{
  "abstract": "Pairwise human-preference platforms such as Chatbot Arena have become central to large language model (LLM) evaluation, yet reliable task-specific ranking remains challenging. Global leaderboards mask task heterogeneity, while ranking each fine-grained task independently is unstable under sparse, imbalanced comparisons. We propose a low-rank framework for task-specific LLM ranking from sparse pairwise comparisons, modeling the task-by-model ability matrix $Θ^\\star \\in \\mathbb{R}^{d_t \\times d_m}$ as low rank so that information is shared across related tasks while task-specific differences are preserved. We first develop a max-norm ($\\ell_\\infty$) accurate estimator for the latent scores, combining a convex initializer with alternating-minimization refinement, and prove task-wise top-$K$ recovery guarantees under sparse sampling. Our main contribution is an uncertainty quantification framework for task-specific ranking. We construct cross-fitted one-step debiased estimators for fixed score contrasts -- such as the task-specific ability gap between two models -- yielding asymptotically valid confidence intervals that attain the semiparametric efficiency bound. We then extend the inference to the high-dimensional ranking regime, where per-task ranks and top-$K$ membership are determined by many dependent score-gap hypotheses. Using Gaussian and multiplier-bootstrap calibration, we obtain simultaneous confidence sets for per-task ranks and valid top-$K$ membership tests across many tasks and models. Experiments on synthetic data and Chatbot Arena show that low-rank sharing improves sample efficiency over independent task-wise Bradley-Terry estimation and produces tighter, better-calibrated ranking certificates, with the largest gains in the sparse regime typical of real LLM benchmarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29395",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiachun Li"
    },
    {
      "name": "David Simchi-Levi"
    },
    {
      "name": "Will Wei Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqr8rj2fxchx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29395",
  "fulltext_url": null,
  "id": "aqr8rj2fxchx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29395",
  "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",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7162768548",
  "pdf_url": "https://arxiv.org/pdf/2605.29395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqr8rj2fxchx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:42Z",
      "native_id": "2605.29395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29395"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons",
  "title_text": "Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:42Z",
  "url": "https://research.draconitic.com/paper/aqr8rj2fxchx8",
  "venue": "arXiv",
  "versions": []
}