How models actually learn, from vanilla gradient descent to Adam
An optimizer lab compares optimizers under controlled conditions. Run the same model, data, batch size, schedule budget, and seed plan, then change the optimizer or one optimizer setting.
Without that control, optimizer comparisons become stories. A faster run may have used a better learning rate, a different schedule, or a luckier seed.
A race track test day has rules for this. If you compare two cars, you keep the track, tyres, fuel load, and weather as controlled as possible. Otherwise you cannot tell whether the car was faster or the conditions were easier. The figure below is a miniature lab bench: the same stretched surface every run, with η, β, and κ as your variables. Change exactly one, run, and compare paths. That is this lesson's whole discipline in one widget.