Backpropagation

Knows that backprop computes gradients automatically so we can update weights.

Traces gradient flow through a 2-layer network by hand; understands forward/backward pass.

Implements autograd from scratch; can debug vanishing/exploding gradients; understands gradient checkpointing.

Implements custom backward passes; understands higher-order derivatives; applies BPTT for sequential models.

Contributes to automatic differentiation research, implicit differentiation, or meta-learning backprop variants.