{
  "abstract": "Feldman's memorization lower bound assigns a frequency coefficient based on how often a point appears in the training sample. We give an exact three-point counterexample to its conditional and averaged forms, using independent fair labels and a permutation-equivariant learner. A sequence of sampling priors makes the ratio of the proposed penalty to actual excess risk grow exponentially, ruling out a universal positive constant-factor repair. The priors vary with sample size, the offending profiles become rare, and both quantities vanish. Retaining the original model, we obtain an exact replacement using full-sample posterior probabilities. Under exchangeability, these depend on multiplicity and the complete frequency profile. We characterize the largest multiplicity-only coefficients valid for unrestricted learners. The original coefficient has the posterior-mean form of Good's exact frequency formula and is an occupancy-weighted average of the corrected coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20402",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenisbek Assylbekov"
    },
    {
      "name": "Rustem Takhanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vtny4jach4ta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20402",
  "fulltext_url": null,
  "id": "1vtny4jach4ta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20402",
  "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|Machine Learning and Algorithms"
    ]
  ],
  "openalex": "W7222121956",
  "pdf_url": "https://arxiv.org/pdf/2610.20402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vtny4jach4ta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.20402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20402"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Posterior Frequencies and the Cost of Not Fitting: A Correction to a Memorization Lower Bound",
  "title_text": "Posterior Frequencies and the Cost of Not Fitting: A Correction to a Memorization Lower Bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/1vtny4jach4ta",
  "venue": "arXiv",
  "versions": []
}