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

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, 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 Llama-3-8B to 70.15% and effectively avoids the logical collapse commonly seen in aggressive quantization.