{
  "abstract": "Prior-Data Fitted Networks (PFNs) replace the hyperparameter refitting of Gaussian Process (GP) surrogates in Bayesian optimisation with a single forward pass, at the cost of a prior that is fixed at meta-training time. We show empirically that a PFN's predictive log-likelihood falls increasingly behind that of a refitted GP as the objective function's lengthscale grows beyond the mode of the PFN's meta-training prior, and that this deficit carries over to optimisation performance. To correct the mismatch without retraining the network, we introduce Anisotropic Trust Region (ATR) warping. Per-dimension lengthscales are estimated by kernel target alignment, and an affine rescaling of the input space maps the objective onto the lengthscale the PFN expects, with a trust region around the anchor determining which observations are retained, leaving the PFN's $\\mathcal{O}(d \\cdot N^2)$ inference cost unchanged. On functions drawn from a Matérn-3/2 kernel, ATR warping improves optimisation performance of the PFN at both extremes of the lengthscale range. Our implementation is publicly available at https://github.com/youngers2006/Trust-Region-Warping-For-PFNs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37737",
  "author_total": 3,
  "authors": [
    {
      "name": "Samuel Younger"
    },
    {
      "name": "Tinkle Chugh"
    },
    {
      "name": "George De Ath"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7655amm13603e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37737",
  "fulltext_url": null,
  "id": "7655amm13603e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37737",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37737",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7655amm13603e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.37737",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37737"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Anisotropic Trust Region Warping for Prior-Data Fitted Networks in Bayesian Optimisation",
  "title_text": "Anisotropic Trust Region Warping for Prior-Data Fitted Networks in Bayesian Optimisation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/7655amm13603e",
  "venue": "arXiv",
  "versions": []
}