Papers › MonarchAttention: Zero-Shot Conversion to Fast, Hardware-Aware Structured Attention

MonarchAttention: Zero-Shot Conversion to Fast, Hardware-Aware Structured Attention

24 May 2025arXiv:2505.18698archive 2025-07-28

Can Yaras, Alec S. Xu, Pierre Abillama, Changwoo Lee, Laura Balzano

Transformers have achieved state-of-the-art performance across various tasks, but suffer from a notable quadratic complexity in sequence length due to the attention mechanism. In this work, we propose MonarchAttention -- a novel approach to sub-quadratic attention approximation via Monarch matrices, an expressive class of structured matrices. Based on the variational form of softmax, we describe an efficient optimization-based algorithm to compute an approximate projection of softmax attention onto the class of Monarch matrices with Θ(N√(N) d) computational complexity and Θ(Nd) memory/IO complexity. Unlike previous approaches, MonarchAttention is both (1) transferable, yielding minimal performance loss with no additional training, even when replacing every attention layer of the transformer, and (2) hardware-efficient, utilizing the highest-throughput tensor core units on modern GPUs. With optimized kernels, MonarchAttention achieves substantial speed-ups in wall-time over FlashAttention-2: 1.4× for shorter sequences (N=256), 4.5× for medium-length sequences (N=4K), and 8.2× for longer sequences (N=16K). We demonstrate the quality of MonarchAttention on diverse tasks and architectures in vision and language problems, showing that it flexibly and accurately approximates softmax attention in a variety of contexts. Our code is available at https://github.com/cjyaras/monarch-attention.

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