One Gradient-Descent Update

The problem, from first principles

03-mse-gradient told you which direction the loss gets WORSE in. To make it better, you move the opposite way — that's the entirety of gradient descent, one arithmetic step repeated many times.

The only design decision is how big a step to take. Too small and training crawls; too large and you can overshoot the minimum entirely, or bounce around it forever without settling. That step size is the learning rate, and it's the one number a training loop has to pick.

From theory to code

Theory gives the update as a single subtraction per parameter: current value minus (step size times gradient). Both weight and bias follow the identical rule — the only branch is what happens when there's no bias to begin with.

Implement gd_step(weight, bias, grad_weight, grad_bias, lr) against that reasoning. The signature and docstring are already in the editor.

Constraints

• Move weight and bias one step in the direction that reduces loss, scaled by lr, using the update rule from Theory.
• Return new values — never mutate weight, bias, grad_weight or grad_bias in place.
• If bias is None (no bias parameter, matching 01-hypothesis-function and 03-mse-gradient), return None for updated_bias too — there is nothing to step.
• Works for weight/grad_weight of any matching shape (scalar, vector, or matrix) — the update rule itself has no shape-specific logic.

Hints

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