NestQuant: Nested Lattice Quantization for Matrix Products and LLMs

TL;DR

NestQuant introduces a nested lattice-based post-training quantization method for large language models, significantly reducing model size and perplexity while maintaining high accuracy across various models and benchmarks.

Contribution

The paper presents a practical, low-complexity nested lattice quantization scheme for LLMs, outperforming existing methods in perplexity reduction and model efficiency.

Findings

Quantizes Llama-3-8B weights and activations to 4 bits with perplexity 6.6

Achieves over 55% reduction in perplexity gap compared to unquantized models

Consistently outperforms state-of-the-art quantization methods on larger models and benchmarks

Abstract

Post-training quantization (PTQ) has emerged as a critical technique for efficient deployment of large language models (LLMs). This work proposes NestQuant, a novel PTQ scheme for weights and activations that is based on self-similar nested lattices. Recent works have mathematically shown such quantizers to be information-theoretically optimal for low-precision matrix multiplication. We implement a practical low-complexity version of NestQuant based on Gosset lattice, making it a drop-in quantizer for any matrix multiplication step (e.g., in self-attention, MLP etc). For example, NestQuant quantizes weights, KV-cache, and activations of Llama-3-8B to 4 bits, achieving perplexity of 6.6 on wikitext2. This represents more than 55% reduction in perplexity gap with respect to unquantized model (perplexity of 6.14) compared to state-of-the-art Metas SpinQuant (perplexity 7.3), OstQuant (7.3) and QuaRot (8.2). Comparisons on bigger models (up to 70B) and on various LLM evaluation benchmarks confirm uniform superiority of NestQuant.