{
  "abstract": "This note revisits the convergence of the Parikh--Boyd two-way block-splitting algorithm for large-scale distributed learning through the He--Yuan prediction--correction framework. Simultaneous row--column partitioning is also relevant to hybrid federated learning, where data may be heterogeneous in both samples and features. We lift the reduced iteration to an equal-dimensional product space and reconstruct the primal and dual coordinates omitted by its implementation. The induced orthogonal-complement structure establishes exact iteration-by-iteration equivalence with the published updates. A mixed variational-inequality representation then yields a fundamental descent inequality, global convergence, an ergodic complexity bound, and current-iterate residual estimates under standard convexity, solvability, exact-subproblem, and invariant-initialization assumptions. The analysis also shows that the reduced state recursion is a metric proximal point iteration. No strong convexity, differentiability, or full-rank condition is imposed. The derivation clarifies which algebraic initialization conditions allow the reduced implementation to inherit the full-space convergence and complexity guarantees without modifying its local updates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27924",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaofei Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7018pasttpt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27924",
  "fulltext_url": null,
  "id": "f7018pasttpt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27924",
  "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",
      "stat.CO"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214170415",
  "pdf_url": "https://arxiv.org/pdf/2609.27924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7018pasttpt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.27924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "A Prediction--Correction Analysis of Two-Way Block Splitting in Distributed Learning",
  "title_text": "A Prediction--Correction Analysis of Two-Way Block Splitting in Distributed Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/f7018pasttpt6",
  "venue": "arXiv",
  "versions": []
}