{
  "abstract": "We study sampling from $π(x)\\propto\\mathrm{e}^{-V(x)}$ on $\\mathbb{R}^d$, where $V$ is $α$-strongly convex and $β$-smooth with condition number $κ=β/α$. For this problem, the proximal sampler preserves the target exactly and recovers overdamped Langevin dynamics in the small-step limit, but its Gaussian resampling step discards directional information. Underdamped Langevin dynamics retains such information through momentum to accelerate exploration, motivating a proximal construction that combines target preservation with directional persistence. We introduce \\textit{reflected proximal dynamics}, which combines proximal sampling with an exact reflection of the auxiliary variable, conditional kinetic motion, and controlled refreshment. We develop two realizations: a flux-resampled underdamped half-turn and a persistent-momentum quarter-turn. From a warm start with constant $χ^2$ divergence, both methods achieve total variation error $\\varepsilon$ using $\\widetilde O(\\sqrtκd^{1/4})$ expected oracle queries. We further remove the supplied warm-start assumption by combining either sampler with existing posterior samplers in a proximal initialization stage with an optimized coarse step size. Accounting for both initialization and sampling yields $\\widetilde O(κ^{6/7}d^{1/4})$ expected oracle queries. In both regimes, the dependence on the target accuracy $\\varepsilon$ is $\\mathrm{polylog}(1/\\varepsilon)$, making reflected proximal dynamics a promising framework for accelerated high-accuracy log-concave sampling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16248",
  "author_total": 3,
  "authors": [
    {
      "name": "Bo Yuan"
    },
    {
      "name": "Wei Guo"
    },
    {
      "name": "Yongxin Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47y77370y9329.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16248",
  "fulltext_url": null,
  "id": "47y77370y9329",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16248",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221762585",
  "pdf_url": "https://arxiv.org/pdf/2610.16248",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47y77370y9329.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16248",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16248"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling",
  "title_text": "Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/47y77370y9329",
  "venue": "arXiv",
  "versions": []
}