{
  "abstract": "The absolute capacity of dense associative memory has mainly been analyzed for unbiased patterns. Here we examine the effect of bias in centered binary patterns under the Krotov-Hopfield single-site criterion $P_{\\mathrm{error}}=1/N$, where $P_{\\mathrm{error}}$ is the probability that a single-site flip lowers the energy of a stored pattern and $N$ is the number of neurons. Each pattern component takes $1-q$ with probability $q$ and $-q$ otherwise, where $0<q\\le1/2$. For polynomial interactions of order $n$, a signal-to-noise analysis gives an absolute capacity of order $N^{n-1}/\\ln N$ at $q=1/2$. For fixed $q<1/2$, however, the capacity is $O(N^{n/2})$ for even $n\\ge4$ and $O(N^{(n+1)/2})$ for odd $n\\ge5$. For $n=3$, both the unbiased and fixed-bias capacities remain $O(N^2/\\ln N)$. For $n\\ge4$, these different asymptotic forms imply a nonuniform large-$N$ limit near $q=1/2$. Asymptotic matching predicts a bias-induced crossover in the region $1-2q=O(\\ln N/N^{\\lfloor n/2\\rfloor-1})$. The crossover originates from a bias-dependent crosstalk mean that reduces the stability of sites carrying the more frequent value $-q$. Computer simulations are compared with the finite-size conditioned-Gaussian predictions. An activity-dependent control potential that cancels the conditional crosstalk mean restores the $N^{n-1}/\\ln N$ capacity for fixed $0<q<1/2$ within the conditioned-Gaussian approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17477",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuto Sakurai"
    },
    {
      "name": "Takeaki Shimokawa"
    },
    {
      "name": "Kazunori Iwata"
    },
    {
      "name": "Kazushi Mimura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7gyrsxtnbjt8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17477",
  "fulltext_url": null,
  "id": "7gyrsxtnbjt8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17477",
  "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",
      "cs.LG"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7213433421",
  "pdf_url": "https://arxiv.org/pdf/2609.17477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7gyrsxtnbjt8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.17477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17477"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory",
  "title_text": "Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/7gyrsxtnbjt8h",
  "venue": "arXiv",
  "versions": []
}