{
  "abstract": "We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00528",
  "author_total": 2,
  "authors": [
    {
      "name": "Pingbing Ming"
    },
    {
      "name": "Han Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4k5c7fq9sp19.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00528",
  "fulltext_url": null,
  "id": "f4k5c7fq9sp19",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00528",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7206158269",
  "pdf_url": "https://arxiv.org/pdf/2609.00528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4k5c7fq9sp19.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.00528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00528"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials",
  "title_text": "Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/f4k5c7fq9sp19",
  "venue": "arXiv",
  "versions": []
}