SGD

The problem, from first principles

04-gd-step (Classical ML) already implemented gradient descent's update rule, but specifically for one weight matrix and one bias vector, linear_regression's own two parameters. A real neural network has dozens, sometimes billions, of parameters spread across many layers, and every single one of them needs the exact same update rule applied, independently, every training step. This question generalizes 04-gd-step's specific update into the general form every optimizer in this track (and every optimizer in torch.optim) actually takes: operate on a LIST of parameters and their gradients, applying one uniform rule to all of them at once.

From theory to code

Theory applies the identical "step opposite the gradient" rule from 04-gd-step to every (parameter, gradient) pair in two lists, independently.

Implement sgd_step(params, grads, lr) against that reasoning. The signature and docstring are already in the editor.

Constraints

• params and grads are parallel lists (same length, matched by index).
• Return a NEW list, don't mutate the input arrays in place.
• Every parameter uses the SAME learning rate lr.

Hints

Open one at a time. Each gives away a little more than the last.