A perceptron is a weighted sum plus a bias, squashed by a nonlinearity like tanh; alone it draws one hyperplane. Stack perceptrons into layers and the compositions of tanh bumps can be summed to trace any continuous shape — Cybenko's universal approximation theorem. Depth helps: each layer composes features from the last, so expressivity grows fast with layers. Training is exactly Lesson 1's loop — measure the mean-squared error, get the exact gradient from the tape, step every weight downhill with Adam (which adapts a per-weight step size). But note what the network does NOT have: any notion of energy, momentum, or the equations of motion. It fits the training points and interpolates smoothly, yet outside the data it can do anything at all. That blind extrapolation, plus the appetite for data, is the whole reason the rest of this course injects physics.