{
  "abstract": "Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks—often referred to as tensor trains (TT) or matrix product states (MPS)—are increasingly being used as a numerical Ansatz for continuum functions by ``quantizing’’ the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient Ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.",
  "abstract_shown": true,
  "affiliations": [
    "Flatiron Institute",
    "PsiQuantum (United States)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Joseph Tindall",
      "orcid": "0000-0003-1335-8637"
    },
    {
      "affs": [
        0
      ],
      "name": "Miles Stoudenmire",
      "orcid": "0000-0003-3389-9692"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Ryan Levy",
      "orcid": "0000-0003-4952-7156"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f9ay57zbzb7f.bib",
  "cited_by": 21,
  "doi": "10.21468/scipostphys.21.4.095",
  "fulltext_url": null,
  "id": "8f9ay57zbzb7f",
  "issns": [
    "2542-4653"
  ],
  "landing_url": "https://scipost.org/10.21468/SciPostPhys.21.4.095",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W4403884692",
  "pdf_url": "https://scipost.org/10.21468/SciPostPhys.21.4.095/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": "Stichting SciPost",
  "ris": "https://research.draconitic.com/paper/8f9ay57zbzb7f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "10.21468/scipostphys.21.4.095",
      "source": "crossref",
      "url": "https://scipost.org/10.21468/SciPostPhys.21.4.095"
    },
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W4403884692",
      "source": "openalex",
      "url": "https://doi.org/10.21468/scipostphys.21.4.095"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2605|Tensor decomposition and applications",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Compressing multivariate functions with tree tensor networks",
  "title_text": "Compressing multivariate functions with tree tensor networks",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:35Z",
  "url": "https://research.draconitic.com/paper/8f9ay57zbzb7f",
  "venue": "SciPost Physics",
  "versions": []
}