backpropagation
3 free lessons tagged backpropagation across Math, AI. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Automatic Differentiation: How Gradients Are Actually Computed
Frameworks do not differentiate formulas symbolically or estimate derivatives numerically. They differentiate the program. This lesson builds forward mode from dual numbers and reverse mode from the backward sweep, shows why a full gradient costs about four function evaluations at any size, and where the answer is not what you meant.
The Chain Rule, and Why Depth Is Hard
A deep network is a composition, so its derivative is a product of Jacobians. This lesson builds the chain rule from one variable up to matrix form, shows that the order you multiply that product in changes the cost tenfold, and explains vanishing gradients as an arithmetic consequence rather than a mystery.
Neural Networks and Backpropagation
Build intuition for how artificial neurons stack into layers, why nonlinear activations are non-negotiable, and how the chain rule turns a forward pass into exact gradients — illustrated with a tiny numpy forward+backward walk-through.