Gradient descent, by hand
Watch a point roll downhill on a non-convex loss surface. Tune the learning rate and starting point and see what happens.
step0
x-1.700
loss f(x)0.388
gradient-3.063
Crank the learning rate past ~0.45 to see it overshoot and bounce; drop it low to watch it crawl.
What you're looking at
The blue curve is a loss landscape with two valleys. The orange dot starts where you place it and, each step, moves opposite the gradient scaled by the learning rate — plain vanilla gradient descent, the same update that trains neural networks, just in one dimension so you can see it.
- Low learning rate → slow, reliable crawl.
- High learning rate → overshoots, bounces, can diverge.
- Starting point → decides which valley you fall into.
It's a React island: zero JavaScript ships for the rest of the site, but this component hydrates and runs entirely client-side.