HeRo-Q: A General Framework for Stable Low Bit Quantization via Hessian Conditioning

TL;DR

HeRo-Q introduces a Hessian conditioning-based framework for stable low-bit quantization of large language models, significantly improving robustness and accuracy in ultra low-bit regimes without architectural changes.

Contribution

The paper presents HeRo-Q, a novel Hessian conditioning method that reshapes the loss landscape to enhance low-bit quantization robustness for large language models.

Findings

Outperforms state-of-the-art quantization methods like GPTQ, AWQ, and SpinQuant.

Achieves 70.15% GSM8K accuracy on Llama3 8B in ultra low-bit W3A16 regime.

Effectively prevents logical collapse in aggressive quantization scenarios.

Abstract

Post Training Quantization (PTQ), a mainstream model compression technique, often leads to the paradoxical 'low error, high loss' phenomenon because it focuses solely on minimizing quantization error. The root cause lies in the Hessian matrix of the LLM loss landscape: a few high curvature directions are extremely sensitive to perturbations. To address this, we propose the Hessian Robust Quantization (HeRo Q) algorithm, which applies a lightweight, learnable rotation-compression matrix to the weight space prior to quantization. This joint framework reshapes the loss landscape by reducing the largest Hessian eigenvalue and reducing its max eigenvalue, thereby significantly enhancing robustness to quantization noise. HeRo-Q requires no architectural modifications, incurs negligible computational overhead, and integrates seamlessly into existing PTQ pipelines. Experiments on Llama and Qwen models show that HeRo Q consistently outperforms state of the art methods including GPTQ, AWQ, and SpinQuant not only achieving superior performance under standard W4A8 settings, but also excelling in the highly challenging W3A16 ultra low bit regime, where it boosts GSM8K accuracy on Llama3 8B to 70.15\% and effectively avoids the logical collapse commonly seen in aggressive quantization.