# QuaSAR: Quantization Compensation via Stable Activation-Aware Rank Truncation

arXiv: https://arxiv.org/abs/2608.14149 · HTML: https://mlsanity.com/paper/2608.14149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 22 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [Towards Efficient Post-training Quantization of Pre-trained Language Models](https://mlsanity.com/paper/2109.15082/) (2021)
- [QuantVLA: Scale-Calibrated Post-Training Quantization for Vision-Language-Action Models](https://mlsanity.com/paper/2602.20309/) (2026)
- [Instance-Aware Group Quantization for Vision Transformers](https://mlsanity.com/paper/2404.00928/) (2024)
- [Quantization without Tears](https://mlsanity.com/paper/2411.13918/) (2024)
- [QERA: an Analytical Framework for Quantization Error Reconstruction](https://mlsanity.com/paper/2410.06040/) (2024)
- [Ridge Regularization: an Essential Concept in Data Science](https://mlsanity.com/paper/2006.00371/) (2020)
- [APHQ-ViT: Post-Training Quantization with Average Perturbation Hessian Based Reconstruction for Vision Transformers](https://mlsanity.com/paper/2504.02508/) (2025)
- [FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation](https://mlsanity.com/paper/2506.11543/) (2025)
- [QwT-v2: Practical, Effective and Efficient Post-Training Quantization](https://mlsanity.com/paper/2505.20932/) (2025)
- [Q-DiT4SR: Exploration of Detail-Preserving Diffusion Transformer Quantization for Real-World Image Super-Resolution](https://mlsanity.com/paper/2602.01273/) (2026)

## Abstract (arXiv)

Recent training-free post-training quantization methods restore model accuracy through closed-form residual compensation. To constrain additional model storage overhead, several existing methods gate layer selection by goodness-of-fit, retaining only those layers whose compensation yields a positive residual fit score and discarding the rest. In this paper, we show that, under the low-bit W4A4 setting, this gating mechanism fails to distinguish poorly predictable quantization error from numerical solver failure. Rank-deficient input activations yield severely ill-conditioned or numerically singular Gram matrices, causing the closed-form solver to become unstable and produce spuriously negative fit scores. Consequently, existing goodness-of-fit gates misclassify affected layers as uncompensable and discard them. Many of these discarded layers can nevertheless provide substantial error recovery when their compensation is computed using a numerically stable solver. To address this problem, we propose a parameter-free truncated pseudoinverse solver which removes collapsed directions prior to inversion. On ViT-B with the W4A4 setting, our training-free method achieves 81.42% top-1 accuracy, outperforming prior post-training methods and fine-tuning-based baselines. Combined with joint low-rank and quantization compression, the proposed method reaches a deployable operating point of 80.26% accuracy at 54.7 MB, providing a well-balanced trade-off between model size and accuracy.