{
  "abstract": "Efficiently and robustly analyzing shape data is critical across many scientific disciplines. While chirality is a fundamental property in numerous applications - most notably in molecular science - existing shape analysis metrics fail to distinguish between a shape and its mirror image. To address this gap, we introduce a multilinear generalization of the Gromov-Wasserstein objective. Under mild assumptions, this objective yields a distance between shapes, represented as probability distributions quotiented by a symmetry group $G$. In particular, for $G = SO(d)$, we introduce the Chiral Gromov-Wasserstein ($\\mathrm{CGW}$) distance, sensitive to chirality. We establish robustness properties for the multilinear Gromov-Wasserstein distances and develop efficient algorithms to compute them, reformulating the underlying optimization problem by projecting couplings onto a low-dimensional space. We derive algorithms for both local and approximate global solutions, yielding a fully polynomial-time approximation scheme for these problems. We validate the framework through numerical experiments that demonstrate the effectiveness of $\\mathrm{CGW}$ as a shape metric for chiral objects.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27774",
  "author_total": 4,
  "authors": [
    {
      "name": "Clément Soubrier"
    },
    {
      "name": "Geoffrey Woollard"
    },
    {
      "name": "Andrew Warren"
    },
    {
      "name": "Khanh Dao Duc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/36ahe4gnfywv3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27774",
  "fulltext_url": null,
  "id": "36ahe4gnfywv3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27774",
  "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.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7166675359",
  "pdf_url": "https://arxiv.org/pdf/2608.27774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/36ahe4gnfywv3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2608.27774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality",
  "title_text": "Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/36ahe4gnfywv3",
  "venue": "arXiv",
  "versions": []
}