Ternary Singular Value Decomposition as a Better Parameterized Form in Linear Mapping
This addresses the problem of reducing computational costs in neural networks for efficient deployment, though it appears incremental as it builds on SVD methods.
The paper tackles network compression by introducing Ternary SVD (TSVD), a parameterized linear mapping that limits matrices to ternary values, achieving state-of-the-art compression performance across models like ConvNext, BERT, and OPT.
We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary matrices form in $\{\pm 1, 0\}$. This means that instead of using the expensive multiplication instructions, TSVD only requires addition instructions when computing $U(\cdot)$ and $V(\cdot)$. We provide direct and training transition algorithms for TSVD like Post Training Quantization and Quantization Aware Training respectively. Additionally, we analyze the convergence of the direct transition algorithms in theory. In experiments, we demonstrate that TSVD can achieve state-of-the-art network compression performance in various types of networks and tasks, including current baseline models such as ConvNext, Swim, BERT, and large language model like OPT.