# PRQuant: Permutation Residual Quantization for Low-Overhead Inference

arXiv: https://arxiv.org/abs/2609.22106 · HTML: https://mlsanity.com/paper/2609.22106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [RPTQ: Reorder-based Post-training Quantization for Large Language Models](https://mlsanity.com/paper/2304.01089/) (2023)
- [Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization](https://mlsanity.com/paper/2509.23202/) (2025)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [DartQuant: Efficient Rotational Distribution Calibration for LLM Quantization](https://mlsanity.com/paper/2511.04063/) (2025)
- [ARCQuant: Boosting NVFP4 Quantization with Augmented Residual Channels for LLMs](https://mlsanity.com/paper/2601.07475/) (2026)
- [Pushing the Limits of Block Rotations in Post-Training Quantization](https://mlsanity.com/paper/2601.22347/) (2026)
- [DuQuant++: Fine-grained Rotation Enhances Microscaling FP4 Quantization](https://mlsanity.com/paper/2604.17789/) (2026)
- [BATQuant: Outlier-resilient MXFP4 Quantization via Learnable Block-wise Optimization](https://mlsanity.com/paper/2603.16590/) (2026)
- [MosaicQuant: Inlier-Outlier Disaggregation for Unified 4-Bit LLM Quantization](https://mlsanity.com/paper/2606.15652/) (2026)
- [OSC: Hardware Efficient W4A4 Quantization via Outlier Separation in Channel Dimension](https://mlsanity.com/paper/2604.12782/) (2026)

## Abstract (arXiv)

Low-bit quantization of linear layers is often dominated by a small number of outlier channels. Existing smoothing, rotation, and residual-based methods can mitigate this issue, but may shift the quantization bottleneck to weights or introduce costly online operations. To address these limitations, we propose PRQuant (Permutation Residual Quantization), a training-free framework that combines channel permutation with offline weight residual compensation. PRQuant identifies the scaled-weight columns with the largest quantization errors and permutes them into contiguous tail blocks. This structure allows the corresponding weight residuals to be precomputed entirely offline, while replacing scattered activation gathering with simple contiguous access during inference, yielding a single regular MXFP4 GEMM for compensated computation. Experiments show that PRQuant substantially reduces down-projection reconstruction error, with scaling and residual compensation providing the main numerical gains while permutation enables a hardware-friendly contiguous layout. Comprehensive experiment results on Qwen3-4B-Instruct-2507 and Qwen3-30B-A3B-Instruct-2507 illustrate that PRQuant achieves up to averagelly 2.6x and 1.8x operator speedup over BF16 respectively, while preserving near plain MXFP4 end-to-end decoding efficiency. Across five downstream benchmarks, PRQuant achieves the best average accuracy among the quantized methods, improving accuracy over MXFP4 by 1.24 and 0.55, respectively.