⛓️ The Chain Rule

The Chain Rule is the mathematical trick that makes Neural Networks possible.

⚙️ The Gear Analogy

Imagine three gears connected together: Gear A turns Gear B, which turns Gear C. If you want to know how fast Gear C turns when you spin Gear A, you multiply the ratios together!

🐍 Python Implementation

PyTorch handles the chain rule automatically during backward(). We call this entire process Backpropagation.

import torch

x = torch.tensor(2.0, requires_grad=True)

# Chain of operations
a = x * 3      # Gear 1
b = a ** 2     # Gear 2
loss = b + 5   # Gear 3

# PyTorch applies the chain rule instantly backwards through the chain!
loss.backward()

print("Derivative of loss with respect to x:", x.grad)