{
  "abstract": "The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations. Recent work narrows this claim to shared local neighborhood relationships, finding that capacity-dependent trends in several global similarity measures largely disappear after calibration. We challenge this interpretation by showing that prior local-global comparisons confound structural scale (local versus global) with what is compared: relational structure, defined by which samples are related, versus metric geometry, characterized by quantitative relations such as distances, similarities, or correlations. To disentangle these factors, we construct a controlled $2\\times2$ framework that evaluates both relational structure and metric geometry at local and global scales. We introduce $H_0$ skeleton overlap as a global counterpart to mutual $k$-nearest neighbors, together with matched distance-aware variants. Across vision-language models, relational structure exhibits robust representational convergence at both scales after calibration, whereas increasingly stringent distance agreement substantially weakens alignment and progressively flattens the capacity-dependent trend. We further extend the analysis beyond ambient Euclidean geometry by evaluating distance agreement under a Riemannian metric approximation and recover the same structure-geometry pattern. The pattern is also reproduced in video-text representations. Together, these results show that relational convergence extends beyond local neighborhoods to global spanning structure, whereas metric geometry exhibits substantially weaker convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27252",
  "author_total": 4,
  "authors": [
    {
      "name": "Junwon You"
    },
    {
      "name": "Mihyun Jang"
    },
    {
      "name": "Sangwoo Mo"
    },
    {
      "name": "Jae-Hun Jung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aytb630s30gqs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27252",
  "fulltext_url": null,
  "id": "aytb630s30gqs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27252",
  "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.CV"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "1707|Multimodal Machine Learning Applications"
    ]
  ],
  "openalex": "W7214218565",
  "pdf_url": "https://arxiv.org/pdf/2609.27252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aytb630s30gqs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "What Converges in the Platonic Representation Hypothesis? Structure over Geometry",
  "title_text": "What Converges in the Platonic Representation Hypothesis? Structure over Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/aytb630s30gqs",
  "venue": "arXiv",
  "versions": []
}