feat: add hard sigmoid activation function

neural_network/activation_functions/hard_sigmoid.py

@@ -0,0 +1,47 @@
+"""
+Hard Sigmoid Activation Function
+
+Use Case: The Hard Sigmoid function serves as a computationally efficient alternative
+to the standard sigmoid function, particularly useful in scenarios where speed is
+critical, such as in deep learning models.
+
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Hard_sigmoid
+"""
+
+import numpy as np
+
+
+def hard_sigmoid(vector: np.ndarray) -> np.ndarray:
+    """
+    Implements the Hard Sigmoid Activation Function.
+
+    Parameters:
+        vector (np.ndarray): The input array for the hard sigmoid activation function.
+
+    Returns:
+        np.ndarray: The output array after applying the hard sigmoid function.
+
+    Formula:
+    f(x) = 0 if x < -2.5
+            = 1 if x > 2.5
+            = (x + 2.5) / 5 if -2.5 <= x <= 2.5
+
+    Examples:
+    >>> hard_sigmoid(np.array([-3, -2, -1, 0, 1, 2, 3]))
+    array([0. , 0.1, 0.3, 0.5, 0.7, 0.9, 1. ])
+
+    >>> hard_sigmoid(np.array([-10, -5, -2.5, 2.5, 10]))
+    array([0., 0., 0., 1., 1.])
+
+    >>> hard_sigmoid(np.array([0]))
+    array([0.5])
+
+    """
+    return np.clip((vector + 2.5) / 5, 0, 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()