{
  "abstract": "Classical PAC-Bayesian generalization theory places prior distributions over Euclidean parameter space $Θ\\subseteq \\mathbb{R}^D$, causing relative entropy to scale with network dimension $D$. For modern overparameterized neural networks where $D \\gg n$, this parameter-counting dependency yields vacuous generalization bounds ($> 1{,}000\\%$). In this work, we resolve this barrier by shifting prior specification from internal parameters to the non-parametric space of data distributions $\\mathcal{M}_1(\\mathcal{Z})$ via a \\textbf{Dirichlet Process (DP)}, $\\mathcal{DP}(α, F_0)$, inducing parameter distributions through push-forward measures under the learning algorithm. By the Data Processing Inequality, parameter-space relative entropy is strictly bounded by the data-space DP divergence, which we evaluate in exact closed form using Digamma functions. The resulting PAC-Bayesian certificate is strictly invariant to network parameter count $D$, width, and depth. On intrinsic $d^*$-dimensional submanifolds, optimal partition scaling achieves the minimax non-parametric rate $\\mathcal{O}(n^{-1/(d^*+2)} \\sqrt{\\ln n})$. Across vision architectures scaling up to 4.2 million parameters ($D = 7{,}850$ to $D = 4{,}203{,}522$) on the full MNIST benchmark, while classical weight-space bounds scale past $940\\%$ (becoming vacuous), our data-space DP-PAC-Bayes certificate remains stable, non-vacuous, and certified at \\textbf{$8.8\\%$--$9.4\\%$}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21340",
  "author_total": 1,
  "authors": [
    {
      "name": "Sumit Vashishtha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vf9sjax8rhx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21340",
  "fulltext_url": null,
  "id": "4vf9sjax8rhx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21340",
  "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.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7222489880",
  "pdf_url": "https://arxiv.org/pdf/2610.21340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vf9sjax8rhx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Dimension-Free PAC-Bayes Generalization for Deep Neural Networks via Dirichlet Processes",
  "title_text": "Dimension-Free PAC-Bayes Generalization for Deep Neural Networks via Dirichlet Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/4vf9sjax8rhx8",
  "venue": "arXiv",
  "versions": []
}