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

• URL: http://arxiv.org/abs/2501.19057v1
• Date: Fri, 31 Jan 2025 11:34:03 GMT
• Title: TeZO: Empowering the Low-Rankness on the Temporal Dimension in the Zeroth-Order Optimization for Fine-tuning LLMs
• Authors: Yan Sun, Tiansheng Huang, Liang Ding, Li Shen, Dacheng Tao,
• Abstract summary: We propose a novel low-rank ZO estimator, TeZO, which captures the low-rankness across both the model and temporal dimension.<n>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.
• Score: 58.19080159470868
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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