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

Large language models (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.

Perturbation-efficient Zeroth-order Optimization for Hardware-friendly On-device Training

Zeroth-order (ZO) optimization is an emerging deep neural network (DNN) training paradigm that offers computational simplicity and memory savings. However, this seemingly promising approach faces a significant and long-ignored challenge. ZO requires generating a substantial number of Gaussian random numbers, which poses significant difficulties and even makes it infeasible for hardware platforms, such as FPGAs and ASICs. In this paper, we identify this critical issue, which arises from the mismatch between algorithm and hardware designers. To address this issue, we proposed PeZO, a perturbation-efficient ZO framework. Specifically, we design random number reuse strategies to significantly reduce the demand for random number generation and introduce a hardware-friendly adaptive scaling method to replace the costly Gaussian distribution with a uniform distribution. Our experiments show that PeZO reduces the required LUTs and FFs for random number generation by 48.6\% and 12.7\%, and saves at maximum 86\% power consumption, all without compromising training performance, making ZO optimization feasible for on-device training. To the best of our knowledge, we are the first to explore the potential of on-device ZO optimization, providing valuable insights for future research.

Harmony in Divergence: Towards Fast, Accurate, and Memory-efficient Zeroth-order LLM Fine-tuning

Large language models (LLMs) excel across various tasks, but standard first-order (FO) fine-tuning demands considerable memory, significantly limiting real-world deployment. Recently, zeroth-order (ZO) optimization stood out as a promising memory-efficient training paradigm, avoiding backward passes and relying solely on forward passes for gradient estimation, making it attractive for resource-constrained scenarios. However, ZO method lags far behind FO method in both convergence speed and accuracy. To bridge the gap, we introduce a novel layer-wise divergence analysis that uncovers the distinct update pattern of FO and ZO optimization. Aiming to resemble the learning capacity of FO method from the findings, we propose \textbf{Di}vergence-driven \textbf{Z}eroth-\textbf{O}rder (\textbf{DiZO}) optimization. DiZO conducts divergence-driven layer adaptation by incorporating projections to ZO updates, generating diverse-magnitude updates precisely scaled to layer-wise individual optimization needs. Our results demonstrate that DiZO significantly reduces the needed iterations for convergence without sacrificing throughput, cutting training GPU hours by up to 48\% on various datasets. Moreover, DiZO consistently outperforms the representative ZO baselines in fine-tuning RoBERTa-large, OPT-series, and Llama-series on downstream tasks and, in some cases, even surpasses memory-intensive FO fine-tuning.