The Secret Weapons of Deep Learning: ReLU and Leaky ReLU

ReLU and Leaky ReLU: Activation Functions in Deep Learning

In the realm of deep learning, activation functions are the gatekeepers of a neural network. They introduce non-linearity into the model, allowing it to learn intricate patterns hidden within the data. Among the most widely used activation functions are the Rectified Linear Unit (ReLU) and its refined cousin, the Leaky ReLU.

Understanding ReLU

The Rectified Linear Unit, or ReLU, is a straightforward yet remarkably effective activation function. Its defining characteristic can be expressed mathematically as follows:

f(x) = max(0, x)

In essence, ReLU outputs the input value directly if it’s positive, and clamps it to zero otherwise. Let’s visualize this with a Python example:

import numpy as np
import matplotlib.pyplot as plt

def relu(x):
    return np.maximum(0, x)

input_vals = np.linspace(-5, 5, 200)
output_vals = relu(input_vals)

plt.plot(input_vals, output_vals)
plt.xlabel("Input (x)")
plt.ylabel("Output (ReLU(x))")
plt.title("ReLU Activation Function")
plt.show()

Why ReLU Works

ReLU possesses several advantages that contribute to its popularity:

• Computational Efficiency: Its basic operation makes it fast to compute.
• Mitigating Vanishing Gradients: During backpropagation in deep neural networks, gradients can become…