{
  "abstract": "Minimal filling architectures describe the smallest hidden-layer widths for which the neurovariety of a polynomial neural network fills its ambient function space. It was conjectured that every such architecture has unimodal hidden widths. We construct counterexamples to this conjecture using a frontier search and certify the main example through finite-field Jacobian computations and recursive dimension bounds. In the opposite direction, we prove that every minimal filling architecture of depth at most three is unimodal. A nonunimodal minimal filling architecture of depth four shows that the depth bound is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.09609",
  "author_total": 2,
  "authors": [
    {
      "name": "Kevin Dao"
    },
    {
      "name": "Jose Israel Rodriguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ban7s23czy9ym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.09609",
  "fulltext_url": null,
  "id": "ban7s23czy9ym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.09609",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7160951764",
  "pdf_url": "https://arxiv.org/pdf/2605.09609",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ban7s23czy9ym.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2605.09609",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.09609"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Minimal Filling Architectures for Polynomial Neural Networks",
  "title_text": "Minimal Filling Architectures for Polynomial Neural Networks",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/ban7s23czy9ym",
  "venue": "arXiv",
  "versions": []
}