{
  "abstract": "We prove uniform-in-time propagation of chaos and last-iterate consistency for a target-adapted Stein variational gradient descent (SVGD) flow on compact connected manifolds. The target has a smooth positive density, and the particles start independently from a fixed smooth nonnegative density ratio. The construction uses the Green--Bessel operator $Q_{r,π}=A_π^{-1}(\\mathrm{Id}+A_π)^{-r}$ of the reversible target Langevin generator. Sufficient Bessel smoothing gives a scalar kernel with finite diagonal, and a positive matrix lift realizes its potential force as a Stein velocity. Population and empirical flows then dissipate the same finite target discrepancy. Population entropy and the target spectral gap give decay of this discrepancy; a finite-time particle comparison reaches a time after which common-energy monotonicity controls every later time. The resulting expected uniform discrepancy is $O((\\log N)^{-1/2})$, with a corresponding logarithmic $W_1$ bound and consistency along every sequence $t_N\\to\\infty$. We also prove an exact finite-mode approximation theorem with an explicit spatial-resolution error and a feature-factorized particle implementation. For confining Euclidean targets, we establish static kernel and moment results and give a conditional dynamical extension under explicit population-regularity and transport hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08122",
  "author_total": 2,
  "authors": [
    {
      "name": "Trevor Teolis"
    },
    {
      "name": "Maarten V. de Hoop"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ev1aj8wshr8cd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08122",
  "fulltext_url": null,
  "id": "ev1aj8wshr8cd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08122",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7212051655",
  "pdf_url": "https://arxiv.org/pdf/2609.08122",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ev1aj8wshr8cd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08122",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08122"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Target-adapted Green-Bessel SVGD: uniform-in-time propagation of chaos and last-iterate consistency",
  "title_text": "Target-adapted Green-Bessel SVGD: uniform-in-time propagation of chaos and last-iterate consistency",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ev1aj8wshr8cd",
  "venue": "arXiv",
  "versions": []
}