Added A General Swish Activation Function inNeural Networks (#10415)

* Added A General Swish Activation Function inNeural Networks

* Added the general swish function in the SiLU function and renamed it as swish.py

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Co-authored-by: Shivansh Bhatnagar <shivansh.bhatnagar.mat22@iitbhu.ac.in>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

neural_network/activation_functions/swish.py

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+"""
+This script demonstrates the implementation of the Sigmoid Linear Unit (SiLU)
+or swish function.
+* https://en.wikipedia.org/wiki/Rectifier_(neural_networks)
+* https://en.wikipedia.org/wiki/Swish_function
+
+The function takes a vector x of K real numbers as input and returns x * sigmoid(x).
+Swish is a smooth, non-monotonic function defined as f(x) = x * sigmoid(x).
+Extensive experiments shows that Swish consistently matches or outperforms ReLU
+on deep networks applied to a variety of challenging domains such as
+image classification and machine translation.
+
+This script is inspired by a corresponding research paper.
+* https://arxiv.org/abs/1710.05941
+* https://blog.paperspace.com/swish-activation-function/
+"""
+
+import numpy as np
+
+
+def sigmoid(vector: np.ndarray) -> np.ndarray:
+    """
+    Mathematical function sigmoid takes a vector x of K real numbers as input and
+    returns 1/ (1 + e^-x).
+    https://en.wikipedia.org/wiki/Sigmoid_function
+
+    >>> sigmoid(np.array([-1.0, 1.0, 2.0]))
+    array([0.26894142, 0.73105858, 0.88079708])
+    """
+    return 1 / (1 + np.exp(-vector))
+
+
+def sigmoid_linear_unit(vector: np.ndarray) -> np.ndarray:
+    """
+    Implements the Sigmoid Linear Unit (SiLU) or swish function
+
+    Parameters:
+        vector (np.ndarray): A  numpy array consisting of real values
+
+    Returns:
+        swish_vec (np.ndarray): The input numpy array, after applying swish
+
+    Examples:
+    >>> sigmoid_linear_unit(np.array([-1.0, 1.0, 2.0]))
+    array([-0.26894142,  0.73105858,  1.76159416])
+
+    >>> sigmoid_linear_unit(np.array([-2]))
+    array([-0.23840584])
+    """
+    return vector * sigmoid(vector)
+
+
+def swish(vector: np.ndarray, trainable_parameter: int) -> np.ndarray:
+    """
+    Parameters:
+        vector (np.ndarray): A  numpy array consisting of real values
+        trainable_parameter: Use to implement various Swish Activation Functions
+
+    Returns:
+        swish_vec (np.ndarray): The input numpy array, after applying swish
+
+    Examples:
+    >>> swish(np.array([-1.0, 1.0, 2.0]), 2)
+    array([-0.11920292,  0.88079708,  1.96402758])
+
+    >>> swish(np.array([-2]), 1)
+    array([-0.23840584])
+    """
+    return vector * sigmoid(trainable_parameter * vector)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()