fix some doc bug test=document_fix (#45488)

* fix some doc bug test=document_fix

* fix some docs issues, test=document_fix

* beta -> \beta in softplus

* threshold -> \varepsilon in softplus

* parameter name

* delta -> \delta in smooth_l1_loss

* fix some docs test=document_fix

* fix docs test=document_fix

* fix docs && 增加空行 test=document_fix

* Update python/paddle/nn/functional/activation.py, test=document_fix

* Update python/paddle/nn/layer/activation.py, test=document_fix
Co-authored-by: NSigureMo <sigure.qaq@gmail.com>

paddle/fluid/operators/activation_op.cc

@@ -170,9 +170,9 @@ class ActivationOpGrad : public framework::OperatorWithKernel {
 };
 
 UNUSED constexpr char SigmoidDoc[] = R"DOC(
-Sigmoid Activation Operator
+Sigmoid Activation
 
-$$out = \\frac{1}{1 + e^{-x}}$$
+$$out = \frac{1}{1 + e^{-x}}$$
 
 )DOC";
 

python/paddle/nn/functional/activation.py

@@ -949,12 +949,14 @@ def silu(x, name=None):
 
         silu(x) = \frac{x}{1 + e^{-x}}
 
+    Where :math:`x` is the input Tensor.
+
     Parameters:
         x (Tensor): The input Tensor with data type float32, float64.
         name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Returns:
-        A Tensor with the same data type and shape as ``x`` .
+        A Tensor with the same data type and shape as :attr:`x`.
 
     Examples:
         .. code-block:: python
@@ -1072,15 +1074,13 @@ def softmax(x, axis=-1, dtype=None, name=None):
 
             import paddle
             import paddle.nn.functional as F
-            import numpy as np
 
-            x = np.array([[[2.0, 3.0, 4.0, 5.0],
+            x = paddle.to_tensor([[[2.0, 3.0, 4.0, 5.0],
                         [3.0, 4.0, 5.0, 6.0],
                         [7.0, 8.0, 8.0, 9.0]],
                         [[1.0, 2.0, 3.0, 4.0],
                         [5.0, 6.0, 7.0, 8.0],
-                        [6.0, 7.0, 8.0, 9.0]]], 'float32')
-            x = paddle.to_tensor(x)
+                        [6.0, 7.0, 8.0, 9.0]]],dtype='float32')
             out1 = F.softmax(x)
             out2 = F.softmax(x, dtype='float64')
             # out1's data type is float32; out2's data type is float64
@@ -1167,14 +1167,15 @@ def softplus(x, beta=1, threshold=20, name=None):
     softplus activation
 
     .. math::
-
-        softplus(x) = \frac{1}{beta} * \log(1 + e^{beta * x}) \\
-        \text{For numerical stability, the implementation reverts to the linear function when: beta * x > threshold.}
+        softplus(x)=\begin{cases}
+                \frac{1}{\beta} * \log(1 + e^{\beta * x}),&x\leqslant\frac{\varepsilon}{\beta};\\
+                x,&x>\frac{\varepsilon}{\beta}.
+            \end{cases}
 
     Parameters:
         x (Tensor): The input Tensor with data type float32, float64.
-        beta (float, optional): The value of beta for softplus. Default is 1
-        threshold (float, optional): The value of threshold for softplus. Default is 20
+        beta (float, optional): The value of :math:`\beta` for softplus. Default is 1
+        threshold (float, optional): The value of :math:`\varepsilon` for softplus. Default is 20
         name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Returns:
@@ -1185,9 +1186,8 @@ def softplus(x, beta=1, threshold=20, name=None):
 
             import paddle
             import paddle.nn.functional as F
-            import numpy as np
 
-            x = paddle.to_tensor(np.array([-0.4, -0.2, 0.1, 0.3]))
+            x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3], dtype='float32')
             out = F.softplus(x) # [0.513015, 0.598139, 0.744397, 0.854355]
     """
 

python/paddle/nn/functional/loss.py

@@ -993,17 +993,17 @@ def smooth_l1_loss(input, label, reduction='mean', delta=1.0, name=None):
 
     .. math::
 
-         loss(x,y) = \frac{1}{n}\sum_{i}z_i
+        loss(x,y) = \frac{1}{n}\sum_{i}z_i
 
 
-    where z_i is given by:
+    where :math:`z_i` is given by:
 
     .. math::
 
         \mathop{z_i} = \left\{\begin{array}{rcl}
-        0.5(x_i - y_i)^2 & & {if |x_i - y_i| < delta} \\
-        delta * |x_i - y_i| - 0.5 * delta^2 & & {otherwise}
-        \end{array} \right.
+                0.5(x_i - y_i)^2 & & {if |x_i - y_i| < \delta} \\
+                \delta * |x_i - y_i| - 0.5 * \delta^2 & & {otherwise}
+            \end{array} \right.
 
     Parameters:
         input (Tensor): Input tensor, the data type is float32 or float64. Shape is
@@ -1017,12 +1017,11 @@ def smooth_l1_loss(input, label, reduction='mean', delta=1.0, name=None):
             If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
             If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
             Default is ``'mean'``.
-        delta (float, optional): Specifies the hyperparameter delta to be used.
+        delta (float, optional): Specifies the hyperparameter :math:`\delta` to be used.
             The value determines how large the errors need to be to use L1. Errors
             smaller than delta are minimized with L2. Parameter is ignored for
             negative/zero values. Default = 1.0
-        name (str, optional): Name for the operation (optional, default is
-            None). For more information, please refer to :ref:`api_guide_Name`.
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Returns:
         Tensor, The tensor variable storing the smooth_l1_loss of input and label.
@@ -1031,14 +1030,12 @@ def smooth_l1_loss(input, label, reduction='mean', delta=1.0, name=None):
         .. code-block:: python
 
             import paddle
-            import numpy as np
 
-            input_data = np.random.rand(3,3).astype("float32")
-            label_data = np.random.rand(3,3).astype("float32")
-            input = paddle.to_tensor(input_data)
-            label = paddle.to_tensor(label_data)
+            input = paddle.rand([3, 3]).astype('float32')
+            label = paddle.rand([3, 3]).astype('float32')
             output = paddle.nn.functional.smooth_l1_loss(input, label)
             print(output)
+            # [0.068004]
     """
     check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                              'smooth_l1_loss')

python/paddle/nn/layer/activation.py

@@ -706,15 +706,15 @@ class LeakyReLU(Layer):
 
 
 class Sigmoid(Layer):
-    """
+    r"""
     this interface is used to construct a callable object of the ``Sigmoid`` class. This layer calcluate the `sigmoid` of input x.
 
     .. math::
 
-        Sigmoid(x) = \\frac{1}{1 + e^{-x}}
+        sigmoid(x) = \frac{1}{1 + e^{-x}}
 
     Parameters:
-        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Shape:
         x: N-D tensor, available dtype is float16, float32, float64.
@@ -726,11 +726,11 @@ class Sigmoid(Layer):
 
         .. code-block:: python
 
-          import paddle
+            import paddle
 
-          m = paddle.nn.Sigmoid()
-          x = paddle.to_tensor([1.0, 2.0, 3.0, 4.0])
-          out = m(x) # [0.7310586, 0.880797, 0.95257413, 0.98201376]
+            m = paddle.nn.Sigmoid()
+            x = paddle.to_tensor([1.0, 2.0, 3.0, 4.0])
+            out = m(x) # [0.7310586, 0.880797, 0.95257413, 0.98201376]
     """
 
     def __init__(self, name=None):
@@ -801,15 +801,15 @@ class Softplus(Layer):
     Softplus Activation
 
     .. math::
-
-        Softplus(x) = \frac{1}{beta} * \log(1 + e^{beta * x}) \\
-        \text{For numerical stability, the implementation reverts to the linear function when: beta * x > threshold.}
+        softplus(x)=\begin{cases}
+                \frac{1}{\beta} * \log(1 + e^{\beta * x}),&x\leqslant\frac{\varepsilon}{\beta};\\
+                x,&x>\frac{\varepsilon}{\beta}.
+            \end{cases}
 
     Parameters:
-        beta (float, optional): The value of beta for Softplus. Default is 1
-        threshold (float, optional): The value of threshold for Softplus. Default is 20
-        name (str, optional): Name for the operation (optional, default is None).
-            For more information, please refer to :ref:`api_guide_Name`.
+        beta (float, optional): The value of :math:`\beta` for Softplus. Default is 1
+        threshold (float, optional): The value of :math:`\varepsilon` for Softplus. Default is 20
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Shape:
         - input: Tensor with any shape.
@@ -819,9 +819,8 @@ class Softplus(Layer):
         .. code-block:: python
 
             import paddle
-            import numpy as np
 
-            x = paddle.to_tensor(np.array([-0.4, -0.2, 0.1, 0.3]))
+            x = paddle.to_tensor([-0.4, -0.2, 0.1, 0.3], dtype='float32')
             m = paddle.nn.Softplus()
             out = m(x) # [0.513015, 0.598139, 0.744397, 0.854355]
     """
@@ -1101,16 +1100,17 @@ class ThresholdedReLU(Layer):
 
 
 class Silu(Layer):
-    """
-    Silu Activation.
+    r"""
+    Silu Activation
+
     .. math::
 
-        Silu(x) = \frac{x}{1 + e^{-x}}
+        silu(x) = \frac{x}{1 + \mathrm{e}^{-x}}
+
+    Where :math:`x` is the input Tensor.
 
     Parameters:
-        x (Tensor): The input Tensor with data type float32, or float64.
-        name (str, optional): Name for the operation (optional, default is None).
-            For more information, please refer to :ref:`api_guide_Name`.
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Shape:
         - input: Tensor with any shape.
@@ -1271,15 +1271,13 @@ class Softmax(Layer):
         .. code-block:: python
 
             import paddle
-            import numpy as np
 
-            x = np.array([[[2.0, 3.0, 4.0, 5.0],
+            x = paddle.to_tensor([[[2.0, 3.0, 4.0, 5.0],
                         [3.0, 4.0, 5.0, 6.0],
                         [7.0, 8.0, 8.0, 9.0]],
                         [[1.0, 2.0, 3.0, 4.0],
                         [5.0, 6.0, 7.0, 8.0],
-                        [6.0, 7.0, 8.0, 9.0]]], 'float32')
-            x = paddle.to_tensor(x)
+                        [6.0, 7.0, 8.0, 9.0]]], dtype='float32')
             m = paddle.nn.Softmax()
             out = m(x)
             # [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],

python/paddle/nn/layer/loss.py

@@ -1138,16 +1138,16 @@ class SmoothL1Loss(Layer):
 
     .. math::
 
-         loss(x,y) = \frac{1}{n}\sum_{i}z_i
+        loss(x, y) = \frac{1}{n}\sum_{i}z_i
 
-    where z_i is given by:
+    where :math:`z_i` is given by:
 
     .. math::
 
         \mathop{z_i} = \left\{\begin{array}{rcl}
-        0.5(x_i - y_i)^2 & & {if |x_i - y_i| < delta} \\
-        delta * |x_i - y_i| - 0.5 * delta^2 & & {otherwise}
-        \end{array} \right.
+                0.5(x_i - y_i)^2 & & {if |x_i - y_i| < \delta} \\
+                \delta * |x_i - y_i| - 0.5 * \delta^2 & & {otherwise}
+            \end{array} \right.
 
     Parameters:
         reduction (str, optional): Indicate how to average the loss by batch_size,
@@ -1156,12 +1156,11 @@ class SmoothL1Loss(Layer):
             If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
             If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
             Default is ``'mean'``.
-        delta (float, optional): Specifies the hyperparameter delta to be used.
+        delta (float, optional): Specifies the hyperparameter :math:`\delta` to be used.
             The value determines how large the errors need to be to use L1. Errors
             smaller than delta are minimized with L2. Parameter is ignored for
-            negative/zero values. Default = 1.0
-        name (str, optional): Name for the operation (optional, default is
-            None). For more information, please refer to :ref:`api_guide_Name`.
+            negative/zero values. Default value is :math:`1.0`.
+        name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
 
     Call Parameters:
 
@@ -1179,14 +1178,12 @@ class SmoothL1Loss(Layer):
         .. code-block:: python
 
             import paddle
-            import numpy as np
-            input_data = np.random.rand(3,3).astype("float32")
-            label_data = np.random.rand(3,3).astype("float32")
-            input = paddle.to_tensor(input_data)
-            label = paddle.to_tensor(label_data)
+            input = paddle.rand([3, 3]).astype("float32")
+            label = paddle.rand([3, 3]).astype("float32")
             loss = paddle.nn.SmoothL1Loss()
             output = loss(input, label)
             print(output)
+            # [0.049606]
     """
 
     def __init__(self, reduction='mean', delta=1.0, name=None):