{
  "abstract": "Test-time training (TTT) adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts. Yet, its performance often suffers from instability and sensitivity to hyperparameters such as update steps and subspace. We explain this behavior through a decision-theoretic lens, treating TTT as implicit Bayesian inference in the kernel regime. Under a Gaussian process benchmark, we show that TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio and aligned with query-relevant eigen-directions. This perspective underpins the following results: (1) we show when fixed update steps and subspaces fail under distribution shifts, motivating adaptive strategies; (2) we prove that selecting update steps via prompt evidence admits a PAC-Bayes guarantee against overfitting; and (3) we characterize the Bayes-optimal update subspace under a linear-Gaussian correction model, yielding a scoring rule for selecting Transformer blocks and heads. Our theory helps explain the empirical instability of TTT, taking a step toward principled guidance for when, how far, and which directions to adapt.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Proceedings of Machine Learning Research, 306:124279-124317, 2026 (ICML 2026)",
  "arxiv": "2606.15569",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomoya Wakayama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jh1exbp4yq6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15569",
  "fulltext_url": null,
  "id": "3jh1exbp4yq6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15569",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7164922841",
  "pdf_url": "https://arxiv.org/pdf/2606.15569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jh1exbp4yq6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2606.15569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt",
  "title_text": "A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/3jh1exbp4yq6w",
  "venue": "arXiv",
  "versions": []
}