ML From Zero: Self-Guided Roadmap & Simulator

The native simulator has one scalar weight and the illustrative loss, weight minus three squared plus one. Reset places the weight at zero point five, so the loss is seven point two five and the derivative is minus five. Compare one native Step at learning rates zero point two and zero point eight. Subtracting rate times derivative produces weight one point five in the first case and four point five in the second. The first stays left of the minimum at three; the second crosses to its right. Both new losses are exactly three point two five because their distances from three are equal. Blue squares mark the initial point and pink squares mark each exact result. Both held curves use the same fifty five pixels per weight unit and eighteen pixels per loss unit. This is a source toy quadratic, not a full neural network training run. Crossing a minimum is not automatically failure, and a bigger learning rate is not generally better. Reset again and set the native learning rate to zero point two. The button named Auto Converge schedules exactly six Step calls. It does not run until a requested tolerance. Define error as weight minus three. Substituting the source derivative into its update gives new error equal to one minus twice the rate, multiplied by old error. At rate zero point two this factor is zero point six. Starting error is minus two point five. Each successive exact held bar therefore shrinks in magnitude by the same factor. All errors remain negative here and extend downward from the zero line at eighty pixels per error unit. After the sixth step the error is minus zero point one one six six four, the weight is two point eight eight three three six, and the true loss is approximately one point zero one three six zero five. The minimum possible loss is one, so the weight is closer without being exactly optimal. The teaching bars show seven exact recurrence states, including the initial state, rather than an invented smooth numeric transition. Set the native rate slider to zero point five and reset the weight. Now one minus twice the rate is exactly zero. A single native Step therefore maps the initial weight zero point five to three, where the source quadratic has loss one and derivative zero. A second Step leaves the weight at three because there is no gradient to subtract. The left plot uses sixty pixels per weight unit and twenty pixels per loss unit, and its pink square sits at the exact source minimum. This one step result relies on this particular quadratic curvature and chosen rate. It is not a promise for arbitrary loss functions, multivariable models, or noisy gradients. The page roadmap and its search challenge are separate learning aids. The search challenge matches local keywords; this explainer does not claim it performs a real web search, independently verifies external discussion threads, or guarantees a career outcome.