Neural Networks: The Foundation of Deep Learning

Neural networks are inspired by the human brain but work quite differently. Let's explore how these mathematical structures learn to recognize patterns.

What is a Neural Network?

A neural network is a computational model consisting of interconnected nodes (neurons) that process information. Each connection has a weight that determines the strength of the signal.

import numpy as np

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

def neural_network(inputs, weights, bias):
    return sigmoid(np.dot(inputs, weights) + bias)

The Learning Process

Neural networks learn through a process called backpropagation:

1. Forward pass - Data flows through the network
2. Calculate error - Compare output to expected result
3. Backward pass - Adjust weights to reduce error
4. Repeat - Continue until the network performs well

Why Neural Networks Work

The universal approximation theorem tells us that neural networks can approximate any continuous function. This mathematical property explains their incredible versatility.

Applications

• Image recognition
• Natural language processing
• Game playing (like AlphaGo)
• Scientific discovery

Neural networks have revolutionized AI by providing a general-purpose learning framework that scales with data and computation.