{
  "abstract": "We are the first to give a certified rule for whether unseen data belong in a pretrained model's context or its weights, built on an exact law for their information value. That value, the code length saved on held-out queries, equals in expectation the bits stored about the query, plus a prior repair, minus a decoding loss, for any model, architecture, dataset and task. The law's ceilings certify the choice from one measurement, and an anytime-valid test makes it from held-out queries, with error controlled whenever it stops. Every certificate the ceilings issue on a trained transformer, TabPFN, an occupancy network and a stereo network is correct. The test picks TabPFN over XGBoost and a trained surrogate over an in-context learner on airfoil pressure, calls the better of GPT-2's cache and fine-tune in 61,948 of 64,000 query streams over 32 comparisons, and errs in at most 3.3% of null streams. The law also diagnoses when learning in context helps and when it does not. Deleting part of a context is held-out validation of that part in any model, and adding parts one at a time traces the learning curve in context: one patch that sees a shape feature cuts an occupancy network's code length there a hundredfold, while eight that miss it nearly double it, and one camera that sees the surface beats four in a stereo network. Ranked by this label-free valuation, a kriging learner's three best support cars beat four drawn at random, and on a yes-or-no claim the valuation recovers a published evidence adjudicator, with AUROC 0.91.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29419",
  "author_total": 2,
  "authors": [
    {
      "name": "Leon Chlon"
    },
    {
      "name": "Julie Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17rkxw47az35r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29419",
  "fulltext_url": null,
  "id": "17rkxw47az35r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29419",
  "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|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7223199801",
  "pdf_url": "https://arxiv.org/pdf/2610.29419",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17rkxw47az35r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:29Z",
      "native_id": "2610.29419",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29419"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "When Thoughts Become Memory: Unifying In-Context Learning and Fine-Tuning",
  "title_text": "When Thoughts Become Memory: Unifying In-Context Learning and Fine-Tuning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/17rkxw47az35r",
  "venue": "arXiv",
  "versions": []
}