Gradient descent: walk downhill on the loss
A ball rolls along the parabola L(w) = (w-3)^2 + 1, starting at w = -1 and updating via w <- w - eta dL/dw with eta = 0.3. Each iteration is tabulated showing w, the slope dL/dw, and the resulting step size, revealing how steps shrink automatically as the curve flattens near the minimum at w = 3. Useful for introducing gradient descent mechanics in calculus or machine learning courses.
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The prompt that made it
A ball on the loss curve L(w) = (w-3)^2 + 1 takes steps w <- w - eta dL/dw from w = -1 with eta = 0.3; each step and slope is tabulated and the steps shrink as the slope flattens near the minimum at w = 3.
Make the next one in this series
- Show what happens to convergence when eta is too large and the ball overshoots past w = 3.
- Compare gradient descent paths on a steep versus shallow parabola side by side.
- Animate gradient descent on a function with two local minima to show getting stuck.
