{
  "abstract": "Spectral features can remain optimal under strongly uneven task preferences when they retain the directions most useful to the tasks. In a local-task model, expected probing gain depends on the task prior only through its covariance $Λ$: with $B$ recording dependence between views, $k$ spectral features span the leading eigenspace of $BB^\\top$, while task-optimal features span that of $BΛB^\\top$. We derive alignment-dependent regret bounds, matching worst-case lower bounds for a flat leading spectrum, and bounds using the leading $2k$ directions with a spectral-tail term; a spectral gap makes the bound quadratic in small anisotropy. We also bound the imbalance from random preference patterns and from averaging independent tasks with an isotropic population covariance. With known $Λ$, changing one term of the spectral contrastive loss selects task-optimal features; with a labelled task bank, we propose a diagnostic and test correction without retraining. Correction reduces synthetic held-out regret from $0.858$ to $0.003$ with $2000$ tasks when less task-relevant directions dominate, and on CIFAR-100 lowers empirical regret by $0.031$--$0.053$ on held-out fine-label tasks using the same images. With a small task bank, however, correction can hurt.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15825",
  "author_total": 3,
  "authors": [
    {
      "name": "Dier Tang"
    },
    {
      "name": "Jing Yee Tan"
    },
    {
      "name": "Guangyue Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekt1b0y9h6ntj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15825",
  "fulltext_url": null,
  "id": "ekt1b0y9h6ntj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15825",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7214802488",
  "pdf_url": "https://arxiv.org/pdf/2609.15825",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekt1b0y9h6ntj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.15825",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Sharp Regret Bounds and a Task-Covariance Correction for Spectral Representation Learning",
  "title_text": "Sharp Regret Bounds and a Task-Covariance Correction for Spectral Representation Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/ekt1b0y9h6ntj",
  "venue": "arXiv",
  "versions": []
}