{
  "abstract": "We study the convergence of Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known up to a normalisation constant. By combining Wasserstein transport with Fisher-Rao birth-death dynamics, WFR flows balance exploration and selection. These flows have been recognised as a promising mechanism to accelerate convergence beyond Langevin dynamics. We show that for a class of strongly log-concave target distributions satisfying additional curvature conditions, WFR flows preserve strong log-concavity, in contrast to Wasserstein flows which enjoy this property only in the Gaussian setting. Exploiting this result, we derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, without requiring a warm-start as required in current estimates. In particular, we show that the convergence rate decomposes additively into Wasserstein and Fisher-Rao contributions, thereby confirming a recent conjecture within this setting. These results provide refined convergence guarantees and further develop the theoretical foundations of WFR gradient flows for sampling and Bayesian inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18118",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesca Romana Crucinio"
    },
    {
      "name": "Sahani Pathiraja"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9t9tcwwy1e99y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18118",
  "fulltext_url": null,
  "id": "9t9tcwwy1e99y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18118",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7213501051",
  "pdf_url": "https://arxiv.org/pdf/2609.18118",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9t9tcwwy1e99y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18118",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18118"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows",
  "title_text": "Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/9t9tcwwy1e99y",
  "venue": "arXiv",
  "versions": []
}