{
  "abstract": "The optimal control of a discrete Schrödinger bridge is a discrete gradient, a difference of vertex potentials, but recent models such as MadSBM instead learn a free control on the edges by cross-entropy. We prove that this leaves the action uncontrolled: cross-entropy identifies the control only up to a state-dependent shift (a gauge), and the action is $\\operatorname{KL}(r\\|p)$ plus a gauge term the loss never constrains. We propose GDSBM, which writes the control as a difference of vertex potentials and adds the action to the loss; pinning the gauge costs no expressiveness and makes the action a property of the model, so the penalty acts on the model and not on the gauge. On peptide generation our MadSBM reimplementation has a free-gauge action of order $10^{8}$ for a gauge-fixed value of $6.5$, against $1.5$ for GDSBM, with no quality loss that three seeds can detect. The gradient form also fits guidance, which becomes the addition of a potential: guided toward a net charge of $+3$ at pH~7, GDSBM is closer than MadSBM, over three seeds, to its exact tempered target in total variation at every guidance strength (at $β=1$, $81\\%$ of samples in the target window against $74\\%$, for a target of $97\\%$); we claim no statistical significance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31361",
  "author_total": 2,
  "authors": [
    {
      "name": "Abdallah BenAbdallah"
    },
    {
      "name": "Mohsen Dlala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exnx59xd9npyw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31361",
  "fulltext_url": null,
  "id": "exnx59xd9npyw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31361",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7223404899",
  "pdf_url": "https://arxiv.org/pdf/2610.31361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exnx59xd9npyw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Gradient Discrete Schrodinger Bridge Matching for Peptide Generation",
  "title_text": "Gradient Discrete Schrodinger Bridge Matching for Peptide Generation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/exnx59xd9npyw",
  "venue": "arXiv",
  "versions": []
}