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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Yaras, Can, Xu, Alec S., Abillama, Pierre, Lee, Changwoo, Balzano, Laura
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911230602510336
author Yaras, Can
Xu, Alec S.
Abillama, Pierre
Lee, Changwoo
Balzano, Laura
author_facet Yaras, Can
Xu, Alec S.
Abillama, Pierre
Lee, Changwoo
Balzano, Laura
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_18698
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle MonarchAttention: Zero-Shot Conversion to Fast, Hardware-Aware Structured Attention
Yaras, Can
Xu, Alec S.
Abillama, Pierre
Lee, Changwoo
Balzano, Laura
Machine Learning
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.
title MonarchAttention: Zero-Shot Conversion to Fast, Hardware-Aware Structured Attention
topic Machine Learning
url https://arxiv.org/abs/2505.18698