S2O: Early Stopping for Sparse Attention via Online Permutation

TL;DR

S2O introduces an online permutation and early stopping mechanism for sparse attention, significantly improving efficiency and sparsity in long-context inference without sacrificing accuracy.

Contribution

It proposes a novel importance-guided online permutation and early stopping method to enhance sparse attention efficiency beyond existing block-based approaches.

Findings

Reduces single-operator MSE by 3.82× at matched sparsity

Achieves 7.51× attention speedup and 3.81× end-to-end speedup

Decreases prefill compute density by 3.31× at matched MSE

Abstract

Attention scales quadratically with sequence length, fundamentally limiting long-context inference. Existing block-granularity sparsification can reduce latency, but coarse blocks impose an intrinsic sparsity ceiling, making further improvements difficult even with carefully engineered designs. We present S2O, which performs early stopping for sparse attention via online permutation. Inspired by virtual-to-physical address mapping in memory systems, S2O revisits and factorizes FlashAttention execution, enabling inference to load non-contiguous tokens rather than a contiguous span in the original order. Motivated by fine-grained structures in attention heatmaps, we transform explicit permutation into an online, index-guided, discrete loading policy; with extremely lightweight preprocessing and index-remapping overhead, it concentrates importance on a small set of high-priority blocks. Building on this importance-guided online permutation for loading, S2O further introduces an early-stopping rule: computation proceeds from high to low importance; once the current block score falls below a threshold, S2O terminates early and skips the remaining low-contribution blocks, thereby increasing effective sparsity and reducing computation under a controlled error budget. As a result, S2O substantially raises the practical sparsity ceiling. On Llama-3.1-8B under a 128K context, S2O reduces single-operator MSE by 3.82$\times$ at matched sparsity, and reduces prefill compute density by 3.31$\times$ at matched MSE; meanwhile, it preserves end-to-end accuracy and achieves 7.51$\times$ attention and 3.81$\times$ end-to-end speedups.