{
  "abstract": "A solid understanding of the predictive success of deep neural networks (DNNs) remains elusive. For example, while many data-dependent metrics exist that seek to predict model quality of DNNs, these metrics may be expensive to compute for large datasets and/or may be impossible to compute when training datasets are not released. A practical and effective predictor of model quality involves analyzing DNN weight matrices, as prior work has established that heavy-tailed spectral distributions in trained weight matrices can be strongly predictive of model quality. However, such metrics lack a rigorous statistical justification. In this work, we aim to understand why these metrics perform well, from a statistical perspective. To do so, we employ a probabilistic framework to derive the marginal likelihood for a DNN, evaluated using only the final layer weights. Across large-scale convolutional DNNs and LLMs, we find that this marginal likelihood predicts model quality. To understand the role heavy-tailed spectra play in predictive performance, we derive the limiting log-marginal likelihood for spectra that follow the (heavy-tailed) High-Temperature Marchenko-Pastur (HTMP) distribution. We show that this limiting quantity is convex in a heaviness parameter, and we derive an optimal heaviness that empirically predicts over-fitting for large-scale DNNs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13123",
  "author_total": 6,
  "authors": [
    {
      "name": "Joseph Wilson"
    },
    {
      "name": "Chris van der Heide"
    },
    {
      "name": "Liam Hodgkinson"
    },
    {
      "name": "Zhichao Wang"
    },
    {
      "name": "Fred Roosta"
    },
    {
      "name": "Michael W. Mahoney"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/126kktzw7451f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13123",
  "fulltext_url": null,
  "id": "126kktzw7451f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13123",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7221518656",
  "pdf_url": "https://arxiv.org/pdf/2610.13123",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/126kktzw7451f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:46Z",
      "native_id": "2610.13123",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13123"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Why Heavy-Tailed Weight Spectra Predict Model Quality",
  "title_text": "Why Heavy-Tailed Weight Spectra Predict Model Quality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/126kktzw7451f",
  "venue": "arXiv",
  "versions": []
}