TeZO: Empowering the Low-Rankness on the Temporal Dimension in the Zeroth-Order Optimization for Fine-tuning LLMs

Zeroth-order optimization (ZO) has demonstrated remarkable promise in efficient fine-tuning tasks for Large Language Models (LLMs). In particular, recent advances incorporate the low-rankness of gradients, introducing low-rank ZO estimators to further reduce GPU memory consumption. However, most existing works focus solely on the low-rankness of each individual gradient, overlooking a broader property shared by all gradients throughout the training, i.e., all gradients approximately reside within a similar subspace. In this paper, we consider two factors together and propose a novel low-rank ZO estimator, TeZO, which captures the low-rankness across both the model and temporal dimension. Specifically, we represent ZO perturbations along the temporal dimension as a 3D tensor and employ Canonical Polyadic Decomposition (CPD) to extract each low-rank 2D matrix, significantly reducing the training cost. TeZO can also be easily extended to the Adam variant while consuming less memory than MeZO-SGD, and requiring about only 35% memory of MeZO-Adam. Both comprehensive theoretical analysis and extensive experimental research have validated its efficiency, achieving SOTA-comparable results with lower overhead of time and memory.