{
  "abstract": "We investigate how geometric priors shape neural approximations of the complex Monge--Amp`ere equation on the quintic Calabi--Yau threefold. This fixed-$ψ$ diagnostic compares four single-patch ans\"atze: a coordinate SIREN potential model, a direct-metric Cholesky baseline, an algebraic section ansatz, and a section-plus-neural hybrid. In a 96-run learning-rate and frequency archive, section-based models reach validation $σ=4.14$--$4.16%$, whereas SIREN and Cholesky remain at $41.29%$ and $44.27%$. Multi-seed controls use a shared affine-$η$ evaluator and five fresh validation clouds. Stable section settings give $3.84$--$4.77%$, compared with $28.46$--$30.59%$ for Cholesky and $34.73$--$38.13%$ for SIREN. Hybrid projective features do not improve best-case accuracy, but they stabilise the stressed regime. They limit $σ$ to $4.26$--$4.41%$, versus $4.45$--$205.45%$ for raw coordinates. Within this protocol, section-based geometric structure is the main driver of accuracy; coordinate-only models plateau at substantially higher error, and raw hybrid flexibility can amplify instability. We provide a projective-scaling derivation, document protocol asymmetries, and identify projectively consistent hybrid corrections as the next step.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: 2026 Mach. Learn.: Sci. Technol. 7 035049",
  "arxiv": "2610.35920",
  "author_total": 1,
  "authors": [
    {
      "name": "D Yang Eng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/722w3jtq5k182.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35920",
  "fulltext_url": null,
  "id": "722w3jtq5k182",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35920",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7224098862",
  "pdf_url": "https://arxiv.org/pdf/2610.35920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/722w3jtq5k182.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Geometric priors for single-patch neural Calabi--Yau metrics on the quintic: a conservative fixed-$ψ$ Ablation study",
  "title_text": "Geometric priors for single-patch neural Calabi--Yau metrics on the quintic: a conservative fixed-ψ Ablation study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/722w3jtq5k182",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/2632-2153/ae7494",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}