Home▸Data Science▸Nesterov Momentum: Look-Ahead Gradient on an Ill-Conditioned Valley

Nesterov Momentum: Look-Ahead Gradient on an Ill-Conditioned Valley

Watch plain gradient descent, classical momentum, and Nesterov accelerated gradient race down a 3D elongated quadratic valley. Tune the condition number, learning rate, and momentum to see why the look-ahead gradient damps oscillation that heavy-ball momentum cannot.

Data Science3DAdvanced60 FPS

Plain gradient descent, classical (heavy-ball) momentum, and Nesterov accelerated gradient all chase the minimum of the same elongated quadratic bowl, rendered as a real 3D surface you can rotate. Because the valley is steep in one axis and shallow in the other, plain GD is forced into a slow, stability-limited zig-zag, while momentum overshoots and oscillates before settling. Nesterov's look-ahead gradient — evaluated at where momentum is about to carry the point, not where it currently stands — damps that oscillation and reaches the floor first. Drag the condition-number, learning-rate, and momentum sliders and watch all three trajectories race down the same surface in real time, with live loss readouts for each.

⚙ Under the hood

Race plain gradient descent, classical momentum, and Nesterov accelerated gradient down an elongated 3D quadratic valley, tuning the condition number, learning rate, and momentum to see why the look-ahead gradient damps oscillation that heavy-ball momentum cannot.

gradient descentnesterov momentumoptimizationmachine learningloss landscapeconvergence

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install