CommVQ: Commutative Vector Quantization for KV Cache Compression
Authors: name: Junyan Li, name: Yang Zhang, name: Muhammad Yusuf Hassan, name: Talha Chafekar, name: Tianle Cai, name: Zhile Ren, name: Pengsheng Guo, name: Foroozan Karimzadeh, name: Colorado Reed, name: Chong Wang, name: Chuang Gan

Large Language Models (LLMs) are increasingly used in applications requiring
long context lengths, but the key-value (KV) cache often becomes a memory
bottleneck on GPUs as context grows. To address this, we propose Commutative
Vector Quantization (CommVQ) to significantly reduce memory usage for
long-context LLM inference. We first introduce additive quantization with a
lightweight encoder and codebook to compress the KV cache, which can be decoded
via simple matrix multiplication. To further reduce computational costs during
decoding, we design the codebook to be commutative with Rotary Position
Embedding (RoPE) and train it using an Expectation-Maximization (EM) algorithm.
This enables efficient integration of decoding into the self-attention
mechanism. Our approach achieves high accuracy with additive quantization and
low overhead via the RoPE-commutative codebook. Experiments on long-context
benchmarks and GSM8K show that our method reduces FP16 KV cache size by 87.5%
with 2-bit quantization, while outperforming state-of-the-art KV cache
quantization methods. Notably, it enables 1-bit KV cache quantization with
minimal accuracy loss, allowing a LLaMA-3.1 8B model to run with a 128K context
length on a single RTX 4090 GPU. The source code is available at:
https://github.com/UMass-Embodied-AGI/CommVQ.