{
  "abstract": "In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore--Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insufficient weight to the truly predictive coordinate. An exact target-mass identity and a two-sign argument convert this obstruction into clipped prediction loss. Hadamard constructions yield $Ω(\\min\\{T,\\sqrt d\\})$ clipped regret for each of the three unit-power rules against a zero-loss one-sparse comparator. For every fixed power $α\\ge1$, one shared paired construction further yields linear regret simultaneously for all three powered rules and selectors among them in sufficiently high dimension. A rank upper bound is tight for powered univariate priming, even with Euclidean-unit inputs, and for unit-power Pearson priming with coordinatewise bounded inputs and target-preserving totalization. A separate algebraic construction gives $Ω(\\min\\{T,d^{1/4}\\})$ regret for unit-power multivariate priming under Euclidean-unit inputs. The univariate lower bound persists under any nonnegative second-stage ridge schedule, while a paired ridge construction yields linear lower bounds for all three powered rules. Exploratory diagnostics on frozen language-model activations are consistent with the same qualitative mechanism. The exact multivariate frontier remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17573",
  "author_total": 4,
  "authors": [
    {
      "name": "Huibo Xu"
    },
    {
      "name": "Shi Fu"
    },
    {
      "name": "Qixin Zhang"
    },
    {
      "name": "Dacheng Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rpykgawh92ye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17573",
  "fulltext_url": null,
  "id": "5rpykgawh92ye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17573",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7203747924",
  "pdf_url": "https://arxiv.org/pdf/2608.17573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rpykgawh92ye.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2608.17573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17573"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates",
  "title_text": "Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/5rpykgawh92ye",
  "venue": "arXiv",
  "versions": []
}