Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start
Thin-shell stability proof along the Gaussian cooling path improves cold-start logconcave sampling complexity to near n^2.5 from n^2.75.
The authors prove that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This yields improved complexity for sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions the complexity is nearly n^2.5, improving the previous n^2.75 bound and matching the abstract Speedy walk.
- Generalizes thin-shell theorem to the Gaussian cooling path
- Cold-start logconcave sampling complexity improves from n^2.75 to nearly n^2.5
- Matches the complexity of the abstract Speedy walk
Full article62 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.15884