[2603.25622] The Geometry of Efficient Nonconvex Sampling

Computer Science > Data Structures and Algorithms arXiv:2603.25622 (cs) [Submitted on 26 Mar 2026] Title:The Geometry of Efficient Nonconvex Sampling Authors:Santosh S. Vempala, Andre Wibisono View a PDF of the paper titled The Geometry of Efficient Nonconvex Sampling, by Santosh S. Vempala and Andre Wibisono View PDF HTML (experimental) Abstract:We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$. Subjects: Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML) Cite as: arXiv:2603.25622 [cs.DS]   (or arXiv:2603.25622v1 [cs.DS] for this version)   https://doi.org/10.48550/arXiv.2603.25622 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andre Wibisono [view email] [v1] Thu, 26 Mar 2026 16:35:53 UTC (820 KB) Full-text links: Access Paper: View a PDF of the paper titled The Geometry of Efficient Nonconvex Sampling, by Santosh S. Vempala and Andre WibisonoView PDFHTML (experimental)TeX Source view license Current browse c...