{
  "abstract": "Symmetry reduces the capacity of a quantum learning model, but the imposed group must match both the measured information and the label transformation. We establish a finite-measurement theory for inferring this group from candidate transformations. The central structural result identifies observable-invisible transformations with the stabilizer of a projected state whenever the probe span is invariant. It turns recovered generators into a valid subgroup and identifies the continuous invisible space with its Lie algebra. For finite dictionaries, an unbiased shadow statistic distinguishes zero from positive squared expectation discrepancies with an inverse-gap measurement rate, improving the inverse-square-gap rate of uniform discrepancy estimation. A commuting qubit lower bound proves the gap dependence optimal at fixed snapshot scale, and simultaneous intervals support data-dependent tolerances. Task validation then tests either the joint distribution through a characteristic kernel or its encoded mean through a classical--quantum discrepancy. An exact group-average identity relates the latter to joint-state asymmetry and specifies its conversion to binary task breaking mass. Projection bias quantifies the cost of excessive symmetry, while an $\\ell_1$ readout bound quantifies the capacity gained by relaxing it. At an invariant pure-state backbone, retained and nontrivial breaking sectors are Fisher-orthogonal. Ising-chain calculations connect finite-shot recovery, label-dependent symmetry, and physical sector drift. These results determine which symmetry the measurements support and provide the statistical and geometric basis for a subsequent release decision.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00157",
  "author_total": 1,
  "authors": [
    {
      "name": "Zeyu Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9j6re98q0xh3n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00157",
  "fulltext_url": null,
  "id": "9j6re98q0xh3n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00157",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215797682",
  "pdf_url": "https://arxiv.org/pdf/2610.00157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9j6re98q0xh3n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00157"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurements",
  "title_text": "Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/9j6re98q0xh3n",
  "venue": "arXiv",
  "versions": []
}