{
  "abstract": "Deep Gaussian processes (DGPs) are appealing Bayesian regression models, but their standard discrete-depth parameterization often becomes harder to optimize as depth grows. We argue that depth is better treated as a latent continuous evolution than as a long discrete stack. We therefore propose a continuous-depth formulation in which the latent representation follows a stochastic differential equation with a depth-indexed drift family equipped with a GP-based prior. This reframes the core design choice as the prior placed on that family, rather than adopting a purely neural continuous-depth parameterization as in neural ODE or neural SDE models. We study two instantiations of this idea: CDGP, a direct GP prior over the state--depth drift, and FlowDGP, a flow-evolved prior that captures richer depth dependence at lower training cost. To motivate the redesign, we analyze how the single-sample DGP objective can become increasingly sensitive under repeated layer composition, while residual DGP is a useful first repair that still remains a finite discrete construction. We also give pathwise sensitivity analysis for the continuous-depth formulation. Experiments on synthetic, benchmark, and large-scale regression tasks show that residual DGP improves over plain DGP, while CDGP and FlowDGP provide a stronger overall story across the regimes we study.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30890",
  "author_total": 9,
  "authors": [
    {
      "name": "Ying Li"
    },
    {
      "name": "Sanyou Wu"
    },
    {
      "name": "Zi Yang"
    },
    {
      "name": "Qiaochu Xu"
    },
    {
      "name": "Yuhao Liu"
    },
    {
      "name": "Zhidi Lin"
    },
    {
      "name": "Michael Minyi Zhang"
    },
    {
      "name": "Petar Djuric"
    },
    {
      "name": "Alexandre H. Thiery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j0paxw18byh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30890",
  "fulltext_url": null,
  "id": "4j0paxw18byh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30890",
  "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",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7223335938",
  "pdf_url": "https://arxiv.org/pdf/2610.30890",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j0paxw18byh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:43Z",
      "native_id": "2610.30890",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30890"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Continuous-depth Deep Gaussian Processes",
  "title_text": "Continuous-depth Deep Gaussian Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/4j0paxw18byh9",
  "venue": "arXiv",
  "versions": []
}