{
  "abstract": "Gaussian-process limits are powerful in describing overparameterized machine learning models, yet their validity in structured tensor-network architectures remains unclear. Here we analytically present a moment-based approach that identifies precise conditions for the emergence and breakdown of Gaussian universality in tensor-network learning models, with a focus on matrix product states. We prove that in the large bond dimension limit, the learning models with both local and global observables converge to Gaussian processes, with explicit finite-size bounds on higher-order moment deviations. Whereas in the large physical dimension limit, the Gaussian universality no longer persists: while the models with local observables retain Gaussian-process behavior, those global cases exhibit persistent non-Gaussian corrections. Our results reveal that Gaussian-process behavior in tensor-network learning is controlled not only by parameter number, but also by architectural scaling, observable locality, and the spectral properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06080",
  "author_total": 3,
  "authors": [
    {
      "name": "Shi-Tuan Wang"
    },
    {
      "name": "Zidu Liu"
    },
    {
      "name": "Li-Wei Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mjrdfk8eh87c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06080",
  "fulltext_url": null,
  "id": "9mjrdfk8eh87c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06080",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7220715294",
  "pdf_url": "https://arxiv.org/pdf/2610.06080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mjrdfk8eh87c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06080"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning",
  "title_text": "Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/9mjrdfk8eh87c",
  "venue": "arXiv",
  "versions": []
}