KerZOO: Kernel Function Informed Zeroth-Order Optimization for Accurate and Accelerated LLM Fine-Tuning (2505.18886v1)

Abstract: LLMs have demonstrated impressive capabilities across numerous NLP tasks. Nevertheless, conventional first-order fine-tuning techniques impose heavy memory demands, creating practical obstacles to real-world applications. Zeroth-order (ZO) optimization has recently emerged as a promising memory-efficient alternative, as it circumvents the need for backpropagation by estimating gradients solely through forward passes--making it particularly suitable for resource-limited environments. Despite its efficiency, ZO optimization suffers from gradient estimation bias, which significantly hinders convergence speed. To address this, we analytically identify and characterize the lower-order bias introduced during ZO-based gradient estimation in LLM fine-tuning. Motivated by tools in mathematical physics, we introduce a kernel-function-based ZO framework aimed at mitigating this bias and improving optimization stability. KerZOO achieves comparable or superior performance to existing ZO baselines in both full-parameter and parameter-efficient fine-tuning settings of LLMs, while significantly reducing the number of iterations required to reach convergence. For example, KerZOO reduces total GPU training hours by as much as 74% and 44% on WSC and MultiRC datasets in fine-tuning OPT-2.7B model and can exceed the MeZO baseline by 2.9% and 2.6% in accuracy. We show that the kernel function is an effective avenue for reducing estimation bias in ZO methods.

Kernel Function Informed Zeroth-Order Optimization for LLM Fine-Tuning

The paper "KerZOO: Kernel Function Informed Zeroth-Order Optimization for Accurate and Accelerated LLM Fine-Tuning" introduces an innovative approach for fine-tuning LLMs under memory constraints using zeroth-order optimization (ZO). The authors present a model called KerZOO, which seeks to mitigate gradient estimation bias—a major limitation affecting the convergence speed and accuracy in ZO methods.

Context and Motivation

Recent advancements in natural language processing have highlighted the efficacy of LLMs in diverse tasks. However, as model sizes increase, traditional fine-tuning methods, heavily reliant on first-order optimization techniques such as backpropagation, impose significant memory demands that hinder scalability in resource-limited environments. Recent alternatives, such as ZO optimization, offer a promising avenue by bypassing the need for gradient computation through backpropagation, instead estimating gradients through forward passes. Despite ZO's advantages in reducing memory consumption, it is currently limited by slower convergence speeds and estimation bias due to its reliance on random perturbations for gradient estimation.

Addressing ZO Limitations with KerZOO

KerZOO seeks to eliminate the lower-order bias present in gradient estimation by ZO methods through the incorporation of kernel functions. By analyzing the lower-order bias mathematically, the authors introduce a kernel-function-based framework that enhances optimization stability. The kernel function effectively reduces estimation bias, leading to more accurate and efficient gradient estimations. KerZOO exhibits significant improvements in performance, reducing GPU training hours by up to 74% on certain datasets, such as the WSC and MultiRC, and achieving approximately 2.6% higher accuracy compared to existing ZO methods.

Numerical Results and Experimental Validation

Through comprehensive experiments on medium-sized models like RoBERTa-large and autoregressive LLMs such as OPT and LLaMA, KerZOO consistently demonstrates superior performance across various tasks, including text classification and generation. Notably, in comparison to MeZO, KerZOO achieves faster convergence and more refined gradient estimation, ostensibly due to its underlying kernel-function framework. Experimental results indicate substantial reductions in the number of iterations needed for convergence, highlighting KerZOO's efficiency compared to traditional ZO approaches.

Practical and Theoretical Implications

The theoretical contributions of KerZOO are particularly noteworthy; these include a detailed characterization of the mathematical basis behind the lower-order bias in ZO gradient estimation. The kernel function design not only improves convergence rates but also maintains high accuracy with substantially reduced computational costs, paving the way for training LLMs on commodity hardware. Practically, such advancements make LLM fine-tuning more accessible across institutions with varying computational capacities.

Future Work and Speculation

The utilization of kernel functions to mitigate gradient estimation bias opens numerous avenues for further research in memory-efficient optimization strategies. This paper hints at potential extensions beyond LLMs, such as applications in model pruning, quantization, or optimization of vision-LLMs. As technologies continue to evolve, rotational strategies might be employed to further reduce estimation bias.

Conclusion

In summary, KerZOO stands as a robust contribution in the field of LLM fine-tuning under memory constraints, leveraging kernel functions to effectively enhance zeroth-order optimization. This paper presents significant advancements in addressing the convergence challenges inherent in existing ZO techniques, positioning KerZOO as a potent tool for scalable, memory-efficient model fine-tuning.