Learning Low-Rank Representations for Model Compression

TL;DR

This paper introduces LR²VQ, a low-rank representation vector quantization method that enhances model compression by combining dimensionality reduction with clustering, leading to significant accuracy improvements over existing VQ techniques.

Contribution

The paper proposes LR²VQ, a novel end-to-end trainable vector quantization method that integrates low-rank approximation with subvector clustering for improved model compression.

Findings

Achieves 2.8%/1.0% top-1 accuracy improvements on ImageNet with ResNet-18/ResNet-50.

Provides a theoretical framework for estimating the optimal clustering dimensionality.

Demonstrates superior performance over previous VQ-based compression algorithms.

Abstract

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied, optimizations of the vectors in favour of clustering performance are not carefully considered, especially via the reduction of vector dimensionality. This paper reports our recent progress on the combination of dimensionality compression and vector quantization, proposing a Low-Rank Representation Vector Quantization ($\text{LR}^2\text{VQ}$) method that outperforms previous VQ algorithms in various tasks and architectures. $\text{LR}^2\text{VQ}$ joins low-rank representation with subvector clustering to construct a new kind of building block that is directly optimized through end-to-end training over the task loss. Our proposed design pattern introduces three hyper-parameters, the number of clusters $k$, the size of subvectors $m$ and the clustering dimensionality $\tilde{d}$. In our method, the compression ratio could be directly controlled by $m$, and the final accuracy is solely determined by $\tilde{d}$. We recognize $\tilde{d}$ as a trade-off between low-rank approximation error and clustering error and carry out both theoretical analysis and experimental observations that empower the estimation of the proper $\tilde{d}$ before fine-tunning. With a proper $\tilde{d}$, we evaluate $\text{LR}^2\text{VQ}$ with ResNet-18/ResNet-50 on ImageNet classification datasets, achieving 2.8\%/1.0\% top-1 accuracy improvements over the current state-of-the-art VQ-based compression algorithms with 43$\times$/31$\times$ compression factor.