Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start

2026-09-14

AI Summary

本文通过证明对数凹概率测度沿高斯冷却路径的薄壳稳定性，改进了从冷启动采样任意对数凹分布的复杂度至近n^2.5。

Abstract

We show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This result leads to improved complexity for the fundamental problem of sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions, the complexity is nearly $n^{2.5}$, improving the previous bound of $n^{2.75}$, and matching the complexity of the abstract Speedy walk.

Problem

• logconcave sampling
• Gaussian cooling
• thin-shell stability
• complexity

Innovation

• logconcave sampling
• thin-shell stability
• Gaussian cooling path
• complexity improvement