Backpropagation

Backpropagation (backward propagation of errors) is the fundamental algorithm for training neural networks. It efficiently calculates how much each weight in the network contributed to the error, enabling targeted adjustments.

How backpropagation works:

1. Forward pass: Input propagates through network to output
2. Loss calculation: Compare output to target, compute error
3. Backward pass: Propagate error gradients back through layers
4. Weight update: Adjust weights to reduce error

Key concepts:

• Gradient: Direction and magnitude of steepest increase
• Chain rule: Calculates gradients through composed functions
• Learning rate: Scales gradient updates
• Loss function: Measures prediction error

Why backpropagation matters:

• Enables training of deep networks
• Computationally efficient (linear in network size)
• Foundation of all modern deep learning
• Makes neural networks practical

Without backpropagation, training the billion-parameter models we use today would be impossible.