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

The increasing demand for long-context generation has made the KV cache in large language models a bottleneck in memory consumption. Quantizing the cache to lower bit widths is an effective way to reduce memory costs; however, previous methods struggle with key cache quantization due to outliers, resulting in suboptimal performance. We propose a novel quantization approach PolarQuant, which provides a new perspective for key cache quantization and efficiently addresses the outlier dilemma. We observe that the distribution of the key states reveals well-structured patterns under polar transformation. Outliers generally appear in only one of the 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-organized patterns, with radii and angles smoothly distributed in polar space. This alleviates the channel-wise outliers, making them well-suited for key cache quantization. PolarQuant divides key vectors into groups of two-dimensional sub-vectors, encoding them as the 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. Our code is available at https://github.com/ericshwu/PolarQuant.