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Technical Report: Activation Residual Hessian Quantization (ARHQ) for Low-Bit LLM Quantization

arXiv 2605.00140 ↗First posted 30 Apr 2026cs.LG cs.CL cs.CVcited by 0

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Abstract (arXiv)

We present Activation Residual Hessian Quantization (ARHQ), a post-training weight splitting method designed to mitigate error propagation in low-bit activation-weight quantization. By constructing an input-side residual Hessian from activation quantization residuals (G_x), ARHQ analytically identifies and isolates error-sensitive weight directions into a high-precision low-rank branch. This is achieved via a closed-form truncated SVD on the scaled weight matrix W G^{1/2}_x . Experimental results on Qwen3-4B-Thinking-2507 demonstrate that ARHQ significantly improves layer-wise SNR and preserves downstream reasoning performance on ZebraLogic even under aggressive quantization. The code is available at https://github.com/BeautMoonQ/ARHQ.

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References · 4

  1. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  2. 2024SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compressioncited by 243
  3. 2024SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Modelscited by 170
  4. 2023ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Modelscited by 169

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  8. 2026HeRo-Q: A General Framework for Stable Low Bit Quantization via Hessian Conditioning