{
  "abstract": "The Lyapunov spectrum of a nonlinear recurrent neural network with random asymmetric couplings is calculated in the limit $N\\to\\infty$. The calculation is based on a finite-$N$ identity that expresses the cumulative distribution of Lyapunov exponents as a response function of the tangent-space dynamics, with the tangent trajectory selected by a minimum-norm condition rather than by an initial condition. A cavity method then determines this response function at large $N$ through a self-consistent single-site problem. This result establishes that the chaos in this network is extensive and gives access to diffeomorphism-invariant properties of the dynamics. This work was done in collaboration with the AI models GPT-6 Astra and Claude Opus 5.5.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12426",
  "author_total": 1,
  "authors": [
    {
      "name": "David G. Clark"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01dbhp5136tff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12426",
  "fulltext_url": null,
  "id": "01dbhp5136tff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12426",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221082367",
  "pdf_url": "https://arxiv.org/pdf/2610.12426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01dbhp5136tff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12426"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Lyapunov spectrum of random neural networks",
  "title_text": "Lyapunov spectrum of random neural networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:59Z",
  "url": "https://research.draconitic.com/paper/01dbhp5136tff",
  "venue": "arXiv",
  "versions": []
}