This sandbox was generated by Claude (Anthropic) for the ML 101 course materials. It trains a real soft-margin support vector machine on a small 2D dataset with an actual dual solver — a simplified SMO — and shows the four things the Module 4 lesson describes in words: the decision boundary, the two margin lines at a functional margin of ±1, the support vectors that alone determine the fit, and the maximum margin the SVM is built to find. Nothing here is sketched — the boundary and the margins are drawn by evaluating the solved decision function f(x) over a grid.

C is the softness dial, and the page shows exactly what it buys. Small C tolerates violations to keep the margin wide; large C insists every point sit outside its margin, so the margin narrows and the boundary bends toward the awkward points. The margin width is 2/‖w‖ and it is computed from the solved w, so you can watch it grow as you lower C. Switch the kernel to RBF and a boundary a straight line could never draw — the circle, the XOR — snaps into place, at the cost of a gamma you can over-tune into overfitting.

SMO is iterative, and this page is honest about it. It runs to a fixed KKT tolerance with a generous pass budget and reports the iteration count and whether it converged. On a small linearly separable set it reaches the analytic maximum-margin answer; where a solve does not settle, the page says so rather than printing an unconverged margin as if it were exact.

Computed: every dataset (seeded and reproducible), the trained dual variables, w and b for the linear kernel, ‖w‖ and the margin 2/‖w‖, the support-vector set, the hinge loss and the number of margin violations, the train accuracy, the C-sweep of margin width and support-vector count, and the boundary by evaluating f() on a grid. Published figures: none — everything is a definition or a direct computation. Chosen rather than computed: the four dataset shapes, the class separation, the label-noise level, the point count, the seed, and the default C, kernel and gamma.