Understanding Neural Networks

Neural networks are a cornerstone of modern artificial intelligence. Inspired by the human brain, they consist of layers of interconnected nodes (neurons) that can learn complex patterns from data.

Key Concepts

• Neuron: Basic processing unit that applies a weighted sum and an activation function.
• Layers: Input, hidden, and output layers define the network architecture.
• Activation Functions: Introduce non‑linearity (e.g., ReLU, Sigmoid, Tanh).
• Training: Adjusts weights using backpropagation and gradient descent.

Simple Example in Python

import numpy as np

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# Input data
X = np.array([[0,0],[0,1],[1,0],[1,1]])
# Expected output
y = np.array([[0],[1],[1],[0]])

# Initialize weights
np.random.seed(42)
W1 = np.random.randn(2,2)
b1 = np.zeros((1,2))
W2 = np.random.randn(2,1)
b2 = np.zeros((1,1))

# Forward pass
def forward(X):
    Z1 = X.dot(W1) + b1
    A1 = sigmoid(Z1)
    Z2 = A1.dot(W2) + b2
    A2 = sigmoid(Z2)
    return A2

print(forward(X))

This code demonstrates a minimal two‑layer neural network that learns the XOR problem.