# PolarQuant: Optimal Gaussian Weight Quantization via Hadamard Rotation for LLM Compression

arXiv: https://arxiv.org/abs/2603.29078 · HTML: https://mlsanity.com/paper/2603.29078/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [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)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)

## Built on by (most cited first, 2 of 2)

- [QAM-W: Joint 2D Codebook Quantization for LLM Weights via Hadamard Rotation and Activation-Aware Scaling](https://mlsanity.com/paper/2605.26339/) (2026)
- [Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach](https://mlsanity.com/paper/2606.21448/) (2026)

## Abstract (arXiv)

We present PolarQuant, a post-training weight quantization method for large language models (LLMs) that exploits the distributional structure of neural network weights to achieve near-lossless compression. PolarQuant operates in three stages: (1) block-wise normalization to the unit hypersphere, (2) Walsh-Hadamard rotation to transform coordinates into approximately Gaussian random variables, and (3) quantization with centroids matched to the Gaussian distribution. Our ablation reveals that Hadamard rotation alone accounts for 98% of the quality improvement, reducing Qwen3.5-9B perplexity from 6.90 (absmax Q5) to 6.40 (Delta = +0.03 from FP16), making it practically lossless without any calibration data. Furthermore, PolarQuant functions as an effective preprocessing step for downstream INT4 quantizers: PolarQuant Q5 dequantized and re-quantized by torchao INT4 achieves perplexity 6.56 versus 6.68 for direct absmax INT4, while maintaining 43.1 tok/s throughput at 6.5 GB VRAM. Code and models are publicly available.