SBVR: Summation of BitVector Representation for Efficient LLM Quantization

Abstract

With the advent of large language models (LLMs), numerous Post-Training Quantization (PTQ) strategies have been proposed to alleviate deployment barriers created by their enormous parameter counts. Quantization achieves compression by limiting the number of representable points in the data. Therefore, the key to achieving efficient quantization is selecting the optimal combination of representation points, or codes, for the given data. Existing PTQ solutions adopt two major approaches to this problem: Round-To-Nearest (RTN)-based methods and codebook-based methods. RTN-based methods map LLM weights onto uniformly distributed integer grids, failing to account for the Gaussian-like weight distribution of LLM weights. Codebook-based methods mitigate this issue by constructing distribution-aware codebooks; however, they suffer from random and strided memory access patterns, resulting in degraded inference speed that is exacerbated by the limited size of GPU L1 cache. To overcome these limitations, we propose a novel LLM quantization method, SBVR (Summation of BitVector Representation), that enables Gaussian-like code representation in a hardware-friendly manner for fast inference. SBVR maps weight values to non-uniform representation points whose distribution follows the actual distribution of LLM weights, enabling more accurate compression. Additionally, we design a custom CUDA kernel that allows matrix-vector multiplication directly in the SBVR format without decompression, thereby enabling high-performance execution of SBVR-compressed models. Our evaluations of SBVR on various models demonstrate state-of-the-art perplexity and accuracy benchmark performance while delivering a 2.21x- 3.04x end-to-end token-generation speedup over naive FP16 models in the 4-bit quantization regime.