Added Squareplus Activation Function (#9977)

* Added Squareplus Activation Function

* Added parameter beta to the function

* Fixed Squareplus Function

* Update neural_network/activation_functions/squareplus.py

---------

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

neural_network/activation_functions/squareplus.py

@@ -0,0 +1,38 @@
+"""
+Squareplus Activation Function
+
+Use Case: Squareplus designed to enhance positive values and suppress negative values.
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Squareplus
+"""
+
+import numpy as np
+
+
+def squareplus(vector: np.ndarray, beta: float) -> np.ndarray:
+    """
+    Implements the SquarePlus activation function.
+
+    Parameters:
+        vector (np.ndarray): The input array for the SquarePlus activation.
+        beta (float): size of the curved region
+
+    Returns:
+        np.ndarray: The input array after applying the SquarePlus activation.
+
+    Formula: f(x) = ( x + sqrt(x^2 + b) ) / 2
+
+    Examples:
+    >>> squareplus(np.array([2.3, 0.6, -2, -3.8]), beta=2)
+    array([2.5       , 1.06811457, 0.22474487, 0.12731349])
+
+    >>> squareplus(np.array([-9.2, -0.3, 0.45, -4.56]), beta=3)
+    array([0.0808119 , 0.72891979, 1.11977651, 0.15893419])
+    """
+    return (vector + np.sqrt(vector**2 + beta)) / 2
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()