{
  "abstract": "The empirical bitstring distribution is the most accessible observable on Rydberg-atom arrays, but the bipartite von~Neumann entropy it constrains is far costlier to obtain. We present a six-term linear closed form for the entropy, built on bitstring-derivable physics scalars, and characterize its accuracy, portability, scaling behaviour, and calibration cost. The feature set is selected with guidance from a trained graph neural network: probing the network localizes its entropy prediction to the two-point correlators on the bipartition boundary, and an exhaustive ground-truth search restricted to those boundary correlators isolates the form. It reaches $0.024$~nats mean absolute error in distribution: $6.4$ times the network's error, but in a form a human can read and apply without retraining. Fit once and applied unchanged, it has lower error than the base network on five of six out-of-distribution pools and ties the sixth. An independent density-matrix renormalization-group study to one hundred atoms -- five times the reach of exact diagonalization -- settles the size-extrapolation question: coefficients frozen at small size fail at scale, but the failure is structured. Refit per size the form holds to $25$--$50$~mnat (cross-validated); two of its six slopes follow clean inverse-size laws, one a downward curving growth, and the others are trendless; the fitted laws deploy the form label-free at roughly $40$--$80$~mnat. The result fixes a label-budget rule: at large sizes, a few dozen labels recalibrate the closed form to match a fine-tuned in-distribution ensemble on the same features, while nonlinear ML models pull ahead only given large labelled datasets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22713",
  "author_total": 1,
  "authors": [
    {
      "name": "Anas Saleh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsr2bwvek9b81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22713",
  "fulltext_url": null,
  "id": "dsr2bwvek9b81",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.22713",
  "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",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7165623618",
  "pdf_url": "https://arxiv.org/pdf/2606.22713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsr2bwvek9b81.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2606.22713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22713"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "An interpretable closed form for entanglement entropy from bitstrings, guided by a graph neural network",
  "title_text": "An interpretable closed form for entanglement entropy from bitstrings, guided by a graph neural network",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/dsr2bwvek9b81",
  "venue": "arXiv",
  "versions": []
}