training loops, backprop, optimizers, and schedulers

The training loop is where a model changes. This chapter practices the loop as inspectable state: forward pass, loss, gradient, optimizer step, schedule, checkpoint, and recovery evidence.

The exercises use small Python dictionaries and lists so every check can run in the browser. Real-world tools may be larger, but the review shape stays the same: input, decision, evidence, blocker, and next step.

By the end of the chapter, learners should be able to turn this topic into a concrete handoff instead of a vague model claim.