Stratified Sparse Attention: Reducing the Sparse-to-Dense Gap at Extreme Sparsity

Abstract

Large Language Model inference over long contexts is increasingly bottlenecked by the cost of attending to a growing Key-Value (KV) cache. Sparse attention reduces this cost by accessing only a fraction of the cache, but existing methods face a trade-off between deterministic retrieval, which captures high-scoring tokens but discards residual attention mass, and sampling, which improves coverage at the cost of higher variance. Hybrid methods combine top-$k$ retrieval with uniform sampling, yet still exhibit a substantial gap from dense attention at aggressive sparsity. We introduce \emph{Stratified Sparse Attention (SSA)}, a unified framework combining deterministic retrieval with score-guided sampling. SSA deterministically attends to high-scoring tokens while sampling the residual using proxy attention scores and correcting for their inclusion probabilities, thereby recovering attention mass beyond the retrieval set. SSA encompasses top-$k$, top-$p$, and hybrid top-$k$+sampling as special cases. Across RULER, LongBench, LOFT, and AIME, and five models ranging from 3B to 27B parameters, SSA consistently improves over the baselines at matched sparsity. On RULER-HARD with Ministral-3-8B, SSA improves accuracy over the strongest practical baseline from 81.8\% to 84.2\% at 32K and from 63.8\% to 69.3\% at 128K under $50\times$ attention sparsity, recovering 94\% and 85\% of dense-attention performance, respectively. With optimized CUDA kernels, SSA achieves up to $2.96\times$ decode speedup over FlashInfer at 1M context, demonstrating that its accuracy gains translate into practical long-context inference acceleration. We open-source our code at https://github.com/skylight-org/SSA-Paper-Code.