Outlier Smoothing with Closed-Form Rotations for W4A4 Large Language Model Quantization

TL;DR

This paper introduces SingleQuant, a novel quantization framework for large language models that uses closed-form rotations to improve efficiency and performance, addressing convergence issues in existing methods.

Contribution

SingleQuant decouples quantization from truncation using geometric rotations, enabling faster and more accurate LLM quantization with theoretical and empirical validation.

Findings

SingleQuant achieves 1,400× speedup in quantization of LLaMA-2-13B.

It improves average task performance by +0.57% over baselines.

Experimental results on 7B-70B LLMs demonstrate superior performance and efficiency.

Abstract

Large Language Models (LLMs) quantization facilitates deploying LLMs in resource-limited settings, but existing methods that combine incompatible gradient optimization and quantization truncation lead to serious convergence pathology. This prolongs quantization time and degrades LLMs' task performance. Our studies confirm that Straight-Through Estimator (STE) on Stiefel manifolds introduce non-smoothness and gradient noise, obstructing optimization convergence and blocking high-fidelity quantized LLM development despite extensive training. To tackle the above limitations, we propose SingleQuant, a single-pass quantization framework that decouples from quantization truncation, thereby eliminating the above non-smoothness and gradient noise factors. Specifically, SingleQuant constructs Alignment Rotation Transformation (ART) and Uniformity Rotation Transformation (URT) targeting distinct activation outliers, where ART achieves smoothing of outlier values via closed-form optimal rotations, and URT reshapes distributions through geometric mapping. Both matrices comprise strictly formulated Givens rotations with predetermined dimensions and rotation angles, enabling promising LLMs task performance within a short time. Experimental results demonstrate SingleQuant's superiority over the selected baselines across diverse tasks on 7B-70B LLMs. To be more precise, SingleQuant enables quantized LLMs to achieve higher task performance while necessitating less time for quantization. For example, when quantizing LLaMA-2-13B, SingleQuant achieves 1,400$\times$ quantization speedup and increases +0.57\% average task performance compared to the selected best baseline.