{
  "abstract": "Local conditional predictions from a black box need not admit a common joint distribution. We study two aspects of their coherent projection: finite-access precision and directional fidelity. For arbitrary deterministic binary conditional tables, we establish matching expected minimax excess conditional-Kullback--Leibler risk $Θ(\\min\\{R\\sqrt{d/B},d^2/B\\})$ under independent uniform exact-table queries, with repeated draws charged, for a local bounded pairwise joint class. The result holds for sufficiently large $d$, $R\\sqrt d\\le M_0$, and $Cd^3\\le B\\le(d2^{d-1})^{1/3}$, where $M_0$ is fixed. A moment estimator attains the upper bound. The main technical contribution is a matching lower-bound construction that respects shared pairwise interactions and frozen exact-table responses, with comparison to the best projection of the same realized table. We then examine directional fidelity in a computable hard-marginal formulation that preserves direct black-box marginals. A preregistered TabPFN-v2 case study combines a Car anchor with a frozen two-dataset, three-split extension. All $1{,}152$ extension optimization instances pass independent numerical checks at registered tolerances. Directional contrasts are dataset-dependent and asymmetric: optimizing one direction need not improve the other. Together, the analyses distinguish accurate approximation of a selected projection from improvement in conditional directions outside its fitted objective.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30708",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuyang Wu"
    },
    {
      "name": "Fanyu Zhou"
    },
    {
      "name": "Jinfeng Zhou"
    },
    {
      "name": "Guangying Lyu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80b7mhk7y4as8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30708",
  "fulltext_url": null,
  "id": "80b7mhk7y4as8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30708",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Explainable Artificial Intelligence (XAI)"
    ]
  ],
  "openalex": "W7223410807",
  "pdf_url": "https://arxiv.org/pdf/2610.30708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80b7mhk7y4as8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Finite-Query Coherent Projection of Black-Box Conditional Predictions",
  "title_text": "Finite-Query Coherent Projection of Black-Box Conditional Predictions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/80b7mhk7y4as8",
  "venue": "arXiv",
  "versions": []
}