{"paper":{"title":"On the query complexity of sampling from non-log-concave distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Chihao Zhang, Yuchen He","submitted_at":"2025-02-10T06:54:16Z","abstract_excerpt":"We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions.\n  Specifically, we show that for any $L,M$ satisfying $LM\\ge d\\ge 5$, $\\epsilon\\in \\left(0,\\frac{1}{32}\\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\\left(\\frac{LM}{d\\epsilon}\\right)^{\\Omega(d)}$ queries to compute a sample whose distribution is within $\\epsilon$ in total v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06200","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06200/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}