{
  "abstract": "Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40047",
  "author_total": 3,
  "authors": [
    {
      "name": "Rafael Pereira Eufrazio"
    },
    {
      "name": "Eduardo Fernandes Montesuma"
    },
    {
      "name": "Charles Casimiro Cavalcante"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8m5zfmytp7m5a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40047",
  "fulltext_url": null,
  "id": "8m5zfmytp7m5a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40047",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7215065479",
  "pdf_url": "https://arxiv.org/pdf/2609.40047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8m5zfmytp7m5a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2609.40047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Gromov-Wasserstein Distillation for Inductive Multi-View Embedding",
  "title_text": "Gromov-Wasserstein Distillation for Inductive Multi-View Embedding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/8m5zfmytp7m5a",
  "venue": "arXiv",
  "versions": []
}