{
  "abstract": "Structural nonlinearity enables nonlinear input--output mappings to emerge from otherwise linear wave dynamics. Repeated interactions with an input-encoded structure can enhance such mappings, but finite-depth implementations restrict the accessible functional order. Here we show that recurrent scattering in a resonant cavity provides a distinct regime for structural nonlinearity. Repeated interactions are coherently accumulated into a non-polynomial response to structural perturbations. The resulting mapping naturally takes a Kolmogorov--Arnold form: perturbation-induced resonance shifts realize the inner univariate mappings, while the resonant spectral response provides the outer mapping. We identify two complementary physical controls of representation capacity: the resonance linewidth governs the functional richness within each branch, whereas combining multiple branches expands the accessible function space. Microwave-cavity measurements validate the two-stage mapping and demonstrate a two-branch nonlinear computation through XOR classification. Our results connect recurrent resonant scattering with controllable non-polynomial computation in linear wave systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22745",
  "author_total": 5,
  "authors": [
    {
      "name": "Junyu Zhu"
    },
    {
      "name": "Enzong Wu"
    },
    {
      "name": "Xiaomeng Li"
    },
    {
      "name": "Hongsheng Chen"
    },
    {
      "name": "Zuojia Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cx48yzpr3ysm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22745",
  "fulltext_url": null,
  "id": "8cx48yzpr3ysm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22745",
  "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",
      "physics.optics"
    ],
    [
      "openalex",
      "1702|Neural Networks and Reservoir Computing"
    ]
  ],
  "openalex": "W7214044669",
  "pdf_url": "https://arxiv.org/pdf/2609.22745",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cx48yzpr3ysm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22745",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22745"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Non-Polynomial Wave Computation through Recurrent Resonant Scattering",
  "title_text": "Non-Polynomial Wave Computation through Recurrent Resonant Scattering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/8cx48yzpr3ysm",
  "venue": "arXiv",
  "versions": []
}