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Gradient Descent Visualizer — Real Numerical Optimization, Live Loss Surface

Watch real gradient descent run on a live loss surface — the gradient is computed numerically via central finite differences, then the standard update rule runs from your chosen starting point, the same core loop that trains neural networks. Himmelblau's function, a genuine optimization benchmark with four known equal-value minima, shows the actual point of the technique: different starting points converge to genuinely different valleys, and a learning rate set too high visibly diverges instead of converging.

How to use Gradient Descent Visualizer

1. Pick a function — a simple bowl, or Himmelblau's four-minima surface.
2. Set a starting point on the loss surface.
3. Adjust the learning rate and watch the descent path.
4. Try a high learning rate on the bowl to see divergence.

Frequently asked questions

Why does starting point change which minimum is found?

Gradient descent only ever follows the local downhill slope from wherever it starts — it has no visibility into the rest of the surface, so on Himmelblau's function (four separate, equally deep valleys) the starting point alone determines which valley it falls into.

Why does a high learning rate cause divergence instead of faster convergence?

Each step moves proportionally to the gradient times the learning rate — too large a step overshoots the minimum entirely and lands somewhere with an even steeper gradient, compounding on the next step until the values blow up, rather than settling down.

Is the gradient computed with real calculus or approximated?

Numerically approximated via central finite differences — evaluating the function at nearby points and computing the slope — which works for any function you plug in without needing a hand-derived symbolic derivative, at a small, well-understood accuracy cost.

Is this actually how neural networks train?

Yes — the same update rule (move against the gradient, scaled by a learning rate) is the core of how neural network weights are optimized, just computed via backpropagation on a vastly higher-dimensional loss surface instead of the numerical method used here for a simple 2D visualization.

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