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× at matched sparsity, and reduces prefill compute density by 3.31× at matched MSE; meanwhile, it preserves end-to-end accuracy and achieves 7.51× attention and 3.81× end-to-end speedups.

Large Language Models (LLMs) with extended context lengths face significant computational challenges during the pre-filling phase, primarily due to the quadratic complexity of self-attention. Existing methods typically employ dynamic pattern matching and block-sparse low-level implementations. However, their reliance on local information for pattern identification fails to capture global contexts, and the coarse granularity of blocks leads to persistent internal sparsity, resulting in suboptimal accuracy and efficiency. To address these limitations, we propose AnchorAttention, a difference-aware, dynamic sparse attention mechanism that efficiently identifies critical attention regions at a finer stripe granularity while adapting to global contextual information, achieving superior speed and accuracy. AnchorAttention comprises three key components: (1) Pattern-based Anchor Computation, leveraging the commonalities present across all inputs to rapidly compute a set of near-maximum scores as anchor; (2) Difference-aware Stripe Sparsity Identification, performing difference-aware comparisons with anchor to quickly obtain discrete coordinates of significant regions in a stripe-like sparsity pattern; (3) Fine-grained Sparse Computation, replacing the traditional contiguous loading strategy with a discrete key-value loading approach to maximize sparsity rates while preserving hardware computational potential. Additionally, we integrate the identification strategy into a single operator to maximize parallelization potential. With its finer-grained sparsity strategy, AnchorAttention achieves higher sparsity rates at the same recall level, significantly reducing computation time. Compared to previous state-of-the-art methods, at a text length of 128k, it achieves a speedup of 1.44× while maintaining higher recall rates.