SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression

Xin Wang, Yu Zheng, Zhongwei Wan, Mi Zhang

Abstract: The advancements in Large Language Models (LLMs) have been hindered by their substantial sizes, which necessitate LLM compression methods for practical deployment. Singular Value Decomposition (SVD) offers a promising solution for LLM compression. However, state-of-the-art SVD-based LLM compression methods have two key limitations: truncating smaller singular values may lead to higher compression loss, and the lack of update on the compressed weight after SVD truncation. In this work, we propose SVD-LLM, a new SVD-based LLM compression method that addresses the limitations of existing methods. SVD-LLM incorporates a truncation-aware data whitening strategy to ensure a direct mapping between singular values and compression loss. Moreover, SVD-LLM adopts a layer-wise closed-form model parameter update strategy to compensate for accuracy degradation under high compression ratios. We evaluate SVD-LLM on a total of 10 datasets and eight models from three different LLM families at four different scales. Our results demonstrate the superiority of SVD-LLM over state-of-the-arts, especially at high model compression ratios.