Added Scaled Exponential Linear Unit Activation Function (#9027)

* Added Scaled Exponential Linear Unit Activation Function

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* Update scaled_exponential_linear_unit.py

* Update scaled_exponential_linear_unit.py

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* Update scaled_exponential_linear_unit.py

* Update scaled_exponential_linear_unit.py

* Update scaled_exponential_linear_unit.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update scaled_exponential_linear_unit.py

* Update scaled_exponential_linear_unit.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: AdarshAcharya5

Diff for: neural_network/activation_functions/scaled_exponential_linear_unit.py

@@ -0,0 +1,44 @@
+"""
+Implements the Scaled Exponential Linear Unit or SELU function.
+The function takes a vector of K real numbers and two real numbers
+alpha(default = 1.6732) & lambda (default = 1.0507) as input and
+then applies the SELU function to each element of the vector.
+SELU is a self-normalizing activation function. It is a variant
+of the ELU. The main advantage of SELU is that we can be sure
+that the output will always be standardized due to its
+self-normalizing behavior. That means there is no need to
+include Batch-Normalization layers.
+References :
+https://iq.opengenus.org/scaled-exponential-linear-unit/
+"""
+
+import numpy as np
+
+
+def scaled_exponential_linear_unit(
+    vector: np.ndarray, alpha: float = 1.6732, lambda_: float = 1.0507
+) -> np.ndarray:
+    """
+    Applies the Scaled Exponential Linear Unit function to each element of the vector.
+    Parameters :
+        vector : np.ndarray
+        alpha : float (default = 1.6732)
+        lambda_ : float (default = 1.0507)
+
+    Returns : np.ndarray
+    Formula : f(x) = lambda_ * x if x > 0
+                     lambda_ * alpha * (e**x - 1) if x <= 0
+    Examples :
+    >>> scaled_exponential_linear_unit(vector=np.array([1.3, 3.7, 2.4]))
+    array([1.36591, 3.88759, 2.52168])
+
+    >>> scaled_exponential_linear_unit(vector=np.array([1.3, 4.7, 8.2]))
+    array([1.36591, 4.93829, 8.61574])
+    """
+    return lambda_ * np.where(vector > 0, vector, alpha * (np.exp(vector) - 1))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()