Implemented Gelu Function (#7368)

* Implemented Gelu Function

* Renamed file and added more description to function

* Extended the name GELU

* Update gaussian_error_linear_unit.py

Co-authored-by: Christian Clauss <cclauss@me.com>

maths/gaussian_error_linear_unit.py

@@ -0,0 +1,53 @@
+"""
+This script demonstrates an implementation of the Gaussian Error Linear Unit function.
+* https://en.wikipedia.org/wiki/Activation_function#Comparison_of_activation_functions
+
+The function takes a vector of K real numbers as input and returns x * sigmoid(1.702*x).
+Gaussian Error Linear Unit (GELU) is a high-performing neural network activation
+function.
+
+This script is inspired by a corresponding research paper.
+* https://arxiv.org/abs/1606.08415
+"""
+
+import numpy as np
+
+
+def sigmoid(vector: np.array) -> np.array:
+    """
+    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 gaussian_error_linear_unit(vector: np.array) -> np.array:
+    """
+    Implements the Gaussian Error Linear Unit (GELU) function
+
+    Parameters:
+        vector (np.array): A  numpy array of shape (1,n)
+        consisting of real values
+
+    Returns:
+        gelu_vec (np.array): The input numpy array, after applying
+        gelu.
+
+    Examples:
+    >>> gaussian_error_linear_unit(np.array([-1.0, 1.0, 2.0]))
+    array([-0.15420423,  0.84579577,  1.93565862])
+
+    >>> gaussian_error_linear_unit(np.array([-3]))
+    array([-0.01807131])
+    """
+    return vector * sigmoid(1.702 * vector)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()