{
  "abstract": "Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined. Second-order regularization can constrain it, but a penalty on the accelerations of sampled particles is a prior on joint particle paths, and different particle representations of the same marginal curve can have different acceleration costs. We therefore introduce Neural Wasserstein Splines (NWSP), a sample-based method that learns a continuous population curve under a Wasserstein smoothness prior. A neural network maps latent variables to the control points of a cubic spline in time, so samples at any time come from the spline basis without numerical integration. We project the generator's velocity onto gradients of a finite dictionary of scalar potentials and differentiate this measure-dependent projection in time, obtaining a finite-dimensional surrogate for the intrinsic Wasserstein acceleration, trained jointly with distributional fit losses. For a fixed dictionary and ridge parameter, we prove that the population penalty depends only on the marginal curve and bound its sensitivity to moment-estimation errors. Learned potentials (NWSP-N) sharpen acceleration estimates. On various synthetic and single-cell benchmarks, NWSP is highly competitive with transport and flow-based methods, ranking in the top two in 11 of 16 settings. The penalty improves on an unregularized spline in 13 of 16 settings and, while competitive with a particle-acceleration penalty, adds provable representation invariance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19878",
  "author_total": 3,
  "authors": [
    {
      "name": "Amartya Banerjee"
    },
    {
      "name": "Harlin Lee"
    },
    {
      "name": "Caroline Moosmüller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60k8hdhjbsnch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19878",
  "fulltext_url": null,
  "id": "60k8hdhjbsnch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19878",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7221918178",
  "pdf_url": "https://arxiv.org/pdf/2610.19878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60k8hdhjbsnch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference",
  "title_text": "Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/60k8hdhjbsnch",
  "venue": "arXiv",
  "versions": []
}