Scout Before You Attend: Sketch-and-Walk Sparse Attention for Efficient LLM Inference

Self-attention dominates the computational and memory cost of long-context LLM inference across both prefill and decode phases. To address this challenge, we introduce **Sketch\&Walk** Attention, a training-free sparse attention method that determines sparsity with lightweight sketches and deterministic walk. Sketch\&Walk applies Hadamard sketching to get inexpensive approximations of attention scores, then aggregates these estimates across layers via a walk mechanism that captures attention influence beyond direct interactions between tokens. The accumulated walk scores are used to select top-$k$ attention blocks, enabling dynamic sparsity with a single training-free algorithm that applies uniformly to both the prefill and decode phases, together with custom sparse attention kernels. Across a wide range of models and tasks, Sketch\&Walk maintains near-lossless accuracy at 20\% attention density and can slightly outperform dense attention in some settings, while achieving up to $6\times$ inference speedup.