{
  "abstract": "Understanding the relationship between generalization and privacy remains a challenge in modern machine learning theory, particularly for deep networks that are trained by variants of differentially private stochastic gradient descent (DP- SGD). In this work we make progress on this persistent open problem. First, we derive explicit upper bounds on the approximate max-information of any algorithm that fulfills $(ε, δ)$-differential privacy or Rényi differential privacy, thereby going beyond the classical results for pure $ε$-differential privacy. Subsequently, we show even stronger guarantees for two common private learning algorithms, output perturbation with the Gaussian mechanism, and streaming DP-SGD, by exploiting the structure of their internal randomization. As an application of our results, we demonstrate how to obtain non-vacuous PAC-Bayes generalization bounds for deep networks, in which the prior distribution is learned by DP-SGD instead of the classical way of choosing it in a data-independent way.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.26222",
  "author_total": 3,
  "authors": [
    {
      "name": "Christoph H. Lampert"
    },
    {
      "name": "Max Cairney-Leeming"
    },
    {
      "name": "Hossein Zakerinia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajx7dsqtyd89q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26222",
  "fulltext_url": null,
  "id": "ajx7dsqtyd89q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26222",
  "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|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7162515424",
  "pdf_url": "https://arxiv.org/pdf/2605.26222",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajx7dsqtyd89q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2605.26222",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26222"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "From Privacy to Generalization: Linear Max-Information Bounds for Differentially Private Learning Algorithms",
  "title_text": "From Privacy to Generalization: Linear Max-Information Bounds for Differentially Private Learning Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/ajx7dsqtyd89q",
  "venue": "arXiv",
  "versions": []
}