# PolarQuant: Leveraging Polar Transformation for Efficient Key Cache Quantization and Decoding Acceleration

arXiv: https://arxiv.org/abs/2502.00527 · HTML: https://mlsanity.com/paper/2502.00527/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 1 Feb 2025.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Atom: Low-bit Quantization for Efficient and Accurate LLM Serving](https://mlsanity.com/paper/2310.19102/) (2023)
- [GEAR: An Efficient KV Cache Compression Recipe for Near-Lossless Generative Inference of LLM](https://mlsanity.com/paper/2403.05527/) (2024)
- [No Token Left Behind: Reliable KV Cache Compression via Importance-Aware Mixed Precision Quantization](https://mlsanity.com/paper/2402.18096/) (2024)
- [PQCache: Product Quantization-based KVCache for Long Context LLM Inference](https://mlsanity.com/paper/2407.12820/) (2024)
- [ZipCache: Accurate and Efficient KV Cache Quantization with Salient Token Identification](https://mlsanity.com/paper/2405.14256/) (2024)
- [QAQ: Quality Adaptive Quantization for LLM KV Cache](https://mlsanity.com/paper/2403.04643/) (2024)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)

## Built on by (most cited first, 10 of 10)

- [PCDVQ: Enhancing Vector Quantization for Large Language Models via Polar Coordinate Decoupling](https://mlsanity.com/paper/2506.05432/) (2025)
- [XQuant: Breaking the Memory Wall for LLM Inference with KV Cache Rematerialization](https://mlsanity.com/paper/2508.10395/) (2025)
- [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)
- [MOSAIC: Masked Outsourcing of Secure AI Computations](https://mlsanity.com/paper/2607.29221/) (2026)
- [Beyond Token Eviction: Mixed-Dimension Budget Allocation for Efficient KV Cache Compression](https://mlsanity.com/paper/2603.20616/) (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)
- [RSLM: Training-Free Vector Quantization for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2608.30384/) (2026)
- [EdgeLLM-Nano: Auditing Polar-Guided Key-Cache Compression and Consistency-Anchored Pruning on a 33.6 MB On-Device Language Model](https://mlsanity.com/paper/2610.14475/) (2026)
- [E8 Lattice Key Quantization for Low-Bit KV-Cache Compression](https://mlsanity.com/paper/2610.15384/) (2026)

## Abstract (arXiv)

The KV cache in large language models is a dominant factor in memory usage, limiting their broader applicability. Quantizing the cache to lower bit widths is an effective way to reduce computational costs; however, previous methods struggle with quantizing key vectors due to outliers, resulting in excessive overhead. We propose a novel quantization approach called PolarQuant, which efficiently addresses the outlier challenge. We observe that outliers typically appear in only one of two dimensions, which are rotated together by a specific angle when rotary position embeddings are applied. When represented as two-dimensional vectors, these dimensions exhibit well-structured patterns, with radii and angles smoothly distributed in polar coordinates. This alleviates the challenge of outliers on per-channel quantization, making them well-suited for quantization. Thus, PolarQuant divides key vectors into groups of two-dimensional sub-vectors, encoding them as the corresponding quantized radius and the polar angle, rather than quantizing original key vectors directly. PolarQuant achieves the superior efficiency in KV cache quantization and accelerates the decoding process by turning the query-key inner product into a table lookup, all while maintaining the downstream performance of full-precision models.