{
  "abstract": "Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also obtain the disorder-averaged ground-state energy landscape of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact error-free threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19195",
  "author_total": 2,
  "authors": [
    {
      "name": "Sumedha"
    },
    {
      "name": "Abhishek Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k0fxp64njqcd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19195",
  "fulltext_url": null,
  "id": "8k0fxp64njqcd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19195",
  "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"
    ],
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7170089199",
  "pdf_url": "https://arxiv.org/pdf/2607.19195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8k0fxp64njqcd.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2607.19195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19195"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Free energy landscape of Dense Associative Memory",
  "title_text": "Free energy landscape of Dense Associative Memory",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/8k0fxp64njqcd",
  "venue": "arXiv",
  "versions": []
}