{
  "abstract": "Overparameterized networks often have ill-conditioned, saddle rich loss landscapes. They are usually trained with first-order methods that struggle on those landscapes, while many second-order methods stay infeasible at scale. Some scalable cubic methods replace the Hessian by a computationally cheap approximation and drop the exact block curvature. This paper introduces ARC-block, a blockwise adaptive regularization with cubics (ARC) optimizer. For each parameter tensor it minimizes a cubic model over the true block Hessian, with a per-block adaptive cubic constant and a monotone guard on the full loss. Large tensors are handled matrix-free in a Lanczos-built Krylov subspace. ARC-block's CubicKrylov subsolver's descent is monotone with a per-block cubic decrease bound. For exact steps, and for Krylov steps that meet the Cartis--Gould--Toint residual test, we provide an $\\mathcal{O}(\\sqrt{B}\\varepsilon^{-3/2})$ sweep bound above a cross-block coupling floor. Another subsolver, ARC-$φ_1$, uses a trust-controlled exponential relaxation step. Among the cubic Newton methods evaluated here, these are the only ones whose steps stay exact on every parameter block (within the Krylov subspace), including on a $91.4$M-parameter implicit neural representation (INR). Run to convergence on FINER 2D image-fitting INR network, ARC-$φ_1$ reaches $133.5$ dB peak signal-to-noise ratio (PSNR), with no post peak collapse. Tuned Adam peaks at $78.2$ dB at $2{,}629$ s (step ${\\sim}625$k, about $44$ minutes), further steps degrade its PSNR. On the same benchmark, SOAP, L-BFGS, and the scalable diagonal cubic method AdaCubic stay at or below Adam's $78.2$ dB peak. Over the benchmark's 20 images, run to a plateau rule, ARC-$φ_1$'s per-image PSNR has median $132.4$ and mean $131.5\\pm3.3$ dB against tuned Adam's $72.8\\pm4.5$ dB.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22129",
  "author_total": 1,
  "authors": [
    {
      "name": "Rodion Podorozhny"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bq0b828vxe4yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22129",
  "fulltext_url": null,
  "id": "bq0b828vxe4yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22129",
  "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"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7204211469",
  "pdf_url": "https://arxiv.org/pdf/2608.22129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bq0b828vxe4yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2608.22129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence",
  "title_text": "Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/bq0b828vxe4yg",
  "venue": "arXiv",
  "versions": []
}