{
  "abstract": "Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $η$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\\min{\\ell_k,2kη_k/U}$ to first relative order, where $\\ell_k=\\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00424",
  "author_total": 3,
  "authors": [
    {
      "name": "Qinchuan Cheng"
    },
    {
      "name": "Jiaqi Liu"
    },
    {
      "name": "Ruixuan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zv5z01drhdmb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00424",
  "fulltext_url": null,
  "id": "8zv5z01drhdmb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00424",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7216010311",
  "pdf_url": "https://arxiv.org/pdf/2610.00424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zv5z01drhdmb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:14Z",
      "native_id": "2610.00424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00424"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model",
  "title_text": "Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/8zv5z01drhdmb",
  "venue": "arXiv",
  "versions": []
}