Added Mish Activation Function (#9942)

* Added Mish Activation Function

* Apply suggestions from code review

---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: kausthub-kannan

neural_network/activation_functions/mish.py

@@ -0,0 +1,39 @@
+"""
+Mish Activation Function
+
+Use Case: Improved version of the ReLU activation function used in Computer Vision.
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Mish
+"""
+
+import numpy as np
+
+
+def mish(vector: np.ndarray) -> np.ndarray:
+    """
+        Implements the Mish activation function.
+
+        Parameters:
+            vector (np.ndarray): The input array for Mish activation.
+
+        Returns:
+            np.ndarray: The input array after applying the Mish activation.
+
+        Formula:
+            f(x) = x * tanh(softplus(x)) = x * tanh(ln(1 + e^x))
+
+    Examples:
+    >>> mish(vector=np.array([2.3,0.6,-2,-3.8]))
+    array([ 2.26211893,  0.46613649, -0.25250148, -0.08405831])
+
+    >>> mish(np.array([-9.2, -0.3, 0.45, -4.56]))
+    array([-0.00092952, -0.15113318,  0.33152014, -0.04745745])
+
+    """
+    return vector * np.tanh(np.log(1 + np.exp(vector)))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()