TriAttention: Efficient Long Reasoning with Trigonometric KV Compression

TL;DR

TriAttention introduces a novel trigonometric series-based method to efficiently compress key-value caches in large language models, enabling long reasoning with reduced memory and increased throughput.

Contribution

It leverages Q/K concentration in pre-RoPE space and trigonometric series to estimate key importance, improving efficiency without sacrificing accuracy.

Findings

Achieves 2.5x higher throughput on AIME25 with 32K tokens

Reduces KV memory by 10.7x compared to full attention

Enables deployment on a single consumer GPU for long context tasks

Abstract

Extended reasoning in large language models (LLMs) creates severe KV cache memory bottlenecks. Leading KV cache compression methods estimate KV importance using attention scores from recent post-RoPE queries. However, queries rotate with position during RoPE, making representative queries very few, leading to poor top-key selection and unstable reasoning. To avoid this issue, we turn to the pre-RoPE space, where we observe that Q and K vectors are highly concentrated around fixed non-zero centers and remain stable across positions -- Q/K concentration. We show that this concentration causes queries to preferentially attend to keys at specific distances (e.g., nearest keys), with the centers determining which distances are preferred via a trigonometric series. Based on this, we propose TriAttention to estimate key importance by leveraging these centers. Via the trigonometric series, we use the distance preference characterized by these centers to score keys according to their positions, and also leverage Q/K norms as an additional signal for importance estimation. On AIME25 with 32K-token generation, TriAttention matches Full Attention reasoning accuracy while achieving 2.5x higher throughput or 10.7x KV memory reduction, whereas leading baselines achieve only about half the accuracy at the same efficiency. TriAttention enables OpenClaw deployment on a single consumer GPU, where long context would otherwise cause out-of-memory with Full Attention.