PolarQuant: Vector Quantization with Polar Transformation

Insu Han, Praneeth Kacham, Amin Karbasi, Vahab Mirrokni, Amir Zandieh
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:5113-5121, 2026.

Abstract

Vector quantization is a prevalent technique for reducing the memory footprint in a wide range of computational problems, such as the training and deployment of deep learning models and vector search systems. We introduce PolarQuant, a novel online vector quantization method that leverages random preconditioning and polar transformation. Our approach efficiently transforms Euclidean vectors into polar coordinates using a recursive algorithm, and then quantizes the resulting angles. A key insight is that, following random preconditioning, the angles in the polar representation exhibit a tightly bounded, highly concentrated, and analytically computable distribution, independent of the input data. This nice distribution eliminates the need for explicit normalization and learned data-dependent quantization codebooks, steps that introduce significant memory and runtime overhead in traditional product/scalar quantization methods. By circumventing this data-dependent step, PolarQuant achieves substantial memory and runtime savings, making it highly suitable for online scenarios such as KV cache compression. The long-context evaluation demonstrates that PolarQuant compresses the KV cache by over 4.2X while achieving the best quality scores compared to the state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-han26c, title = { PolarQuant: Vector Quantization with Polar Transformation }, author = {Han, Insu and Kacham, Praneeth and Karbasi, Amin and Mirrokni, Vahab and Zandieh, Amir}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {5113--5121}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/han26c/han26c.pdf}, url = {https://proceedings.mlr.press/v300/han26c.html}, abstract = { Vector quantization is a prevalent technique for reducing the memory footprint in a wide range of computational problems, such as the training and deployment of deep learning models and vector search systems. We introduce PolarQuant, a novel online vector quantization method that leverages random preconditioning and polar transformation. Our approach efficiently transforms Euclidean vectors into polar coordinates using a recursive algorithm, and then quantizes the resulting angles. A key insight is that, following random preconditioning, the angles in the polar representation exhibit a tightly bounded, highly concentrated, and analytically computable distribution, independent of the input data. This nice distribution eliminates the need for explicit normalization and learned data-dependent quantization codebooks, steps that introduce significant memory and runtime overhead in traditional product/scalar quantization methods. By circumventing this data-dependent step, PolarQuant achieves substantial memory and runtime savings, making it highly suitable for online scenarios such as KV cache compression. The long-context evaluation demonstrates that PolarQuant compresses the KV cache by over 4.2X while achieving the best quality scores compared to the state-of-the-art methods. } }
Endnote
%0 Conference Paper %T PolarQuant: Vector Quantization with Polar Transformation %A Insu Han %A Praneeth Kacham %A Amin Karbasi %A Vahab Mirrokni %A Amir Zandieh %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-han26c %I PMLR %P 5113--5121 %U https://proceedings.mlr.press/v300/han26c.html %V 300 %X Vector quantization is a prevalent technique for reducing the memory footprint in a wide range of computational problems, such as the training and deployment of deep learning models and vector search systems. We introduce PolarQuant, a novel online vector quantization method that leverages random preconditioning and polar transformation. Our approach efficiently transforms Euclidean vectors into polar coordinates using a recursive algorithm, and then quantizes the resulting angles. A key insight is that, following random preconditioning, the angles in the polar representation exhibit a tightly bounded, highly concentrated, and analytically computable distribution, independent of the input data. This nice distribution eliminates the need for explicit normalization and learned data-dependent quantization codebooks, steps that introduce significant memory and runtime overhead in traditional product/scalar quantization methods. By circumventing this data-dependent step, PolarQuant achieves substantial memory and runtime savings, making it highly suitable for online scenarios such as KV cache compression. The long-context evaluation demonstrates that PolarQuant compresses the KV cache by over 4.2X while achieving the best quality scores compared to the state-of-the-art methods.
APA
Han, I., Kacham, P., Karbasi, A., Mirrokni, V. & Zandieh, A.. (2026). PolarQuant: Vector Quantization with Polar Transformation . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:5113-5121 Available from https://proceedings.mlr.press/v300/han26c.html.

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