{max})$
+
+)DOC");
   }
 };
 
@@ -249,11 +336,14 @@ class SoftReluOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of SoftRelu operator");
     AddOutput("Y", "Output of SoftRelu operator");
-    AddComment(
-        "SoftRelu activation operator, soft_relu = log(1 + exp(max(min(x, "
-        "threshold), threshold)))");
     AddAttr<AttrType>("threshold", "The threshold value of SoftRelu")
         .SetDefault(static_cast<AttrType>(40));
+    AddComment(R"DOC(
+SoftRelu activation operator.
+
+$y = \ln(1 + \exp(\max(\min(x, threshold), threshold))$
+
+)DOC");
   }
 };
 
@@ -262,19 +352,19 @@ class ELUOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   ELUOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X",
-             "(Tensor) The input of ELU operator, it shouldn't be empty. Input "
-             "is flattened and treated as a 1D array.");
-    AddOutput("Y",
-              "(Tensor) The output of ELU operator. It has the same shape as "
-              "the input.");
-    AddAttr<AttrType>(
-        "alpha", "(float, default 1.0) Alpha value in the elu formulation.")
-        .SetDefault(static_cast<AttrType>(1.));
+    AddInput("X", "Input of ELU operator");
+    AddOutput("Y", "Output of ELU operator");
+    AddAttr<AttrType>("alpha", "The alpha value of ELU")
+        .SetDefault(static_cast<AttrType>(1.0f));
     AddComment(R"DOC(
-        ELU activation operator. It applies this element-wise computation on
-        the input: f(x) = max(0, x) + min(0, alpha * (exp(x) - 1)).
-        Check .. _Link: https://arxiv.org/abs/1511.07289 for more details.)DOC");
+ELU activation operator.
+
+Applies the following element-wise computation on the input according to
+https://arxiv.org/abs/1511.07289.
+
+$y = \max(0, x) + \min(0, \alpha * (e^x - 1))$
+
+)DOC");
   }
 };
 
@@ -285,9 +375,14 @@ class Relu6OpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Relu6 operator");
     AddOutput("Y", "Output of Relu6 operator");
-    AddComment("Relu6 activation operator, relu6 = min(max(0, x), 6)");
     AddAttr<AttrType>("threshold", "The threshold value of Relu6")
         .SetDefault(static_cast<AttrType>(6));
+    AddComment(R"DOC(
+Relu6 activation operator.
+
+$y = \min(\max(0, x), 6)$
+
+)DOC");
   }
 };
 
@@ -298,9 +393,14 @@ class PowOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of Pow operator");
     AddOutput("Y", "Output of Pow operator");
-    AddComment("Pow activation operator, pow(x, factor) = x^factor");
     AddAttr<AttrType>("factor", "The exponential factor of Pow")
         .SetDefault(static_cast<AttrType>(1));
+    AddComment(R"DOC(
+Pow activation operator.
+
+$y = x^{factor}$
+
+)DOC");
   }
 };
 
@@ -311,11 +411,16 @@ class STanhOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of STanh operator");
     AddOutput("Y", "Output of STanh operator");
-    AddComment("STanh activation operator, stanh = b * tanh(a * x)");
     AddAttr<AttrType>("scale_a", "The scale parameter of a for the input")
         .SetDefault(static_cast<AttrType>(2 / 3));
     AddAttr<AttrType>("scale_b", "The scale parameter of b for the input")
         .SetDefault(static_cast<AttrType>(1.7159));
+    AddComment(R"DOC(
+STanh activation operator.
+
+$$y = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}}$$
+
+)DOC");
   }
 };
 
@@ -327,12 +432,19 @@ class ThresholdedReluOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of ThresholdedRelu operator");
     AddOutput("Y", "Output of ThresholdedRelu operator");
-    AddComment(
-        "ThresholdedRelu activation operator, "
-        "thresholded_relu = x for x > threshold, "
-        "thresholded_relu = 0 otherwise.");
     AddAttr<AttrType>("threshold", "The threshold location of activation")
         .SetDefault(static_cast<AttrType>(1.0));
+    AddComment(R"DOC(
+ThresholdedRelu activation operator.
+
+$$
+y = \begin{cases} 
+    x, \text{if } x > threshold \\
+    0,  \text{otherwise}
+    \end{cases}
+$$
+
+)DOC");
   }
 };
 
@@ -344,27 +456,23 @@ class HardSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "Input of HardSigmoid operator");
     AddOutput("Y", "Output of HardSigmoid operator");
+    AddAttr<AttrType>("slope", "Slope for linear approximation of sigmoid")
+        .SetDefault(static_cast<AttrType>(0.2));
+    AddAttr<AttrType>("offset", "Offset for linear approximation of sigmoid")
+        .SetDefault(static_cast<AttrType>(0.5));
     AddComment(R"DOC(
-Hard Sigmoid activation operator.
+HardSigmoid activation operator.
 
-Segment-wise linear approximation of sigmoid[1].
-This is much faster than sigmoid.
+Segment-wise linear approximation of sigmoid(https://arxiv.org/abs/1603.00391), 
+which is much faster than sigmoid.
 
-hard_sigmoid = max(0, min(1, slope * x + shift))
+$y = \max(0, \min(1, slope * x + shift))$
 
 The slope should be positive. The offset can be either positive or negative.
-The default slope and shift are set from [1].
+The default slope and shift are set according to the above reference.
 It is recommended to use the defaults for this activation.
 
-References:
-  [1] Noisy Activation Functions
-      (https://arxiv.org/abs/1603.00391)
-
-    )DOC");
-    AddAttr<AttrType>("slope", "Slope for linear approximation of sigmoid")
-        .SetDefault(static_cast<AttrType>(0.2));
-    AddAttr<AttrType>("offset", "Offset for linear approximation of sigmoid")
-        .SetDefault(static_cast<AttrType>(0.5));
+)DOC");
   }
 };
 
diff --git a/paddle/operators/activation_op.h b/paddle/operators/activation_op.h
index ddd966e26c9abad0d83f8b5c6e3e7d9ad65158a8..ceb4b4e40b67473f42e67e3f02f8e012e1b1eb50 100644
--- a/paddle/operators/activation_op.h
+++ b/paddle/operators/activation_op.h
@@ -232,7 +232,7 @@ struct HardShrinkGradFunctor : public BaseActivationFunctor<T> {
   }
 };
 
-// softshrink(x) = x - lambda, if x > lambda; x + lambda, if x < lambda; 0
+// softshrink(x) = x - lambda, if x > lambda; x + lambda, if x < -lambda; 0
 // otherwise
 template <typename T>
 struct SoftShrinkFunctor : public BaseActivationFunctor<T> {