{
  "abstract": "Deep Gaussian processes (DGPs) are flexible priors for compositional regression functions, but inference for intermediate layers faces questions. The basic obstruction is an adjacent-layer symmetry: applying an invertible transformation and its inverse to two adjacent layers leaves the composed regression map unchanged. Under explicit symmetry and prior-comparability conditions, we show that the posterior may not concentrate on any prescribed intermediate-layer representation, even when the composed regression function is estimable. We then introduce an augmented $ρ$-fractional posterior that reweights layer decompositions by a non-saturating identity-deviation penalty. The augmentation changes posterior odds between symmetry-related decompositions by an exponential penalty ratio. Under proper choices of the penalty and a prior mass condition, it preserves function-level fractional posterior contraction, while shrinking the redundant layers towards the identity mapping. Thus, the likelihood does not identify a unique ``true'' set of layers; the augmentation favors identity-biased parsimonious decompositions within an equivalence class of layers; uniqueness of a selected representative is not established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23842",
  "author_total": 2,
  "authors": [
    {
      "name": "Yichen Zhu"
    },
    {
      "name": "Hengrui Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0cv4gt10hemtf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23842",
  "fulltext_url": null,
  "id": "0cv4gt10hemtf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23842",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7222960151",
  "pdf_url": "https://arxiv.org/pdf/2610.23842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0cv4gt10hemtf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Canonical Layer Inference for Deep Gaussian Processes via Symmetry-Breaking Augmentation",
  "title_text": "Canonical Layer Inference for Deep Gaussian Processes via Symmetry-Breaking Augmentation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/0cv4gt10hemtf",
  "venue": "arXiv",
  "versions": []
}