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

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.

Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Probability (math.PR)

arXiv:2609.15884 [cs.DS]

(or arXiv:2609.15884v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2609.15884 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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