{
  "abstract": "Loss-difference conditional mutual information (ld-CMI) uses the smallest of the standard observations in the supersample hierarchy of generalization bounds: it measures what a learner's loss differences reveal about which candidate of each pair it was trained on. Accuracy is known to force information into the model; data processing does not carry such lower bounds to losses. We show, by bounding three moments of the loss differences, that accuracy also forces ld-CMI. For linear predictors with a smooth convex loss of nonzero slope at zero, such as the logistic loss, plus a regularizer whose curvature and growth are both of power $r\\ge2$, on product distributions over a scaled sign cube in dimension at least linear in $n$, every proper learner with expected excess risk at most $\\varepsilon$ on these distributions at the optimal sample size $n\\asymp\\varepsilon^{-2+2/r}$ has worst-case ld-CMI of order $n$ bits, and $Θ(n/(1+(τ/\\varepsilon)^2))$ bits under Gaussian noise of standard deviation $τ$ on the loss differences. The same holds without a regularizer, at $n\\asymp\\varepsilon^{-2}$. Consequently, range-scaled ld-CMI bounds cannot vanish on these distributions, although every proper learner's generalization gap is $O(n^{-1/2})$. We also show that model-level information does not determine noisy loss-difference information, and that the growth, slope and dimension conditions are needed, the last up to a logarithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09206",
  "author_total": 1,
  "authors": [
    {
      "name": "Hazar Yueksel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1hyvq4dg6rzr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09206",
  "fulltext_url": null,
  "id": "1hyvq4dg6rzr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09206",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Machine Learning and Algorithms"
    ]
  ],
  "openalex": "W7220958343",
  "pdf_url": "https://arxiv.org/pdf/2610.09206",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1hyvq4dg6rzr6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.09206",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09206"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "An Accuracy-Information Tradeoff for Loss-Difference Conditional Mutual Information",
  "title_text": "An Accuracy-Information Tradeoff for Loss-Difference Conditional Mutual Information",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/1hyvq4dg6rzr6",
  "venue": "arXiv",
  "versions": []
}