{
  "abstract": "Stationary tail computation for high-dimensional reflected Brownian motions (RBMs) remains computationally challenging. Building on NN4MGF's shared-coordinate basic-adjoint-relationship (BAR) framework, we develop Holomorphic Cauchy Networks (HCNs). Native complex-valued rational Cauchy subnetworks enforce holomorphicity on pole-free domains, removing sampled Cauchy-Riemann penalties and their input-derivative graphs. Exact origin anchoring and boundary-coordinate exclusion enforce structural identities, while anchored interactions represent dependent transforms. Under holomorphic-log assumptions, we establish simultaneous value and first-derivative approximation for the constrained architectures and a mixed-derivative lower bound for coordinate-only representations under nonzero cross-covariance. Closed-form real-axis derivatives and sequential backpropagation further control memory. On the same NVIDIA H100 NVL, the tested 30D HCN configuration uses approximately tenfold less peak allocated memory and has 9.7-fold lower mean update time than NN4MGF; extrapolation to the respective scheduled update counts gives a projected full-schedule update-time ratio of 58.2. With 64 million sampled base inputs per high-dimensional run, HCN reaches 50 dimensions on a laptop GPU with 6.367% mean relative error over thresholds 1 through 8. Degree-matched comparisons yield lower reported mean relative errors over the primary evaluation ranges, including 1.422% versus 6.684% on the 2D Harrison non-product benchmark. An exploratory 10D correlated example illustrates the interaction extension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36558",
  "author_total": 1,
  "authors": [
    {
      "name": "Kehan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cj5vata8w6cdq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36558",
  "fulltext_url": null,
  "id": "cj5vata8w6cdq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36558",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7224122926",
  "pdf_url": "https://arxiv.org/pdf/2610.36558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cj5vata8w6cdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions",
  "title_text": "Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/cj5vata8w6cdq",
  "venue": "arXiv",
  "versions": []
}