Linear-Classifier

the perceptron is the hydrogen atom of neural networks: one neuron, one weight vector, one threshold — and yet it already exhibits the two behaviours that define the whole field. 𐃏 it learns from mistakes with a provable convergence guarantee, and it fails on problems its geometry cannot express. this page covers both, then swaps the hard threshold for a sigmoid so that gradient descent can take over — a companion to the sign-loss perceptron page, which treats the classical algorithm on its own.