Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limits
Stein variational gradient descent (SVGD) transports interacting particles toward a target distribution through deterministic kernelized dynamics. Singular Riesz kernels are attractive because they can provide quantitative population-level convergence, but at the finite-particle level the corresponding Stein energy has infinite self-interaction. We study periodic Riesz SVGD with self-interaction removed and prove a many-particle, long-time sampling theorem. Throughout the range in which the singular Stein energy is locally integrable, under a uniform bound on the initial relative entropy per particle, the time-averaged empirical-measure law converges weakly to the point mass \(δ_π\) at th...
| Authors | Trevor Teolis, Maarten V. de Hoop |
|---|---|
| Primary category | math.AP |
| Published | 16 July 2026 |
| Last updated at source | 16 July 2026 |
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