Title: Effective Interaction between Quantization and Low-Rank Decomposition based on LLMs
Primary area: foundation or frontier models, including LLMs
Keywords: Quantization, Low-Rank Decomposition, LLMs

Abstract: As the parameter size of language models continues to grow, effective model compression is required to reduce their computational and memory overhead. Low-rank decomposition and quantization are two prominent compression methods that have been proven to significantly reduce the computational and memory requirements of Large Language Models (LLMs) while maintaining model accuracy. However, how these two methods interact when combined remains a critical question for developers, as many assume they are orthogonal, meaning their combination would not introduce additional errors beyond those independently introduced by each method. This paper provides the first mathematical proof that low-rank decomposition and quantization are non-orthogonal. We validate these findings through a series of experiments on large language models. Our results demonstrate that these methods are non-orthogonal, and their combination leads to significant performance degradation. Importantly, we propose a novel approach Diagonal Adhesive Method (DAM), which can effectively combine the two methods and mitigate the performance loss. Our research provides deep insights into model compression and lays a solid theoretical and experimental foundation for future related studies.