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

arXiv:2609.15884 · cs.DS, cs.LG, math.PR · Submitted 2026-09-14 · Read on arXiv

cs.DS, cs.LG, math.PR

Submitted: 2026-09-14

Updated: 2026-09-14

Comments: 24 pages

Project page: https://chewisinho.github.io

License: http://creativecommons.org/licenses/by/4.0/

The gist: We show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem.

Terminology

Query Complexity — 8× in this paper · explained in 2 episodes
Accuracy — 3× in this paper · explained in 1 episode
Trace — 3× in this paper · explained in 2 episodes
Adaptation — 1× in this paper · explained in 1 episode
Core — 1× in this paper · explained in 2 episodes
Differential Privacy — 1× in this paper · explained in 4 episodes
Generalization — 1× in this paper · explained in 13 episodes
Score Function — 1× in this paper · explained in 4 episodes
Spectral Gap — 1× in this paper · explained in 5 episodes

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.

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

Terminology

Abstract

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