{
  "abstract": "Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region mechanism. Building on the Additively Preconditioned Trust-Region Strategy (APTS), we propose a non-monotone variant with a nonlinear additive Schwarz preconditioner that combines parallel subdomain corrections with global coarse-space directions. A windowed acceptance criterion allows controlled objective increases, avoiding needless rejection of effective coarse steps. The resulting non-monotone APTS (NAPTS) preserves accuracy while reducing CPU time by 30\\% and cutting rejected steps to one third of those in APTS.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: In: Domain Decomposition Methods in Science and Engineering XXIX, Lecture Notes in Computational Science and Engineering, vol. 157, Springer (2026)",
  "arxiv": "2605.14860",
  "author_total": 5,
  "authors": [
    {
      "name": "Andrea Angino"
    },
    {
      "name": "Bindi Çapriqi"
    },
    {
      "name": "Shega Likaj"
    },
    {
      "name": "Ken Trotti"
    },
    {
      "name": "Rolf Krause"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/459b8fawvmyst.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14860",
  "fulltext_url": null,
  "id": "459b8fawvmyst",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14860",
  "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.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7161269321",
  "pdf_url": "https://arxiv.org/pdf/2605.14860",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/459b8fawvmyst.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2605.14860",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14860"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training",
  "title_text": "A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/459b8fawvmyst",
  "venue": "arXiv",
  "versions": []
}