{
  "abstract": "The unadjusted Langevin algorithm (ULA) and its stochastic-gradient variant, SGLD, are workhorses of modern Bayesian machine learning, but can be fragile when faced with a target distribution possessing a non-Lipschitz drift. In such settings, the expected squared jump distance can grow rapidly, leading to numerical instability or the need for prohibitively small step-sizes. We propose the saturated unadjusted Langevin algorithm (SULA) that pairs a saturated gradient drift with a gradient-informed state-dependent diffusion, while preserving first-order consistency with the Langevin diffusion. The drift and diffusion terms are chosen to guarantee that the one-step squared update is independent of the gradient. Consequently, SULA is robust to the choice of step-size and preserves estimation and prediction quality. We provide sufficient conditions under which SULA with a step-size $h$ converges weakly to the Langevin diffusion at the standard $O(h)$ rate, the SULA chain is geometrically ergodic, and that the bias of its invariant measure relative to the target is $O(h)$. Further, we develop SG-SULA, a stochastic-gradient version of SULA that rescales the stochastic gradient using a Gaussian CDF correction under Gaussianity of the gradient noise. Numerical experiments on various examples demonstrate SULA's robustness to tuning and SG-SULA's improved predictive performance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19670",
  "author_total": 2,
  "authors": [
    {
      "name": "Ritik Soni"
    },
    {
      "name": "Dootika Vats"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ntd6j6s5fy30.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19670",
  "fulltext_url": null,
  "id": "9ntd6j6s5fy30",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19670",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7222009396",
  "pdf_url": "https://arxiv.org/pdf/2610.19670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ntd6j6s5fy30.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "SULA: Robust Langevin Sampling via Drift-Diffusion Saturation",
  "title_text": "SULA: Robust Langevin Sampling via Drift-Diffusion Saturation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/9ntd6j6s5fy30",
  "venue": "arXiv",
  "versions": []
}