Don’t just say ‘class A’ — say ‘73% A’. Logistic regression squashes a weighted sum through an S-curve (the sigmoid) to give a PROBABILITY between 0 and 1, with the decision boundary where it crosses 50%. It’s the honest, calibrated workhorse of classification — and a single-neuron network with a sigmoid. Slide the input and read the probability climb.
Logistic regression models P(y=1 | x) = σ(w·x + b), where σ(z) = 1/(1+e⁻ḹ) is the logistic sigmoid. It outputs a calibrated probability in (0,1); the decision boundary is where w·x+b = 0 (p = 0.5), a hyperplane. Weights are fit by maximizing likelihood (minimizing cross-entropy) via [[the-gradient-descent|gradient descent]] — a convex problem with a unique optimum. It is the canonical linear probabilistic classifier and equals a one-neuron sigmoid network. A fail-loud self-check throws unless σ(0)=0.5 and the probability rises past the boundary. ◆ real machine learning, node-verified.
Linear in the features (a straight boundary) unless you add interaction/nonlinear terms; the probabilities are calibrated only if the model is well-specified. The sigmoid and 0.5-boundary are exact.