HLWQ — Hadamard-Lloyd Weight Quantization

Status: name reservation (v0.0.1). The full implementation will land in subsequent releases.

HLWQ is a post-training weight quantization technique for large language models. It compresses each block of weights via three steps:

1. Per-block normalization to the unit hypersphere
2. Walsh-Hadamard rotation to transform coordinates into approximately Gaussian random variables
3. Lloyd-Max scalar quantization with centroids matched to the post-rotation Gaussian distribution

The combination achieves near-lossless compression at 5 bits per weight on Qwen3.5-9B (PPL 6.40 vs FP16 baseline 6.37), without any calibration data.

Reference

Vicentino, C. PolarQuant: Optimal Gaussian Weight Quantization via Hadamard Rotation for LLM Compression. arXiv:2603.29078, 2026.

Naming history

This technique was originally published under the name PolarQuant in the arxiv paper above. It is being rebranded to HLWQ (Hadamard-Lloyd Weight Quantization) to disambiguate from an unrelated, earlier algorithm also named PolarQuant published by Google Research:

Han, I., Kacham, P., Karbasi, A., Mirrokni, V., and Zandieh, A. PolarQuant: Quantizing KV Caches with Polar Transformation. arXiv:2502.02617, 2025.

Han et al.'s PolarQuant addresses KV cache compression with a random rotation (polar transformation). HLWQ addresses weight compression with a deterministic Walsh-Hadamard rotation. The applications and rotation mechanisms differ; only the historical name overlapped, and HLWQ is the disambiguated brand going forward.

License

Apache-2.0