# Pushing the Limits of Block Rotations in Post-Training Quantization

arXiv: https://arxiv.org/abs/2601.22347 · HTML: https://mlsanity.com/paper/2601.22347/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [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)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [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)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [Evaluating Quantized Large Language Models](https://mlsanity.com/paper/2402.18158/) (2024)
- [ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantization](https://mlsanity.com/paper/2502.02631/) (2025)
- [Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization](https://mlsanity.com/paper/2509.23202/) (2025)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [FrameQuant: Flexible Low-Bit Quantization for Transformers](https://mlsanity.com/paper/2403.06082/) (2024)
- [Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos](https://mlsanity.com/paper/2508.04853/) (2025)
- [ButterflyQuant: Ultra-low-bit LLM Quantization through Learnable Orthogonal Butterfly Transforms](https://mlsanity.com/paper/2509.09679/) (2025)

## Built on by (most cited first, 11 of 11)

- [LoopQ: Quantization for Looped Language Models](https://mlsanity.com/paper/2605.16343/) (2026)
- [OrbitQuant: Data-Agnostic Quantization for Image and Video Diffusion Transformers](https://mlsanity.com/paper/2607.02461/) (2026)
- [dMX: Differentiable Mixed-Precision Assignment for Low-Precision Floating-Point Formats](https://mlsanity.com/paper/2606.04115/) (2026)
- [Optimal Post-Training Quantization Scales and Where to Find Them](https://mlsanity.com/paper/2606.10890/) (2026)
- [Contraction-Gauge Preconditioning for Quantized Matrix Multiplication](https://mlsanity.com/paper/2607.18745/) (2026)
- [Signed Symmetric Quantization for Few-Bit Integers](https://mlsanity.com/paper/2607.08779/) (2026)
- [When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation](https://mlsanity.com/paper/2608.13365/) (2026)
- [Transforms for LLM Quantization: The Great Inversion and Format Co-Design](https://mlsanity.com/paper/2608.25188/) (2026)
- [PRQuant: Permutation Residual Quantization for Low-Overhead Inference](https://mlsanity.com/paper/2609.22106/) (2026)
- [The Devil Is in the Reconstruction Loss Scale: Rethinking Optimization in LLM Quantization](https://mlsanity.com/paper/2610.00983/) (2026)
- [CORAL-KV: Compact Cross-Layer Prediction and Residual Coding for Autoregressive Video KV Caches](https://mlsanity.com/paper/2610.12514/) (2026)

## Abstract (arXiv)

Recent post-training quantization (PTQ) methods have adopted block rotations to diffuse outliers prior to rounding. While this reduces the overhead of online full-vector rotations, the effect of block structure on outlier suppression remains poorly understood. To fill this gap, we present the first systematic, non-asymptotic analysis of outlier suppression for block Hadamard rotations. Our analysis reveals that outlier suppression is fundamentally limited by the geometry of the input vector. In particular, in the deterministic worst case, post-rotation outliers are minimized when the pre-rotation ℓ1 norm mass is evenly distributed across blocks. Guided by these insights, we introduce PeRQ (Permute, Rotate, then Quantize), a PTQ framework that redistributes activation mass via permutations prior to rotation. We propose a greedy mass diffusion algorithm to calibrate permutations by equalizing the expected blockwise ℓ1 norms. To avoid adding inference overhead, we identify permutation-equivariant regions in transformer architectures to merge these permutations into model weights before deployment. Experiments show that PeRQ consistently improves accuracy across all block sizes, recovering up to 90% of the full-vector rotation perplexity when quantizing Llama3 1B to INT4 with block size 16, compared to 46% without permutations.