Sigmoid

logistic regression is the method that seems only ever to be used for classification yet insists on calling itself regression. the resolution: it is regression — of the log-odds of a bernoulli success probability onto a linear predictor. 𐃏 this page develops it the honest way, as a generalised linear model: bernoulli response, canonical logit link, likelihood fitted by fisher scoring, inference through the deviance. the machine-learning reading (cross-entropy loss, linear decision boundaries) falls out at the end as a corollary.

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.