Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning

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: this https URL.

Accepted to 40th Conference on Neural Information Processing Systems (NeurIPS 2026). Code: this https URL

Machine Learning (cs.LG); Optimization and Control (math.OC)

G.1.6; I.2.6; F.2.1

arXiv:2610.02190 [cs.LG]

(or arXiv:2610.02190v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.02190 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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