Add SiLU (apache#19497)

* add silu activation

* Update activations.md

* add activation images

* update activation docs

* add silu test

* add silu test

docs/python_docs/python/api/gluon/nn/index.rst

@@ -147,6 +147,8 @@ Advanced Activation Layers
     nn.ELU
     nn.SELU
     nn.Swish
+    nn.SiLU
+    nn.GELU
 
 API Reference
 -------------

docs/python_docs/python/tutorials/packages/gluon/blocks/activations/activations.md

@@ -19,7 +19,7 @@
 
 Deep neural networks are a way to express a nonlinear function with lots of parameters from input data to outputs. The nonlinearities that allow neural networks to capture complex patterns in data are referred to as activation functions. Over the course of the development of neural networks, several nonlinear activation functions have been introduced to make gradient-based deep learning tractable. 
 
-If you are looking to answer the question, 'which activation function should I use for my neural network model?', you should probably go with *ReLU*. Unless you're trying to implement something like a gating mechanism, like in LSTMs or GRU cells, then you should opt for sigmoid and/or tanh in those cells. However, if you have a working model architecture and you're trying to improve its performance by swapping out activation functions or treating the activation function as a hyperparameter, then you may want to try hand-designed activations like SELU or a function discovered by reinforcement learning and exhaustive search like Swish. This guide describes these activation functions and others implemented in MXNet in detail.
+If you are looking to answer the question, 'which activation function should I use for my neural network model?', you should probably go with *ReLU*. Unless you're trying to implement something like a gating mechanism, like in LSTMs or GRU cells, then you should opt for sigmoid and/or tanh in those cells. However, if you have a working model architecture and you're trying to improve its performance by swapping out activation functions or treating the activation function as a hyperparameter, then you may want to try hand-designed activations like SELU, SiLU, or GELU. This guide describes these activation functions and others implemented in MXNet in detail.
 
 ## Visualizing Activations
 In order to compare the various activation functions and to understand the nuances of their differences we have a snippet of code to plot the activation functions (used in the forward pass) and their gradients (used in the backward pass).
@@ -237,24 +237,40 @@ visualize_activation(mx.gluon.nn.SELU())
 ![selu activation and gradient](images/selu.png)
 
 
-### Swish
-Swish is an activation function that attempts to address the shortcomings of ReLU by combining ideas from ReLU and sigmoid. Swish was discovered by searching the space of activation functions using a combination of exhaustive and reinforcement learning-based search and was introduced in the paper by [Ramchandran et al](https://arxiv.org/pdf/1710.05941.pdf).
+### SiLU
+The SiLU is an activation function that attempts to address the shortcomings of ReLU by combining ideas from ReLU and sigmoid. The SiLU serves as a smooth approximation to the ReLU and was originally introduced in [Hendrycks et al](https://arxiv.org/abs/1606.08415).
 
-The swish function is given as 
+The silu function is given as 
 
-$$ swish(x) = x\cdot\sigma(\beta x)$$
+$$ silu(x) = x\cdot\sigma(x)$$
 
-where $\sigma$ is the sigmoid activation function $\sigma(x) = \frac{1}{1 + e^{-x}}$ described above and $\beta$ is a hyperparameter set to 1 by default in MXNet.
+where $\sigma$ is the sigmoid activation function $\sigma(x) = \frac{1}{1 + e^{-x}}$ described above.
 
 
 ```{.python .input}
-visualize_activation(mx.gluon.nn.Swish())
+visualize_activation(mx.gluon.nn.SiLU())
 ```
 
 
-![swish activation and gradient](images/swish.png)
+![silu activation and gradient](images/silu.png)
 
+### GELU
+The GELU is a smooth approximation to the ReLU and was introduced in [Hendrycks et al](https://arxiv.org/abs/1606.08415). It is a common activation function in architectures such as Transformers, BERT, and GPT.
 
+The gelu function is given as 
+
+$$ gelu(x) = x\cdot\Phi(x),$$
+
+whereas the ReLU can be written as $x\cdot\mathbf{1}(x>0)$, so $Phi(x)$ serves as a smooth approximation to the ReLU's indicator function.
+
+Note $\Phi(x) = \frac{1}{\sqrt{2 \pi}} \exp\left\{-\frac{x^2}{2}\right\}$ is the standard normal cumulative distribution.
+
+
+```{.python .input}
+visualize_activation(mx.gluon.nn.GELU())
+```
+
+![gelu activation and gradient](images/gelu.png)
 
 ## Summary
 
@@ -263,7 +279,7 @@ visualize_activation(mx.gluon.nn.Swish())
 * Sigmoids like the logistic (sigmoid) function and tanh where the first kinds of activation functions used in neural networks. They have since fallen out of use because of their tendency to saturate and have vanishing gradients.
 * Rectifiers like ReLU do not saturate like the Sigmoids and so address the vanishing gradient problem making them the de facto activation functions. ReLU however is still plagued by the dying ReLU problem.
 * LeakyReLU and PReLU are two similar approaches to improve ReLU and address the dying ReLU by introducing a parameter $\alpha$ (learned in PReLU) that leaks to the gradient of negative inputs
-* MXNet also implements custom state-of-the-art activations like ELU, SELU and Swish.
+* MXNet also implements custom state-of-the-art activations like ELU, SELU, SiLU, and GELU.
 
 
 

python/mxnet/gluon/nn/activations.py

@@ -18,7 +18,7 @@
 # coding: utf-8
 # pylint: disable= arguments-differ
 """Basic neural network layers."""
-__all__ = ['Activation', 'LeakyReLU', 'PReLU', 'ELU', 'SELU', 'Swish', 'GELU']
+__all__ = ['Activation', 'LeakyReLU', 'PReLU', 'ELU', 'SELU', 'Swish', 'GELU', 'SiLU']
 
 from ... import initializer
 from ..block import HybridBlock
@@ -215,7 +215,7 @@ def hybrid_forward(self, F, x):
 
 class Swish(HybridBlock):
     r"""
-    Swish Activation function
+    Swish Activation function (SiLU with a hyperparameter)
         https://arxiv.org/pdf/1710.05941.pdf
 
     Parameters
@@ -240,3 +240,32 @@ def hybrid_forward(self, F, x):
             return x * F.npx.sigmoid(self._beta * x)
         else:
             return x * F.sigmoid(self._beta * x, name='fwd')
+
+
+class SiLU(HybridBlock):
+    r"""
+    Sigmoid Linear Units
+        Originally proposed "Gaussian Error Linear Units (GELUs)", Hendrycks et al, 2016
+        https://arxiv.org/abs/1606.08415
+
+    Parameters
+    ----------
+    beta : float
+        silu(x) = x * sigmoid(x)
+
+
+    Inputs:
+        - **data**: input tensor with arbitrary shape.
+
+    Outputs:
+        - **out**: output tensor with the same shape as `data`.
+    """
+
+    def __init__(self, **kwargs):
+        super(SiLU, self).__init__(**kwargs)
+
+    def hybrid_forward(self, F, x):
+        if is_np_array():
+            return x * F.npx.sigmoid(x)
+        else:
+            return x * F.sigmoid(x, name='fwd')

tests/python/unittest/test_gluon.py

@@ -1302,6 +1302,13 @@ def swish_test(x):
     for test_point, ref_point in zip(swish_test(point_to_validate), swish(point_to_validate)):
         assert test_point == ref_point
 
+    silu = mx.gluon.nn.SiLU()
+    def silu_test(x):
+        return x * mx.nd.sigmoid(x)
+
+    for test_point, ref_point in zip(silu_test(point_to_validate), silu(point_to_validate)):
+        assert test_point == ref_point
+
     elu = mx.gluon.nn.ELU()
     def elu_test(x):
         def elu(x):

tests/python/unittest/test_numpy_gluon.py

@@ -483,6 +483,13 @@ def test_activations_swish():
     out = act_layer(mx.np.random.uniform(size=(10,)))
     out.asnumpy()
 
+
+@use_np
+def test_activations_silu():
+    act_layer = nn.SiLU()
+    out = act_layer(mx.np.random.uniform(size=(10,)))
+    out.asnumpy()
+
 @use_np
 def test_concatenate():
     model = nn.HybridConcatenate(axis=1)