{
  "abstract": "In this article, we extend learning rules from real binary to complex-valued spins. This formulation allows for a robust and natural representation of grayscale patterns, where spins behave as multi-state neurons and can be stored in a complex-valued weight matrix. We describe a rule that performs better than standard methods, such as Hebbian learning, to encode information in a suitable form for pattern retrieval with networks of oscillators. Since in neural networks it is of interest to have local and incremental learning rules, we prove the extension of a result by Diederich and Opper with our complex-valued spin formulation. We then test the behavior of the associative memory for the system of oscillators under different circumstances for both real-valued, as well as complex-valued correlated and random patterns.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30800",
  "author_total": 2,
  "authors": [
    {
      "name": "Federico Sbravati"
    },
    {
      "name": "Aida Todri-Sanial"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bg5sf40w4j0vd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30800",
  "fulltext_url": null,
  "id": "bg5sf40w4j0vd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30800",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7204922502",
  "pdf_url": "https://arxiv.org/pdf/2608.30800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bg5sf40w4j0vd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30800"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Learning rules for complex-valued patterns in networks of oscillators",
  "title_text": "Learning rules for complex-valued patterns in networks of oscillators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/bg5sf40w4j0vd",
  "venue": "arXiv",
  "versions": []
}