Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures

Yiming Chen, Yuan Zhang, Liyuan Cao, Kun Yuan, Zaiwen Wen

Keywords: zeroth-order optimization, large language model fine-tuning, stochastic optimization

TL;DR: We propose a new zeroth-order algorithm with low-rank gradient estimation structures, enhancing the fine-tuning of large language models.

Abstract: Parameter-efficient fine-tuning (PEFT) significantly reduces memory costs when adapting large language models (LLMs) for downstream applications. However, traditional first-order (FO) fine-tuning algorithms incur substantial memory overhead due to the need to store activation values for back-propagation during gradient computation, particularly in long-context fine-tuning tasks. Zeroth-order (ZO) algorithms offer a promising alternative by approximating gradients using finite differences of function values, thus eliminating the need for activation storage. Nevertheless, existing ZO methods struggle to capture the low-rank gradient structure common in LLM fine-tuning, leading to suboptimal performance. This paper proposes a low-rank ZO gradient estimator and introduces a novel **lo**w-rank **ZO** algorithm (LOZO) that effectively captures this structure in LLMs. We provide convergence guarantees for LOZO by framing it as a subspace optimization method. Additionally, its low-rank nature enables LOZO to integrate with momentum techniques while incurring negligible extra memory costs. Extensive experiments across various model sizes and downstream tasks demonstrate that LOZO and its momentum-based variant outperform existing ZO methods and closely approach the performance of FO algorithms.

Primary Area: optimization

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Submission Number: 6337