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arXiv · 2505.18698

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

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

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 $Θ(N\sqrt{N} d)$ 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: $1.4\times$ for shorter sequences $(N=256)$, $4.5\times$ for medium-length sequences $(N=4K)$, and $8.2\times$ 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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Can Yaras, Alec S. Xu, Pierre Abillama, Changwoo Lee, Laura Balzano. 2025-10-25. MonarchAttention: Zero-Shot Conversion to Fast, Hardware-Aware Structured Attention. https://arxiv.org/abs/2505.18698

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