{
  "abstract": "We establish fractional-posterior contraction for shallow ReLU networks in Gaussian random-design regression with a $β$-Hölder target, using priors independent of the sample size and smoothness parameters. For any fixed design law $P_X$ on $[0,1]^d$, we obtain contraction in Rényi divergence and, after clipping posterior draws at a bound on the target range, in squared $\\mathcal{L}^2(P_X)$ loss at rate $(\\log n/n)^{2β/(2β+d)}$. This matches the classical Hölder minimax rate up to a logarithmic factor. These priors have random finite width and use width-dependent uniform or Gaussian weight distributions, or width-independent Student $t$ distributions, including Cauchy distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23308",
  "author_total": 3,
  "authors": [
    {
      "name": "Hien Duy Nguyen"
    },
    {
      "name": "Jacob Westerhout"
    },
    {
      "name": "Julyan Arbel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbjcky1eqw7yn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23308",
  "fulltext_url": null,
  "id": "fbjcky1eqw7yn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23308",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7222980525",
  "pdf_url": "https://arxiv.org/pdf/2610.23308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbjcky1eqw7yn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Sieve-free ReLU Bayesian priors with near-minimax posterior contraction",
  "title_text": "Sieve-free ReLU Bayesian priors with near-minimax posterior contraction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/fbjcky1eqw7yn",
  "venue": "arXiv",
  "versions": []
}