{
  "abstract": "Step-size selection remains a central challenge in large-scale neural network optimization; conservative steps slow convergence, while aggressive steps can destabilize it. We combine \\textbf{Z}ero-and-\\textbf{F}irst-\\textbf{O}rder optimization~(ZFO) and propose a lightweight framework that decouples direction selection from step-size. ZFO uses a trusted first-order optimizer to determine the direction and performs zeroth-order evaluations only along this one-dimensional subspace to choose how far to move. Using the current {gradient information} and two additional objective function evaluations, ZFO instances construct a local model of the objective function along the proposed direction and select a curvature-aware step within a bounded search interval. This yields an adaptive step-selection mechanism that costs less than a full line search. We provide theoretical guarantees to show that shared-sample evaluations produce reliable finite-difference curvature estimates, that the induced local model selects a near-optimal step along the search interval, and that ZFO converges to a neighborhood of a stationary point. Across the evaluated settings, language models and datasets, ZFO frequently improves optimization and final performance relative to fixed-step first-order baselines, with the magnitude and preferred local model depending on the objective. Our code is publicly available at: https://github.com/nizswan/Zeroth-First-Order-Framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: 40th Conference on Neural Information Processing Systems (NeurIPS 2026)",
  "arxiv": "2610.02190",
  "author_total": 3,
  "authors": [
    {
      "name": "Cristian McGee"
    },
    {
      "name": "El Houcine Bergou"
    },
    {
      "name": "Aritra Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22qqrxjmgk1hm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02190",
  "fulltext_url": null,
  "id": "22qqrxjmgk1hm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02190",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7216515338",
  "pdf_url": "https://arxiv.org/pdf/2610.02190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22qqrxjmgk1hm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02190"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning",
  "title_text": "Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/22qqrxjmgk1hm",
  "venue": "arXiv",
  "versions": []
}