# PolarQuant: Quantizing KV Caches with Polar Transformation

arXiv: https://arxiv.org/abs/2502.02617 · HTML: https://mlsanity.com/paper/2502.02617/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- First posted on arXiv 4 Feb 2025.

## Placed in

- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Built on by (most cited first, 27 of 27)

- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [KVLinC : KV Cache Quantization with Hadamard Rotation and Linear Correction](https://mlsanity.com/paper/2510.05373/) (2025)
- [PCDVQ: Enhancing Vector Quantization for Large Language Models via Polar Coordinate Decoupling](https://mlsanity.com/paper/2506.05432/) (2025)
- [Reconstructing KV Caches with Cross-layer Fusion For Enhanced Transformers](https://mlsanity.com/paper/2512.03870/) (2025)
- [OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond](https://mlsanity.com/paper/2605.19660/) (2026)
- [XQuant: Breaking the Memory Wall for LLM Inference with KV Cache Rematerialization](https://mlsanity.com/paper/2508.10395/) (2025)
- [Hierarchical vs. Flat Iteration in Shared-Weight Transformers](https://mlsanity.com/paper/2604.14442/) (2026)
- [CalibQuant: 1-Bit KV Cache Quantization for Multimodal LLMs](https://mlsanity.com/paper/2502.14882/) (2025)
- [TurboAngle: Near-Lossless KV Cache Compression via Uniform Angle Quantization](https://mlsanity.com/paper/2603.27467/) (2026)
- [SuperLocalMemory V3.3: The Living Brain -- Biologically-Inspired Forgetting, Cognitive Quantization, and Multi-Channel Retrieval for Zero-LLM Agent Memory Systems](https://mlsanity.com/paper/2604.04514/) (2026)
- [Open-TQ-Metal: Fused Compressed-Domain Attention for Long-Context LLM Inference on Apple Silicon](https://mlsanity.com/paper/2604.16957/) (2026)
- [eOptShrinkQ: Near-Lossless KV Cache Compression Through Optimal Spectral Denoising and Quantization](https://mlsanity.com/paper/2605.02905/) (2026)
- [SPHERICAL KV: Angle-Domain Attention and Rate-Distortion Retention for Efficient Long-Context Inference](https://mlsanity.com/paper/2605.18856/) (2026)
- [OCTOPUS: Optimized KV Cache for Transformers via Octahedral Parametrization Under optimal Squared error quantization](https://mlsanity.com/paper/2605.21226/) (2026)
- [Fewer Tokens, Smaller Cache: Reward-Coordinated Efficient Reasoning](https://mlsanity.com/paper/2608.04771/) (2026)
- [RoPE-Aware Bit Allocation for KV-Cache Quantization](https://mlsanity.com/paper/2606.24033/) (2026)
- [SPECTRA: Pushing the KV Cache Beyond the 2-Bit Cliff via Spectral Transform Coding](https://mlsanity.com/paper/2608.07915/) (2026)
- [Embedding Compression via Spherical Coordinates](https://mlsanity.com/paper/2602.00079/) (2026)
- [3DTurboQuant: Training-Free Near-Optimal Quantization for 3D Reconstruction Models](https://mlsanity.com/paper/2604.05366/) (2026)
- [Direction-Preserving Number Representations](https://mlsanity.com/paper/2605.07662/) (2026)
- [IVF-TQ: Calibration-Free Streaming Vector Search via a Codebook-Free Residual Layer](https://mlsanity.com/paper/2605.17415/) (2026)
- [Hurwitz Quaternion Multiplicative Quantization for KV Cache Compression](https://mlsanity.com/paper/2605.27646/) (2026)
- [PuzzleKV: Page-Wise Low-Rank Decomposition for KV Cache Compression](https://mlsanity.com/paper/2608.23843/) (2026)
- [Transforms for LLM Quantization: The Great Inversion and Format Co-Design](https://mlsanity.com/paper/2608.25188/) (2026)
- [Jacap: Robust KV Cache Eviction via Jacobian-Based Nonlinear Information Capacity Preservation](https://mlsanity.com/paper/2609.08131/) (2026)
- [QuantMLA: Function-Aligned Dual-Path Quantization for Low-Bit MLA KV Caching](https://mlsanity.com/paper/2609.36760/) (2026)
- [SoloQ: Calibration-Free Quantization for Diffusion Language Models](https://mlsanity.com/paper/2610.07121/) (2026)

## Abstract (arXiv)

Large language models (LLMs) require significant memory to store Key-Value (KV) embeddings in their KV cache, especially when handling long-range contexts. Quantization of these KV embeddings is a common technique to reduce memory consumption. This work introduces PolarQuant, a novel quantization method employing random preconditioning and polar transformation. Our method transforms the KV embeddings into polar coordinates using an efficient recursive algorithm and then quantizes resulting angles. Our key insight is that, after random preconditioning, the angles in the polar representation exhibit a tightly bounded and highly concentrated distribution with an analytically computable form. This nice distribution eliminates the need for explicit normalization, a step required by traditional quantization methods which introduces significant memory overhead because quantization parameters (e.g., zero point and scale) must be stored in full precision per each data block. PolarQuant bypasses this normalization step, enabling substantial memory savings. The long-context evaluation demonstrates that PolarQuant compresses the KV cache by over x4.2 while achieving the best quality scores compared to the state-of-the-art methods.