{
  "abstract": "Bayesian variants of Low-Rank Adaptation (LoRA) provide principled uncertainty estimation when fine-tuning large foundation models, but require specifying the prior over the low-rank weight updates. We address this hyperparameter selection problem by introducing a closed-form prior-predictive estimator that operates before fine-tuning. We analyze a second-order expansion of the network and quantify how the low-rank prior drives function-space deviations from the pretrained outputs. We also show that these prior-predictive quantities depend on the prior only through the product of the adaptation rank and the fourth power of the prior scale. Because the training targets share a single draw of the latent weight update, we can leverage the covariance between example residuals to derive a moment-matching estimator. Furthermore, our theoretical analysis establishes that the optimal prior precision scales as $r^{-1/2}$ with the rank $r$, allowing a single estimate to generalize across all ranks. Controlled experiments across regression and classification tasks validate our approximation and show that our estimator recovers the true prior scale. On RoBERTa-large, our approach improves predictive negative log-likelihood (NLL) and calibration over both MAP and marginal-likelihood selection without requiring validation data, while achieving competitive out-of-distribution detection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35457",
  "author_total": 3,
  "authors": [
    {
      "name": "Tomasz Kuśmierczyk"
    },
    {
      "name": "Eliezer de Souza da Silva"
    },
    {
      "name": "Marcin Sendera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5h49hqc8p25cm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35457",
  "fulltext_url": null,
  "id": "5h49hqc8p25cm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35457",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7223915220",
  "pdf_url": "https://arxiv.org/pdf/2610.35457",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5h49hqc8p25cm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.35457",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35457"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Prior Predictive Matching for Bayesian LoRA",
  "title_text": "Prior Predictive Matching for Bayesian LoRA",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/5h49hqc8p25cm",
  "venue": "arXiv",
  "versions": []
}