diff --git a/python/paddle/fluid/layers/nn.py b/python/paddle/fluid/layers/nn.py
index efa60b70001e5..162ad5887cc87 100644
--- a/python/paddle/fluid/layers/nn.py
+++ b/python/paddle/fluid/layers/nn.py
@@ -1189,6 +1189,7 @@ def chunk_eval(input,
             num_correct_chunks)
 
 
+@deprecated(since="2.0.0", update_to="paddle.nn.functional.softmax")
 def softmax(input, use_cudnn=False, name=None, axis=-1):
     """
     This operator implements the softmax layer. The calculation process is as follows:
@@ -8601,7 +8602,7 @@ def log(x, name=None):
     return out
 
 
-@templatedoc()
+@deprecated(since="2.0.0", update_to="paddle.nn.functional.relu")
 def relu(x, name=None):
     """
     ${comment}
@@ -9260,7 +9261,7 @@ def pad2d(input,
     return out
 
 
-@templatedoc()
+@deprecated(since="2.0.0", update_to="paddle.nn.functional.elu")
 def elu(x, alpha=1.0, name=None):
     """
     :alias_main: paddle.nn.functional.elu
@@ -9576,6 +9577,7 @@ def swish(x, beta=1.0, name=None):
     return out
 
 
+@deprecated(since="2.0.0", update_to="paddle.nn.functional.prelu")
 def prelu(x, mode, param_attr=None, name=None):
     """
     :api_attr: Static Graph
diff --git a/python/paddle/fluid/tests/unittests/test_activation_op.py b/python/paddle/fluid/tests/unittests/test_activation_op.py
index db32976f046d3..bf10bcd084ba7 100644
--- a/python/paddle/fluid/tests/unittests/test_activation_op.py
+++ b/python/paddle/fluid/tests/unittests/test_activation_op.py
@@ -525,6 +525,63 @@ def test_errors(self):
             F.hardshrink(x_fp16)
 
 
+def ref_hardtanh(x, min=-1.0, max=1.0):
+    out = np.copy(x)
+    out[np.abs(x - min) < 0.005] = min + 0.02
+    out[np.abs(x - max) < 0.005] = max + 0.02
+    out = np.minimum(np.maximum(x, min), max)
+    return out
+
+
+class TestHardtanhAPI(unittest.TestCase):
+    # test paddle.nn.Hardtanh, paddle.nn.functional.hardtanh
+    def setUp(self):
+        self.x_np = np.random.uniform(-3, 3, [10, 12]).astype('float32')
+        self.place=paddle.CUDAPlace(0) if core.is_compiled_with_cuda() \
+            else paddle.CPUPlace()
+
+    def test_static_api(self):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.data('X', [10, 12])
+            out1 = F.hardtanh(x)
+            m = paddle.nn.Hardtanh()
+            out2 = m(x)
+            exe = paddle.static.Executor(self.place)
+            res = exe.run(feed={'X': self.x_np}, fetch_list=[out1, out2])
+        out_ref = ref_hardtanh(self.x_np)
+        for r in res:
+            self.assertEqual(np.allclose(out_ref, r), True)
+
+    def test_dygraph_api(self):
+        paddle.disable_static(self.place)
+        x = paddle.to_variable(self.x_np)
+        out1 = F.hardtanh(x)
+        m = paddle.nn.Hardtanh()
+        out2 = m(x)
+        out_ref = ref_hardtanh(self.x_np)
+        for r in [out1, out2]:
+            self.assertEqual(np.allclose(out_ref, r.numpy()), True)
+
+        out1 = F.hardtanh(x, -2.0, 2.0)
+        m = paddle.nn.Hardtanh(-2.0, 2.0)
+        out2 = m(x)
+        out_ref = ref_hardtanh(self.x_np, -2.0, 2.0)
+        for r in [out1, out2]:
+            self.assertEqual(np.allclose(out_ref, r.numpy()), True)
+        paddle.enable_static()
+
+    def test_errors(self):
+        with paddle.static.program_guard(paddle.static.Program()):
+            # The input type must be Variable.
+            self.assertRaises(TypeError, F.hardtanh, 1)
+            # The input dtype must be float16, float32, float64.
+            x_int32 = paddle.data(name='x_int32', shape=[12, 10], dtype='int32')
+            self.assertRaises(TypeError, F.hardtanh, x_int32)
+            # support the input dtype is float16
+            x_fp16 = paddle.data(name='x_fp16', shape=[12, 10], dtype='float16')
+            F.hardtanh(x_fp16)
+
+
 def ref_softshrink(x, threshold=0.5):
     out = np.copy(x)
     out = (out < -threshold) * (out + threshold) + (out > threshold) * (
diff --git a/python/paddle/fluid/tests/unittests/test_prelu_op.py b/python/paddle/fluid/tests/unittests/test_prelu_op.py
index 0a38bd277bfd1..16388ff8f5f04 100644
--- a/python/paddle/fluid/tests/unittests/test_prelu_op.py
+++ b/python/paddle/fluid/tests/unittests/test_prelu_op.py
@@ -18,23 +18,134 @@
 import numpy as np
 import paddle.fluid as fluid
 import six
-import paddle.fluid as fluid
+import paddle.fluid.core as core
 from paddle.fluid import Program, program_guard
 from op_test import OpTest, skip_check_grad_ci
+import paddle
+import paddle.nn.functional as F
+
+
+def ref_prelu(x, weight):
+    x_t = x.copy()
+    weight = weight.reshape(1, -1, 1, 1)
+    neg_indices = x <= 0
+    assert x.shape == neg_indices.shape
+    x_t[neg_indices] = (x_t * weight)[neg_indices]
+    return (x_t, )
+
+
+def ref_prelu_nn(x, num_parameters, init):
+    weight_np = np.full((num_parameters), init)
+    return ref_prelu(x, weight_np)
 
 
-class TestPReluOpError(unittest.TestCase):
-    def test_errors(self):
-        with program_guard(Program()):
+class TestFunctionalPReluAPI(unittest.TestCase):
+    def setUp(self):
+        self.place = paddle.CUDAPlace(0) if core.is_compiled_with_cuda(
+        ) else paddle.CPUPlace()
+        self.x_np = np.random.uniform(-1., 1., [1, 2, 3, 4]).astype('float32')
+        self.weight_np_0 = np.random.randn(1).astype('float32')
+        self.weight_np_1 = np.random.randn(self.x_np.shape[1]).astype('float32')
+
+    def static_check(self, weight_np):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.data('X', self.x_np.shape, 'float32')
+            weight = paddle.data('Alpha', weight_np.shape, 'float32')
+            out = F.prelu(x, weight)
+            exe = paddle.static.Executor(self.place)
+            res = exe.run(feed={'X': self.x_np,
+                                'Alpha': weight_np},
+                          fetch_list=[out])
+        out_ref = ref_prelu(self.x_np, weight_np)
+        self.assertEqual(np.allclose(out_ref, res[0]), True)
+
+    def dygraph_check(self, weight_np):
+        paddle.disable_static(self.place)
+        x = paddle.to_tensor(self.x_np)
+        weight = paddle.to_tensor(weight_np)
+        out = F.prelu(x, weight)
+        out_ref = ref_prelu(self.x_np, weight_np)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+        paddle.enable_static()
+
+    def test_static_api(self):
+        self.static_check(self.weight_np_0)
+        self.static_check(self.weight_np_1)
+
+    def test_dygraph_api(self):
+        self.dygraph_check(self.weight_np_0)
+        self.dygraph_check(self.weight_np_1)
+
+    def test_error(self):
+        with paddle.static.program_guard(paddle.static.Program()):
+            weight_fp32 = paddle.data(
+                name='weight_fp32', shape=[1], dtype='float32')
             # The input type must be Variable.
-            self.assertRaises(TypeError, fluid.layers.prelu, 0.1, 'all')
+            self.assertRaises(TypeError, F.prelu, x=1, weight=weight_fp32)
             # The input dtype must be float16, float32, float64.
-            x_int32 = fluid.data(name='x_int32', shape=[12, 10], dtype='int32')
-            self.assertRaises(TypeError, fluid.layers.prelu, x_int32, 'all')
-            # support the input dtype is float32
-            x_fp16 = fluid.layers.data(
-                name='x_fp16', shape=[12, 10], dtype='float32')
-            fluid.layers.prelu(x_fp16, 'all')
+            x_int32 = paddle.data(name='x_int32', shape=[2, 3], dtype='int32')
+            self.assertRaises(TypeError, F.prelu, x=x_int32, weight=weight_fp32)
+            # support the input dtype is float16
+            x_fp16 = paddle.data(name='x_fp16', shape=[2, 3], dtype='float16')
+            F.prelu(x=x_fp16, weight=weight_fp32)
+
+
+class TestNNPReluAPI(unittest.TestCase):
+    def setUp(self):
+        self.place = paddle.CUDAPlace(0) if core.is_compiled_with_cuda(
+        ) else paddle.CPUPlace()
+        self.x_np = np.ones([1, 2, 3, 4]).astype('float32')
+
+    def test_static_api(self):
+        startup_program = paddle.static.Program()
+        train_program = paddle.static.Program()
+        with paddle.static.program_guard(train_program, startup_program):
+            x = paddle.data(name='X', shape=self.x_np.shape, dtype='float32')
+            m = paddle.nn.PReLU()
+            out = m(x)
+            exe = paddle.static.Executor(self.place)
+            exe.run(startup_program)
+            res = exe.run(train_program,
+                          feed={'X': self.x_np},
+                          fetch_list=[out])
+        out_ref = ref_prelu_nn(self.x_np, 1, 0.25)
+        self.assertEqual(np.allclose(out_ref, res[0]), True)
+
+    def test_dygraph_api(self):
+        paddle.disable_static(self.place)
+
+        x = paddle.to_tensor(self.x_np)
+        m = paddle.nn.PReLU()
+        out = m(x)
+        out_ref = ref_prelu_nn(self.x_np, 1, 0.25)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+
+        x = paddle.to_tensor(self.x_np)
+        m = paddle.nn.PReLU(num_parameters=self.x_np.shape[1])
+        out = m(x)
+        out_ref = ref_prelu_nn(self.x_np, self.x_np.shape[1], 0.25)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+
+        x = paddle.to_tensor(self.x_np)
+        m = paddle.nn.PReLU(init=0.5)
+        out = m(x)
+        out_ref = ref_prelu_nn(self.x_np, 1, 0.5)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+
+        x = paddle.to_tensor(self.x_np)
+        m = paddle.nn.PReLU(weight_attr=fluid.ParamAttr(name="weight"))
+        out = m(x)
+        out_ref = ref_prelu_nn(self.x_np, 1, 0.25)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+
+        x = paddle.to_tensor(self.x_np)
+        m = paddle.nn.PReLU(weight_attr=fluid.ParamAttr(
+            initializer=fluid.initializer.Constant(0.5)))
+        out = m(x)
+        out_ref = ref_prelu_nn(self.x_np, 1, 0.5)
+        self.assertEqual(np.allclose(out_ref, out.numpy()), True)
+
+        paddle.enable_static()
 
 
 class PReluTest(OpTest):
diff --git a/python/paddle/fluid/tests/unittests/test_softmax_op.py b/python/paddle/fluid/tests/unittests/test_softmax_op.py
index 25e95216968b5..04d5cc941a463 100644
--- a/python/paddle/fluid/tests/unittests/test_softmax_op.py
+++ b/python/paddle/fluid/tests/unittests/test_softmax_op.py
@@ -35,6 +35,15 @@ def stable_softmax(x):
     return exps / np.sum(exps)
 
 
+def ref_softmax(x, axis=None, dtype=None):
+    x_t = x.copy()
+    if dtype is not None:
+        x_t = x_t.astype(dtype)
+    if axis is None:
+        axis = -1
+    return np.apply_along_axis(stable_softmax, axis, x_t)
+
+
 class TestSoftmaxOp(OpTest):
     def get_x_shape(self):
         return [10, 10]
@@ -93,20 +102,6 @@ def test_check_grad(self):
                 check_dygraph=(self.use_mkldnn == False))
 
 
-class TestSoftmaxOpError(unittest.TestCase):
-    def test_errors(self):
-        with program_guard(Program(), Program()):
-            # The input type of softmax_op must be Variable.
-            x1 = fluid.create_lod_tensor(
-                np.array([[-1]]), [[1]], fluid.CPUPlace())
-            self.assertRaises(TypeError, fluid.layers.softmax, x1)
-            # The input dtype of softmax_op must be float16, float32 or float64.
-            x2 = fluid.layers.data(name='x2', shape=[4], dtype="int32")
-            self.assertRaises(TypeError, fluid.layers.softmax, x2)
-            x3 = fluid.layers.data(name='x3', shape=[4], dtype="float16")
-            fluid.layers.softmax(x3)
-
-
 class TestSoftmaxOp2(TestSoftmaxOp):
     def get_x_shape(self):
         return [2, 3, 4, 5]
@@ -224,41 +219,59 @@ def get_x_shape(self):
         return [2, 3, 4, 5]
 
 
-class TestNnFunctionalSoftmaxApi(unittest.TestCase):
+class TestSoftmaxAPI(unittest.TestCase):
     def setUp(self):
         self.place = paddle.CUDAPlace(0) if core.is_compiled_with_cuda(
         ) else paddle.CPUPlace()
         self.x_np = np.random.uniform(-1., 1., [2, 3, 4, 5]).astype('float32')
         self.out_ref = np.apply_along_axis(stable_softmax, -1, self.x_np)
 
-    def test_api_static(self):
-        with program_guard(Program()):
+    def test_static_check(self):
+        with paddle.static.program_guard(paddle.static.Program()):
             x = paddle.data('X', self.x_np.shape, 'float32')
-            out = F.softmax(x)
+            out1 = F.softmax(x)
+            m = paddle.nn.Softmax()
+            out2 = m(x)
             exe = paddle.static.Executor(self.place)
-            res = exe.run(feed={'X': self.x_np}, fetch_list=[out])
-        self.assertEqual(np.allclose(self.out_ref, res[0]), True)
+            res = exe.run(feed={'X': self.x_np}, fetch_list=[out1, out2])
+        out_ref = ref_softmax(self.x_np, axis=-1, dtype=None)
+        for r in res:
+            self.assertEqual(np.allclose(out_ref, r), True)
 
-    def test_api_imperative(self):
+    def test_dygraph_check(self):
         paddle.disable_static(self.place)
 
-        x = paddle.to_variable(self.x_np)
-        out = F.softmax(x)
-        self.assertEqual(np.allclose(self.out_ref, out.numpy()), True)
-
-        out = F.softmax(x, axis=0)
-        out_ref = np.apply_along_axis(stable_softmax, 0, self.x_np)
+        x = paddle.to_tensor(self.x_np)
+        out1 = F.softmax(x)
+        m = paddle.nn.Softmax()
+        out2 = m(x)
+        out_ref = ref_softmax(self.x_np, axis=-1, dtype=None)
+        for r in [out1, out2]:
+            self.assertEqual(np.allclose(out_ref, r.numpy()), True)
+
+        out1 = F.softmax(x, axis=0)
+        m = paddle.nn.Softmax(axis=0)
+        out2 = m(x)
+        out_ref = ref_softmax(self.x_np, axis=0, dtype=None)
+        for r in [out1, out2]:
+            self.assertEqual(np.allclose(out_ref, r.numpy()), True)
+
+        out = F.softmax(x, dtype=np.float64)
+        out_ref = ref_softmax(self.x_np, axis=-1, dtype=np.float64)
         self.assertEqual(np.allclose(out_ref, out.numpy()), True)
 
         paddle.enable_static()
 
     def test_error(self):
-        with program_guard(Program(), Program()):
-            # The x should be variable and its dtype should be float32, float64.
-            self.assertRaises(TypeError, F.softmax, [1])
-
-            x = paddle.data(name='x', shape=[2, 3], dtype='int32')
-            self.assertRaises(TypeError, F.softmax, x)
+        with paddle.static.program_guard(paddle.static.Program()):
+            # The input type must be Variable.
+            self.assertRaises(TypeError, F.softmax, 1)
+            # The input dtype must be float16, float32, float64.
+            x_int32 = paddle.data(name='x_int32', shape=[2, 3], dtype='int32')
+            self.assertRaises(TypeError, F.softmax, x_int32)
+            # support the input dtype is float16
+            x_fp16 = paddle.data(name='x_fp16', shape=[2, 3], dtype='float16')
+            F.softmax(x_fp16)
 
 
 if __name__ == "__main__":
diff --git a/python/paddle/nn/__init__.py b/python/paddle/nn/__init__.py
index 3dd1c1d94fbd7..84c466c977eea 100644
--- a/python/paddle/nn/__init__.py
+++ b/python/paddle/nn/__init__.py
@@ -55,14 +55,15 @@
 from .layer.activation import ELU
 from .layer.activation import GELU
 from .layer.activation import Hardshrink
-# from .layer.activation import PReLU        #DEFINE_ALIAS
+from .layer.activation import Hardtanh
+from .layer.activation import PReLU
 from .layer.activation import ReLU
 from .layer.activation import ReLU6  #DEFINE_ALIAS
 from .layer.activation import SELU  #DEFINE_ALIAS
 from .layer.activation import LeakyReLU  #DEFINE_ALIAS
 from .layer.activation import Sigmoid  #DEFINE_ALIAS
 from .layer.activation import LogSigmoid
-# from .layer.activation import Softmax        #DEFINE_ALIAS
+from .layer.activation import Softmax  #DEFINE_ALIAS
 from .layer.activation import Softplus  #DEFINE_ALIAS
 from .layer.activation import Softshrink  #DEFINE_ALIAS
 from .layer.activation import Softsign  #DEFINE_ALIAS
diff --git a/python/paddle/nn/functional/__init__.py b/python/paddle/nn/functional/__init__.py
index ff2b1edf6723b..7c903ccf53c58 100644
--- a/python/paddle/nn/functional/__init__.py
+++ b/python/paddle/nn/functional/__init__.py
@@ -30,13 +30,14 @@
 from .activation import erf  #DEFINE_ALIAS
 from .activation import gelu  #DEFINE_ALIAS
 from .activation import hardshrink  #DEFINE_ALIAS
+from .activation import hardtanh  #DEFINE_ALIAS
 from .activation import hard_sigmoid  #DEFINE_ALIAS
 from .activation import hard_swish  #DEFINE_ALIAS
 from .activation import hsigmoid  #DEFINE_ALIAS
 from .activation import leaky_relu  #DEFINE_ALIAS
 from .activation import logsigmoid  #DEFINE_ALIAS
 from .activation import maxout  #DEFINE_ALIAS
-# from .activation import prelu        #DEFINE_ALIAS
+from .activation import prelu  #DEFINE_ALIAS
 from .activation import relu  #DEFINE_ALIAS
 from .activation import relu6  #DEFINE_ALIAS
 from .activation import selu  #DEFINE_ALIAS
diff --git a/python/paddle/nn/functional/activation.py b/python/paddle/nn/functional/activation.py
index 16a86ce2e8cb6..619492a1b2bb1 100644
--- a/python/paddle/nn/functional/activation.py
+++ b/python/paddle/nn/functional/activation.py
@@ -30,13 +30,14 @@
     'erf',
     'gelu',
     'hardshrink',
+    'hardtanh',
     'hard_sigmoid',
     'hard_swish',
     'hsigmoid',
     'leaky_relu',
     'logsigmoid',
     'maxout',
-    #       'prelu',
+    'prelu',
     'relu',
     'relu6',
     'selu',
@@ -49,7 +50,7 @@
     'swish',
     'tanhshrink',
     'thresholded_relu',
-    'log_softmax'
+    'log_softmax',
 ]
 
 import warnings
@@ -64,7 +65,7 @@ def elu(x, alpha=1.0, name=None):
     """
     elu activation.
 
-    ..  math::
+    .. math::
 
         elu(x) = max(0, x) + min(0, \\alpha * (e^{x}-1))
 
@@ -80,16 +81,16 @@ def elu(x, alpha=1.0, name=None):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([[-1,6],[1,15.6]]))
-        out = F.elu(x, alpha=0.2) 
-        # [[-0.12642411  6.        ]
-        #  [ 1.          15.6      ]]
+            x = paddle.to_tensor(np.array([[-1,6],[1,15.6]]))
+            out = F.elu(x, alpha=0.2) 
+            # [[-0.12642411  6.        ]
+            #  [ 1.          15.6      ]]
     """
 
     if in_dygraph_mode():
@@ -111,10 +112,15 @@ def gelu(x, approximate=False, name=None):
     gelu activation.
 
     if approximate is True
-    ..  math::
+
+    .. math::
+
         gelu(x) = 0.5 * x * (1 + tanh(\\sqrt{\\frac{2}{\\pi}} * (x + 0.044715x^{3})))
+
     else
-    ..  math::
+
+    .. math::
+
         gelu(x) = 0.5 * x * (1 + erf(\\frac{x}{\\sqrt{2}}))
     
     Parameters:
@@ -129,23 +135,15 @@ def gelu(x, approximate=False, name=None):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
-
-        paddle.disable_static()
-
-        data = np.random.randn(2, 3).astype("float32")
-        x = paddle.to_tensor(data)
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        out = F.gelu(x)
+            paddle.disable_static()
 
-        data
-        # array([[ 0.87165993, -1.0541513 , -0.37214822],
-        #         [ 0.15647964,  0.32496083,  0.33045998]], dtype=float32)
-        out
-        # array([[ 0.70456535, -0.15380788, -0.13207214],
-        #        [ 0.08796856,  0.20387867,  0.2080159 ]], dtype=float32)
+            x = paddle.to_tensor(np.array([[-1, 0.5],[1, 1.5]]))
+            out1 = F.gelu(x) # [-0.158655 0.345731 0.841345 1.39979]
+            out2 = F.gelu(x, True) # [-0.158808 0.345714 0.841192 1.39957]
     """
 
     if in_dygraph_mode():
@@ -187,17 +185,16 @@ def hardshrink(x, threshold=0.5, name=None):
         A Tensor with the same data type and shape as ``x`` .
 
     Examples:
-
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_variable(np.array([-1, 0.3, 2.5]))
-        out = F.hardshrink(x) # [-1., 0., 2.5]
+            x = paddle.to_tensor(np.array([-1, 0.3, 2.5]))
+            out = F.hardshrink(x) # [-1., 0., 2.5]
 
     """
     if in_dygraph_mode():
@@ -215,6 +212,58 @@ def hardshrink(x, threshold=0.5, name=None):
     return out
 
 
+def hardtanh(x, min=-1.0, max=1.0, name=None):
+    """
+    hardtanh activation
+
+    .. math::
+
+        hardtanh(x)= \\begin{cases}
+                        max, \\text{if } x > max \\\\
+                        min, \\text{if } x < min \\\\
+                        x,  \\text{otherwise}
+                      \\end{cases}
+
+    Args:
+        x (Tensor): The input Tensor with data type float32, float64.
+        min (float, optional): The minimum value of the linear region range. Default is -1.
+        max (float, optional): The maximum value of the linear region range. Default is 1.
+        name (str, optional): Name for the operation (optional, default is None).
+            For more information, please refer to :ref:`api_guide_Name`.
+
+    Returns:
+        A Tensor with the same data type and shape as ``x`` .
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
+
+            paddle.disable_static()
+
+            x = paddle.to_tensor(np.array([-1.5, 0.3, 2.5]))
+            out = F.hardtanh(x) # [-1., 0.3, 1.]
+    """
+
+    if in_dygraph_mode():
+        return core.ops.brelu(x, 't_min', min, 't_max', max)
+
+    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
+                             'hardtanh')
+
+    helper = LayerHelper('hardtanh', **locals())
+    out = helper.create_variable_for_type_inference(dtype=x.dtype)
+    helper.append_op(
+        type='brelu',
+        inputs={'X': x},
+        outputs={'Out': out},
+        attrs={'t_min': min,
+               't_max': max})
+    return out
+
+
 def hsigmoid(input,
              label,
              weight,
@@ -272,7 +321,6 @@ def hsigmoid(input,
         Variable: A tensor with the cost of hierarchical sigmoid, its shape is [N, 1] and data type is the same as :attr:`input`.
 
     Examples:
-
         .. code-block:: python
 
             from paddle import fluid, nn
@@ -338,11 +386,86 @@ def hsigmoid(input,
     return out
 
 
+def prelu(x, weight, name=None):
+    """
+    prelu activation.
+
+    .. math::
+
+        prelu(x) = max(0, x) + weight * min(0, x)
+
+    Parameters:
+        x (Tensor): The input Tensor with data type float32, float64.
+        weight (Tensor): The learnable parameter with data type same as ``x``.
+            The weight shape is [1] or [in], where `in` is the input channel of ``x``.
+        name (str, optional): Name for the operation (optional, default is None).
+            For more information, please refer to :ref:`api_guide_Name`.
+
+    Returns:
+        A Tensor with the same data type and shape as ``x`` .
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
+
+            paddle.disable_static()
+
+            data = np.array([[[[-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(data)
+            w = paddle.to_tensor(np.array([0.25]).astype('float32'))
+            out = F.prelu(x, w)
+            # [[[[-0.5 ,  3.  , -1.  ,  5.  ],
+            #    [ 3.  , -1.  ,  5.  , -1.5 ],
+            #    [-1.75, -2.  ,  8.  ,  9.  ]],
+            #   [[ 1.  , -0.5 , -0.75,  4.  ],
+            #    [-1.25,  6.  ,  7.  , -2.  ],
+            #    [ 6.  ,  7.  ,  8.  ,  9.  ]]]]
+    """
+    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'prelu')
+    check_variable_and_dtype(weight, 'weight',
+                             ['float16', 'float32', 'float64'], 'prelu')
+
+    helper = LayerHelper('prelu', **locals())
+    assert len(weight.shape
+               ) == 1, "The dim count of weight shape should be 1 in prelu()."
+
+    # NOTE(): The input of this API should be ``N,C,...`` format, 
+    # which means x.shape[0] is batch_size and x.shape[0] is channel.
+    mode = 'all'
+    if weight.shape[0] > 1:
+        assert len(
+            x.shape
+        ) > 1, "The dim count of x should be equal or larger than 2 in prelu() when weight shape is not [1]."
+        assert weight.shape[0] == x.shape[
+            1], "The weight size should be equal to x input channel in prelu() when weight shape is not [1]."
+        mode = 'channel'
+
+    if in_dygraph_mode():
+        return core.ops.prelu(x, weight, 'mode', mode)
+
+    out = helper.create_variable_for_type_inference(x.dtype)
+    helper.append_op(
+        type="prelu",
+        inputs={"X": x,
+                "Alpha": weight},
+        outputs={"Out": out},
+        attrs={"mode": mode})
+    return out
+
+
 def relu(x, name=None):
     """
-    ReLU Activation.
+    relu activation.
 
-    .. math:
+    .. math::
 
         out = max(x, 0)
 
@@ -357,14 +480,14 @@ def relu(x, name=None):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([-2, 0, 1]).astype('float32'))
-        out = F.relu(x) # [0., 0., 1.]
+            x = paddle.to_tensor(np.array([-2, 0, 1]).astype('float32'))
+            out = F.relu(x) # [0., 0., 1.]
     """
 
     if in_dygraph_mode():
@@ -381,9 +504,9 @@ def logsigmoid(x, name=None):
     """
     logsigmoid activation.
 
-    .. math:
+    .. math::
 
-        logsigmoid(x) = \log \frac{1}{1 + e^{-x}}
+        logsigmoid(x) = log \\frac{1}{1 + e^{-x}}
     
     Parameters:
         x (Tensor): The input Tensor with data type float32, float64.
@@ -396,14 +519,14 @@ def logsigmoid(x, name=None):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([1.0, 2.0, 3.0, 4.0]))
-        out = F.logsigmoid(x) # [0.7310586, 0.880797, 0.95257413, 0.98201376]
+            x = paddle.to_tensor(np.array([1.0, 2.0, 3.0, 4.0]))
+            out = F.logsigmoid(x) # [-0.313262 -0.126928 -0.0485874 -0.0181499]
     """
 
     if in_dygraph_mode():
@@ -514,7 +637,7 @@ def selu(x,
     return out
 
 
-def softmax(x, axis=-1, name=None):
+def softmax(x, axis=-1, dtype=None, name=None):
     """
     This operator implements the softmax layer. The calculation process is as follows:
 
@@ -541,7 +664,7 @@ def softmax(x, axis=-1, name=None):
 
     .. math::
 
-        out[i, j] = \\frac{\exp(x[i, j])}{\sum_j(exp(x[i, j])}
+        softmax[i, j] = \\frac{\\exp(x[i, j])}{\\sum_j(exp(x[i, j])}
 
     Example:
 
@@ -590,44 +713,89 @@ def softmax(x, axis=-1, name=None):
                          [0.26762315, 0.26762315, 0.26762315, 0.26762315],
                          [0.72747516, 0.72747516, 0.72747516, 0.72747516]]]
 
-    Args:
-        x (Tensor): The input multi-dimension Tensor with data type float32, float64.
-        axis (int, optional): The axis along which to perform softmax calculations.
-            It should be in range [-D, D), where D is the dimensions of ``x`` .
-            When ``axis`` < 0, it works the same way as :math:`axis + D` .
-            Default is -1.
+    Parameters:
+        x (Tensor): The input Tensor with data type float32, float64.
+        axis (int, optional): The axis along which to perform log_softmax
+            calculations. It should be in range [-D, D), where D is the
+            dimensions of ``x`` . If ``axis`` < 0, it works the same way as
+            :math:`axis + D` . Default is -1.
+        dtype (str|np.dtype|core.VarDesc.VarType, optional): The desired data
+            type of the output tensor. If dtype is specified, ``x`` is casted
+            to ``dtype`` before the operation is performed. This is useful for 
+            preventing data type overflows. Supported dtype: float32, float64.
+            If ``dtype`` is None, the output Tensor has the same dtype as x.
+            Default is None.
         name (str, optional): Name for the operation (optional, default is None).
             For more information, please refer to :ref:`api_guide_Name`.
 
     Returns:
-        A Tensor with the same data type and shape as ``x`` .
+        A Tensor with the same shape and data type (use ``dtype`` if it is
+        specified) as x.
 
     Examples:
-
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = np.array([[[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)
-        out = F.softmax(x)
-        # [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
-        #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
-        #   [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
-        # [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
-        #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
-        #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]
+            x = np.array([[[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)
+            out1 = F.softmax(x)
+            out2 = F.softmax(x, dtype='float64')
+            # out1's data type is float32; out2's data type is float64
+            # out1 and out2's value is as follows:
+            # [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
+            # [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]
     """
-    return paddle.fluid.layers.softmax(input=x, axis=axis, name=name)
+
+    if (dtype is not None) and (not isinstance(dtype, core.VarDesc.VarType)):
+        dtype = convert_np_dtype_to_dtype_(dtype)
+    use_cudnn = True if axis is -1 else False
+
+    if in_dygraph_mode():
+        outs_cast = x if dtype is None \
+            else core.ops.cast(x, 'in_dtype', x.dtype, 'out_dtype', dtype)
+        return core.ops.softmax(outs_cast, 'axis', axis, 'use_cudnn', use_cudnn)
+
+    if dtype is None:
+        check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
+                                 'softmax')
+    else:
+        check_dtype(dtype, 'dtype', ['float32', 'float64'], 'softmax',
+                    'If dtype is not None, it only support float32 or float64.')
+
+    helper = LayerHelper("softmax", **locals())
+    outs_cast = x
+    if dtype is not None:
+        outs_cast = helper.create_variable_for_type_inference(dtype)
+        helper.append_op(
+            type='cast',
+            inputs={'X': x},
+            outputs={'Out': outs_cast},
+            attrs={'in_dtype': x.dtype,
+                   'out_dtype': dtype})
+
+    outs_softmax = helper.create_variable_for_type_inference(outs_cast.dtype)
+    helper.append_op(
+        type='softmax',
+        inputs={'X': outs_cast},
+        outputs={'Out': outs_softmax},
+        attrs={'axis': axis,
+               'use_cudnn': use_cudnn})
+
+    return outs_softmax
 
 
 def softplus(x, beta=1, threshold=20, name=None):
@@ -820,7 +988,7 @@ def log_softmax(x, axis=-1, dtype=None, name=None):
     .. math::
 
         Out[i, j] = log(softmax(x)) 
-                  = log(\\frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])})
+                  = log(\frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])})
 
     Parameters:
         x (Tensor): The input Tensor with data type float32, float64.
@@ -844,33 +1012,31 @@ def log_softmax(x, axis=-1, dtype=None, name=None):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import paddle.nn.functional as F
-        import numpy as np
+            import paddle
+            import paddle.nn.functional as F
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
+
+            x = np.array([[[-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)
+            out1 = F.log_softmax(x)
+            out2 = F.log_softmax(x, dtype='float64')
+            # out1's data type is float32; out2's data type is float64
+            # out1 and out2's value is as follows:
+            # [[[ -7.1278396   -2.1278396   -9.127839    -0.12783948]
+            #   [ -2.1270514   -9.127051    -0.12705144 -11.127051  ]
+            #   [-16.313261   -17.313261    -1.3132617   -0.31326184]]
+            #  [[ -3.0518122   -6.051812    -7.051812    -0.051812  ]
+            #   [-12.313267    -1.3132664   -0.3132665  -15.313267  ]
+            #   [ -3.4401896   -2.4401896   -1.4401896   -0.44018966]]]
+    """
 
-        x = np.array([[[-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)
-        out1 = F.log_softmax(x)
-        out2 = F.log_softmax(x, dtype='float64')
-        # out1's data type is float32; out2's data type is float64
-        # out1 and out2's value is as follows:
-        # [[[ -7.1278396   -2.1278396   -9.127839    -0.12783948]
-        #   [ -2.1270514   -9.127051    -0.12705144 -11.127051  ]
-        #   [-16.313261   -17.313261    -1.3132617   -0.31326184]]
-        #  [[ -3.0518122   -6.051812    -7.051812    -0.051812  ]
-        #   [-12.313267    -1.3132664   -0.3132665  -15.313267  ]
-        #   [ -3.4401896   -2.4401896   -1.4401896   -0.44018966]]]
-    """
-
-    if axis is None:
-        axis = -1
     if (dtype is not None) and (not isinstance(dtype, core.VarDesc.VarType)):
         dtype = convert_np_dtype_to_dtype_(dtype)
 
diff --git a/python/paddle/nn/layer/activation.py b/python/paddle/nn/layer/activation.py
index bb294467bb3dd..bfa2e2f25d873 100644
--- a/python/paddle/nn/layer/activation.py
+++ b/python/paddle/nn/layer/activation.py
@@ -18,25 +18,28 @@
     'ELU',
     'GELU',
     'Hardshrink',
-    #       'PReLU',
+    'Hardtanh',
+    'PReLU',
     'ReLU',
     'ReLU6',
     'SELU',
     'LeakyReLU',
     'Sigmoid',
-    #       'Softmax',
+    'Softmax',
     'Softplus',
     'Softshrink',
     'Softsign',
     'Tanhshrink',
     'LogSigmoid',
     'LogSoftmax',
-    'HSigmoid'
+    'HSigmoid',
 ]
 
 from ...fluid.dygraph import layers
 from ...fluid import core
 from ...fluid.framework import in_dygraph_mode
+from ...fluid.param_attr import ParamAttr
+from ...fluid.initializer import Constant
 from .. import functional as F
 
 
@@ -44,7 +47,7 @@ class ELU(layers.Layer):
     """
     ELU Activation.
 
-    ..  math::
+    .. math::
     
         ELU(x) = max(0, x) + min(0, \\alpha * (e^{x}-1))
 
@@ -60,16 +63,16 @@ class ELU(layers.Layer):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import numpy as np
+            import paddle
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([[-1,6],[1,15.6]]))
-        m = paddle.nn.ELU(0.2)
-        out = m(x) 
-        # [[-0.12642411  6.        ]
-        #  [ 1.          15.6      ]]
+            x = paddle.to_tensor(np.array([[-1,6],[1,15.6]]))
+            m = paddle.nn.ELU(0.2)
+            out = m(x)
+            # [[-0.12642411  6.        ]
+            #  [ 1.          15.6      ]]
     """
 
     def __init__(self, alpha=1.0, name=None):
@@ -87,13 +90,13 @@ class GELU(layers.Layer):
 
     If approximate is True
 
-    ..  math::
+    .. math::
 
         GELU(x) = 0.5 * x * (1 + tanh(\\sqrt{\\frac{2}{\\pi}} * (x + 0.044715x^{3})))
 
     else
 
-    ..  math::
+    .. math::
 
         GELU(x) = 0.5 * x * (1 + erf(\\frac{x}{\\sqrt{2}}))
 
@@ -109,23 +112,18 @@ class GELU(layers.Layer):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import numpy as np
-
-        paddle.disable_static()
+            import paddle
+            import numpy as np
 
-        data = np.random.randn(2, 3).astype("float32")
-        x = paddle.to_tensor(data)
+            paddle.disable_static()
 
-        m = paddle.nn.GELU()
-        out = m(x)
+            x = paddle.to_tensor(np.array([[-1, 0.5],[1, 1.5]]))
+            
+            m = paddle.nn.GELU()
+            out = m(x) # [-0.158655 0.345731 0.841345 1.39979]
 
-        data
-        # array([[ 0.87165993, -1.0541513 , -0.37214822],
-        #         [ 0.15647964,  0.32496083,  0.33045998]], dtype=float32)
-        out
-        # array([[ 0.70456535, -0.15380788, -0.13207214],
-        #        [ 0.08796856,  0.20387867,  0.2080159 ]], dtype=float32)
+            m = paddle.nn.GELU(True)
+            out = m(x) # [-0.158808 0.345714 0.841192 1.39957]
     """
 
     def __init__(self, approximate=False, name=None):
@@ -170,7 +168,7 @@ class Hardshrink(layers.Layer):
 
         paddle.disable_static()
 
-        x = paddle.to_variable(np.array([-1, 0.3, 2.5]))
+        x = paddle.to_tensor(np.array([-1, 0.3, 2.5]))
         m = paddle.nn.Hardshrink()
         out = m(x) # [-1., 0., 2.5]
     """
@@ -184,6 +182,51 @@ def forward(self, x):
         return F.hardshrink(x, self._threshold, self._name)
 
 
+class Hardtanh(layers.Layer):
+    """
+    Hardtanh Activation
+
+    .. math::
+
+        Hardtanh(x)= \\begin{cases}
+                        max, \\text{if } x > max \\\\
+                        min, \\text{if } x < min \\\\
+                        x,  \\text{otherwise}
+                      \\end{cases}
+
+    Parameters:
+        min (float, optional): The value of min for Hardtanh. Default is -1.
+        max (float, optional): The value of max for Hardtanh. Default is 1.
+        name (str, optional): Name for the operation (optional, default is None).
+            For more information, please refer to :ref:`api_guide_Name`.
+    
+    Shape:
+        - input: Tensor with any shape.
+        - output: Tensor with the same shape as input.
+    
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import numpy as np
+
+            paddle.disable_static()
+
+            x = paddle.to_tensor(np.array([-1.5, 0.3, 2.5]))
+            m = paddle.nn.Hardtanh()
+            out = m(x) # # [-1., 0.3, 1.]
+    """
+
+    def __init__(self, min=-1.0, max=1.0, name=None):
+        super(Hardtanh, self).__init__()
+        self._min = min
+        self._max = max
+        self._name = name
+
+    def forward(self, x):
+        return F.hardtanh(x, self._min, self._max, self._name)
+
+
 class HSigmoid(layers.Layer):
     """
 	:alias_main: paddle.nn.HSigmoid
@@ -320,11 +363,78 @@ def forward(self, input, label, path_table=None, path_code=None):
         return out
 
 
+class PReLU(layers.Layer):
+    """
+    PReLU Activation.
+
+    .. math::
+
+        PReLU(x) = max(0, x) + weight * min(0, x)
+
+    Parameters:
+        num_parameters (int, optional): Number of `weight` to learn. The supported values are:
+            1 - a single parameter `alpha` is used for all input channels; 
+            Number of channels - a seperate `alpha` is used for each input channel.
+            Default is 1.
+        init (float, optional): Init value of learnable `weight`. Default is 0.25.
+        weight_attr(ParamAttr, optional): The parameter attribute for the learnable `weight`. 
+            Default is None. For more information, please refer to :ref:`api_fluid_ParamAttr`.
+        name (str, optional): Name for the operation (optional, default is None).
+            For more information, please refer to :ref:`api_guide_Name`.
+    
+    Shape:
+        - input: Tensor with any shape.
+        - output: Tensor with the same shape as input.
+    
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import numpy as np
+
+            paddle.disable_static()
+
+            data = np.array([[[[-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(data)
+            m = paddle.nn.PReLU(1, 0.25)
+            out = m(x)
+            # [[[[-0.5 ,  3.  , -1.  ,  5.  ],
+            #    [ 3.  , -1.  ,  5.  , -1.5 ],
+            #    [-1.75, -2.  ,  8.  ,  9.  ]],
+            #   [[ 1.  , -0.5 , -0.75,  4.  ],
+            #    [-1.25,  6.  ,  7.  , -2.  ],
+            #    [ 6.  ,  7.  ,  8.  ,  9.  ]]]]
+    """
+
+    def __init__(self, num_parameters=1, init=0.25, weight_attr=None,
+                 name=None):
+        super(PReLU, self).__init__()
+        self._num_parameters = num_parameters
+        self._init = init
+        self._weight_attr = weight_attr
+        self._name = name
+
+        self._weight = self.create_parameter(
+            attr=self._weight_attr,
+            shape=[num_parameters],
+            dtype='float32',
+            is_bias=False,
+            default_initializer=Constant(init))
+
+    def forward(self, x):
+        return F.prelu(x, self._weight)
+
+
 class ReLU(layers.Layer):
     """
     ReLU Activation.
 
-    .. math:
+    .. math::
 
         ReLU(x) = max(x, 0)
 
@@ -339,14 +449,14 @@ class ReLU(layers.Layer):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import numpy as np
+            import paddle
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([-2, 0, 1]).astype('float32'))
-        m = paddle.nn.ReLU()
-        out = m(x) # [0., 0., 1.]
+            x = paddle.to_tensor(np.array([-2, 0, 1]).astype('float32'))
+            m = paddle.nn.ReLU()
+            out = m(x) # [0., 0., 1.]
     """
 
     def __init__(self, name=None):
@@ -488,7 +598,7 @@ class Sigmoid(layers.Layer):
     
     .. math::
 
-        output = \\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`.
@@ -509,7 +619,7 @@ class Sigmoid(layers.Layer):
           paddle.disable_static()
           input_data = np.array([1.0, 2.0, 3.0, 4.0]).astype('float32')
           m = paddle.nn.Sigmoid()
-          x = paddle.to_variable(input_data)
+          x = paddle.to_tensor(input_data)
           output = m(x)
           print(output.numpy()) # [0.7310586, 0.880797, 0.95257413, 0.98201376]
     """
@@ -687,9 +797,9 @@ class LogSigmoid(layers.Layer):
     """
     LogSigmoid Activation.
     
-    .. math:
+    .. math::
 
-        LogSigmoid(x) = \log \frac{1}{1 + e^{-x}}
+        LogSigmoid(x) = log \\frac{1}{1 + e^{-x}}
 
     Parameters:
         x (Tensor): The input Tensor with data type float32, or float64.
@@ -703,14 +813,14 @@ class LogSigmoid(layers.Layer):
     Examples:
         .. code-block:: python
 
-        import paddle
-        import numpy as np
+            import paddle
+            import numpy as np
 
-        paddle.disable_static()
+            paddle.disable_static()
 
-        x = paddle.to_tensor(np.array([1.0, 2.0, 3.0, 4.0]))
-        m = paddle.nn.LogSigmoid()
-        out = m(x) # [0.7310586, 0.880797, 0.95257413, 0.98201376]
+            x = paddle.to_tensor(np.array([1.0, 2.0, 3.0, 4.0]))
+            m = paddle.nn.LogSigmoid()
+            out = m(x) # [-0.313262 -0.126928 -0.0485874 -0.0181499]
     """
 
     def __init__(self, name=None):
@@ -721,6 +831,137 @@ def forward(self, x):
         return F.logsigmoid(x, self._name)
 
 
+class Softmax(layers.Layer):
+    """
+    Softmax Activation.
+
+    This operator implements the softmax layer. The calculation process is as follows:
+
+    1. The dimension :attr:`axis` of ``x`` will be permuted to the last.
+
+    2. Then ``x`` will be logically flattened to a 2-D matrix. The matrix's second
+    dimension(row length) is the same as the dimension :attr:`axis` of ``x``,
+    and the first dimension(column length) is the product of all other dimensions
+    of ``x``. For each row of the matrix, the softmax operator squashes the
+    K-dimensional(K is the width of the matrix, which is also the size of ``x``'s
+    dimension :attr:`axis`) vector of arbitrary real values to a K-dimensional
+    vector of real values in the range [0, 1] that add up to 1.
+
+    3. After the softmax operation is completed, the inverse operations of steps 1 and 2
+    are performed to restore the two-dimensional matrix to the same dimension as the ``x`` .
+
+    It computes the exponential of the given dimension and the sum of exponential
+    values of all the other dimensions in the K-dimensional vector input.
+    Then the ratio of the exponential of the given dimension and the sum of
+    exponential values of all the other dimensions is the output of the softmax
+    operator.
+
+    For each row :math:`i` and each column :math:`j` in the matrix, we have:
+
+    .. math::
+
+        Softmax[i, j] = \\frac{\\exp(x[i, j])}{\\sum_j(exp(x[i, j])}
+
+    Example:
+
+    .. code-block:: text
+
+        Case 1:
+          Input:
+            x.shape = [2, 3, 4]
+            x.data = [[[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]]]
+
+          Attrs:
+            axis = -1
+
+          Output:
+            out.shape = [2, 3, 4]
+            out.data = [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+                         [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
+                        [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]
+
+        Case 2:
+          Input:
+            x.shape = [2, 3, 4]
+            x.data = [[[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]]]
+          Attrs:
+            axis = 1
+
+          Output:
+            out.shape = [2, 3, 4]
+            out.data = [[[0.00657326, 0.00657326, 0.01714783, 0.01714783],
+                         [0.01786798, 0.01786798, 0.04661262, 0.04661262],
+                         [0.97555875, 0.97555875, 0.93623955, 0.93623955]],
+                        [[0.00490169, 0.00490169, 0.00490169, 0.00490169],
+                         [0.26762315, 0.26762315, 0.26762315, 0.26762315],
+                         [0.72747516, 0.72747516, 0.72747516, 0.72747516]]]
+
+    Parameters:
+        axis (int, optional): The axis along which to perform log_softmax
+            calculations. It should be in range [-D, D), where D is the
+            dimensions of ``x`` . If ``axis`` < 0, it works the same way as
+            :math:`axis + D` . Default is -1.
+        dtype (str|np.dtype|core.VarDesc.VarType, optional): The desired data
+            type of the output tensor. If dtype is specified, ``x`` is casted
+            to ``dtype`` before the operation is performed. This is useful for 
+            preventing data type overflows. Supported dtype: float32, float64.
+            If ``dtype`` is None, the output Tensor has the same dtype as x.
+            Default is None.
+        name (str, optional): Name for the operation (optional, default is None).
+            For more information, please refer to :ref:`api_guide_Name`.
+
+    Shape:
+        - input: Tensor with any shape.
+        - output: Tensor with the same shape as input.
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import numpy as np
+
+            paddle.disable_static()
+
+            x = np.array([[[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)
+            m = paddle.nn.Softmax()
+            out = m(x)
+            # [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
+            # [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
+            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]
+    """
+
+    def __init__(self, axis=-1, name=None):
+        super(Softmax, self).__init__()
+        self._axis = axis
+        self._dtype = None
+        self._name = name
+
+    def forward(self, x):
+        return F.softmax(x, self._axis, self._dtype, self._name)
+
+
 class LogSoftmax(layers.Layer):
     """
     This operator implements the log_softmax layer. The calculation process is as follows:
@@ -728,7 +969,7 @@ class LogSoftmax(layers.Layer):
     .. math::
 
         Out[i, j] = log(softmax(x)) 
-                  = log(\\frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])})
+                  = log(\frac{\exp(X[i, j])}{\sum_j(exp(X[i, j])})
 
     Parameters:
         axis (int, optional): The axis along which to perform log_softmax