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

2026-06-08 · Source: cs.CL updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Cloud Computing & IT Infrastructure · Depth: Expert, extended

Summary

PolarQuant is a novel quantization method designed to efficiently reduce the memory footprint of the KV cache in large language models (LLMs) and accelerate their decoding process. It addresses the challenge of quantizing key vectors, which often contain outliers, by transforming them into polar coordinates. The method observes that outliers in two-dimensional sub-vectors, rotated by rotary position embeddings (RoPE), form stable circular patterns when viewed in polar coordinates, with smoothly distributed radii and angles. PolarQuant quantizes these radii and angles (e.g., 4-bit angles and 2-bit radii for a 3-bit equivalent) instead of directly quantizing original key vectors. This approach eliminates token grouping overhead and on-the-fly dequantization, achieving up to a 1.27x speedup in query-key multiplication on an NVIDIA A800-SXM4-80GB GPU for models like Llama-2-7B-Chat, Llama-3.1-8B-Instruct, and Mistral-7B-Instruct-v0.2, while maintaining performance on LongBench, MMLU, and GSM8K benchmarks.

Key takeaway

For AI Architects and Machine Learning Engineers optimizing LLM inference, PolarQuant offers a compelling solution to reduce KV cache memory and accelerate decoding. By transforming key vectors into polar coordinates for quantization, you can achieve up to a 1.27x speedup in query-key multiplication and lower quantization parameter costs compared to previous methods, without sacrificing performance on long-context tasks. Consider integrating PolarQuant's Triton kernels to enhance throughput for your generative LLM deployments.

Key insights

PolarQuant leverages polar coordinate transformation to efficiently quantize LLM key caches, mitigating outliers and accelerating decoding via table lookups.

Principles

• Outliers in RoPE-rotated 2D key sub-vectors form stable circular patterns.
• Quantizing polar coordinates (radius, angle) simplifies key cache compression.
• Non-negative radii eliminate zero-point storage, reducing quantization parameters.

Method

PolarQuant divides key vectors into 2D sub-vectors, converts them to radius $r$ and polar angle $\theta$, then asymmetrically quantizes $r$ (n-bit) and $\theta$ (m-bit) into integers, mapping to $2^{n+m}$ regions.

In practice

• Implement Triton kernels for query-key multiplication speedup.
• Apply 4-bit angle and 2-bit radius quantization for 3-bit equivalent.
• Use for Llama-2-7B, Llama-3.1-8B, Mistral-7B models.

Topics

• KV Cache Quantization
• Large Language Models
• Rotary Position Embedding
• Polar Transformation
• Decoding Acceleration
• Triton Kernels

Best for: MLOps Engineer, AI Engineer, NLP Engineer, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CL updates on arXiv.org.