The interactive film is in the book's Companion

Play it, pause it, turn it and drag it with Mathematics for AI and Machine Learning.

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Stein Variational Gradient Descent: Pull and Push

Chapter 21 · Mathematics for AI and Machine Learning · Advanced · 1:29

An interactive live film: fifty particles move deterministically over a 2D Gaussian target drawn as a 3D surface, pulled by the kernel-smoothed score and pushed apart by the kernel gradient; switch the repulsion off and they collapse to the mode, drag the mode or the kernel bandwidth and the cloud follows.

Narration

Here is a target density pi, a Gaussian bump over the plane, drawn as a surface. Its mode is the orange star on the floor.

Fifty blue particles start in a tight bunch in the corner, far from the mode.

The rest of the narration is in the book's Companion.

More from Chapter 21

Interactive1:35Fokker-Planck: A Random Cloud, a Deterministic DensityChapter 21Preview1:29Detailed Balance: Stationary Is Not the Same as StillChapter 21Preview1:28Forward Diffusion and the Heat Equation: All Distributions Become GaussianChapter 21Preview1:27Guidance Does Not Sample the Sharpened DistributionChapter 21Preview1:50Metastability and the Kramers Escape RateChapter 21Preview1:26Reverse Time: Why We Must Learn the ScoreChapter 21Preview1:34Unification: SDEs, Probability Flow ODEs, and Fokker-Planck DynamicsChapter 21Preview1:52Discretization Changes the Stationary DistributionChapter 21