Attend at the Right Resolution: Head-Adaptive Sparse Attention via Query-Key Interaction Structure

Wajih Hassan Raza, Ahsan Bilal, Yidan Shen, Renjie Hu, Xin Fu +1

Attention is a major scalability bottleneck in large language models (LLMs), with its computational cost and key-value (KV) memory traffic becoming increasingly prohibitive as context length grows. Sparse attention addresses this bottleneck by restricting each query to a subset of the context, but its effectiveness hinges on identifying relevant regions both cheaply and reliably. Existing training-free methods primarily rely on runtime relevance estimates, with selection dimensionality and granularity typically governed by fixed heuristics rather than the intrinsic interaction structure of pretrained attention heads. We take a different perspective: the query-key operator of each pretrained head defines a characteristic response structure that determines the resolution needed for sparse selection, both across feature directions and across context tokens. Building on this insight, we propose Head-Adaptive Sparse Attention (HASA), a training-free sparse attention framework that jointly adapts selection resolution along these two dimensions. Along the feature dimension, the singular spectrum of each head's query-key operator determines an effective rank, yielding a compact,…