Backpropagation

Backpropagation is the fundamental algorithm for training neural networks by computing how each weight contributes to the error.

Process: 1. Forward Pass: Input flows through network, produces output 2. Loss Calculation: Compare output to expected result 3. Backward Pass: Calculate gradient of loss for each weight 4. Update: Adjust weights to reduce loss

• **Key Concepts:**
• Chain Rule: Calculates gradients layer by layer
• Gradient Descent: Uses gradients to update weights
• Learning Rate: Controls size of weight updates

Why It Works: - Efficiently computes gradients for all weights - Enables training of deep networks - Foundation of modern deep learning

Challenges: - Vanishing gradients in deep networks - Exploding gradients - Local minima