HSR-Enhanced Sparse Attention Acceleration

Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, but their performance on long-context tasks is often limited by the computational complexity of attention mechanisms. This paper introduces a novel approach to accelerate attention computation in LLMs, particularly for long-context scenarios. We leverage the inherent sparsity within attention mechanisms, both in conventional Softmax attention and ReLU attention (with $\mathsf{ReLU}^\alpha$ activation, $\alpha \in \mathbb{N}_+$), to significantly reduce the running time complexity. Our method employs a Half-Space Reporting (HSR) data structure to rapidly identify non-zero or "massively activated" entries in the attention matrix. We present theoretical analyses for two key scenarios: attention generation and full attention computation with long input context. Our approach achieves a running time of $O(mn^{4/5})$ significantly faster than the naive approach $O(mn)$ for attention generation, where $n$ is the context length, $m$ is the query length, and $d$ is the hidden dimension. We can also reduce the running time of full attention computation from $O(mn)$ to $O(mn^{1 - 1 / \lfloor d/2\rfloor} + mn^{4/5})$. Importantly, our method introduces no error for ReLU attention and only provably negligible error for Softmax attention, where the latter is supported by our empirical validation. This work represents a significant step towards enabling efficient long-context processing in LLMs, potentially broadening their applicability across various domains.