Train a Model with Your Engine

You built the autograd engine. Now use it to actually learn, the loop that trains every neural network. The Value class is given (it now also wraps plain numbers, so w * x works when x is a float). Your job is the training loop.

Fit a single weight w so w * x predicts y. One step of gradient descent is always the same moves:

w = Value(0.0)
for step in range(steps):
    loss = Value(0.0)
    for x, y in zip(xs, ys):
        diff = w * x + (-y)          # prediction minus target
        loss = loss + diff * diff    # squared error, summed
    w.grad = 0.0                     # 1) reset the gradient
    loss.backward()                  # 2) backprop to fill w.grad
    w.data -= lr * w.grad            # 3) step downhill

Two easy mistakes: zero the gradient before each backward() or old gradients pile up (backward uses +=); and subtract lr * w.grad to go downhill, not add. Over enough steps w slides to the value that minimises the loss, the line of best fit.

Write fit(xs, ys, steps, lr) starting from w = Value(0.0), returning the final w.data. Press Run to watch it learn y = 2x.