Logistic Regression: Sigmoid Decision Boundary (2D)

Logistic regression is the workhorse of binary classification: a linear score run through a sigmoid to turn it into a probability. This 2D-canvas companion to the 3D sim renders that idea as a flat colour field — a scatter of labeled points sits over a background shaded by p(x), the sigmoid probability, with the white decision-boundary line marking exactly where the model is 50/50. Drag the weight sliders to reshape the field and watch the boundary slide across the canvas, click anywhere to drop your own labeled point and see it join the loss calculation live, or click Train step to run one real batch gradient-descent update against the binary cross-entropy loss and watch the model converge on its own.