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Related papers: The I/O Complexity of Attention, or How Optimal is…

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Transformers are slow and memory-hungry on long sequences, since the time and memory complexity of self-attention are quadratic in sequence length. Approximate attention methods have attempted to address this problem by trading off model…

Machine Learning · Computer Science 2022-06-24 Tri Dao , Daniel Y. Fu , Stefano Ermon , Atri Rudra , Christopher Ré

We revisit the I/O complexity of attention in large language models. Given query-key-value matrices $Q,K,V\in\mathbb{R}^{n\times d}$, and a machine with fast memory size $M$, the goal is to compute the "attention matrix" $A=\text{softmax}(Q…

Machine Learning · Computer Science 2026-05-25 Pál András Papp , Aleksandros Sobczyk , Anastasios Zouzias

Large Language Models (LLMs) exhibit exceptional proficiency in handling extensive context windows in natural language. Nevertheless, the quadratic scaling of attention computation relative to sequence length creates substantial efficiency…

Machine Learning · Computer Science 2026-01-26 Xiaoyu Li , Yingyu Liang , Zhenmei Shi , Zhao Song , Song Yue , Jiahao Zhang

Attention with bias, which extends standard attention by introducing prior knowledge as an additive bias matrix to the query-key scores, has been widely deployed in vision, language, protein-folding and other advanced scientific models,…

Machine Learning · Computer Science 2025-10-27 Haixu Wu , Minghao Guo , Yuezhou Ma , Yuanxu Sun , Jianmin Wang , Wojciech Matusik , Mingsheng Long

Scaling Transformers to longer sequence lengths has been a major problem in the last several years, promising to improve performance in language modeling and high-resolution image understanding, as well as to unlock new applications in…

Machine Learning · Computer Science 2023-07-18 Tri Dao

Attention, as a core layer of the ubiquitous Transformer architecture, is the bottleneck for large language models and long-context applications. FlashAttention elaborated an approach to speed up attention on GPUs through minimizing memory…

Machine Learning · Computer Science 2024-07-16 Jay Shah , Ganesh Bikshandi , Ying Zhang , Vijay Thakkar , Pradeep Ramani , Tri Dao

The transformer's attention mechanism has revolutionized AI and machine learning, with its efficient computation being crucial to its performance. However, calculating attention involves matrix operations interspersed with softmax…

Machine Learning · Computer Science 2025-05-21 Kosmas Alexandridis , Vasileios Titopoulos , Giorgos Dimitrakopoulos

Transformer-based language models have found many diverse applications requiring them to process sequences of increasing length. For these applications, the causal self-attention -- which is the only component scaling quadratically w.r.t.…

Machine Learning · Computer Science 2023-06-05 Matteo Pagliardini , Daniele Paliotta , Martin Jaggi , François Fleuret

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…

Machine Learning · Computer Science 2025-10-28 Can Yaras , Alec S. Xu , Pierre Abillama , Changwoo Lee , Laura Balzano

Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching…

Hardware Architecture · Computer Science 2025-01-15 Rya Sanovar , Srikant Bharadwaj , Renee St. Amant , Victor Rühle , Saravan Rajmohan

As the foundation of large language models (LLMs), self-attention module faces the challenge of quadratic time and memory complexity with respect to sequence length. FlashAttention accelerates attention computation and reduces its memory…

Machine Learning · Computer Science 2024-09-27 Shimao Chen , Zirui Liu , Zhiying Wu , Ce Zheng , Peizhuang Cong , Zihan Jiang , Yuhan Wu , Lei Su , Tong Yang

The computational and memory demands of vanilla attention scale quadratically with the sequence length $N$, posing significant challenges for processing long sequences in Transformer models. FlashAttention alleviates these challenges by…

Machine Learning · Computer Science 2025-03-04 Guoxia Wang , Jinle Zeng , Xiyuan Xiao , Siming Wu , Jiabin Yang , Lujing Zheng , Zeyu Chen , Jiang Bian , Dianhai Yu , Haifeng Wang

The Transformer architecture has revolutionized deep learning, delivering the state-of-the-art performance in areas such as natural language processing, computer vision, and time series prediction. However, its core component,…

Machine Learning · Computer Science 2025-07-24 Haolin Jin , Mengbai Xiao , Yuan Yuan , Xiao Zhang , Dongxiao Yu , Guanghui Zhang , Haoliang Wang

The transformer architecture predominates across various models. As the heart of the transformer, attention has a computational complexity of $O(N^2)$, compared to $O(N)$ for linear transformations. When handling large sequence lengths,…

Machine Learning · Computer Science 2025-10-02 Jintao Zhang , Jia Wei , Haofeng Huang , Pengle Zhang , Jun Zhu , Jianfei Chen

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear…

Machine Learning · Computer Science 2022-08-02 Tan Nguyen , Richard G. Baraniuk , Robert M. Kirby , Stanley J. Osher , Bao Wang

Transformers have been successfully used in various fields and are becoming the standard tools in computer vision. However, self-attention, a core component of transformers, has a quadratic complexity problem, which limits the use of…

Computer Vision and Pattern Recognition · Computer Science 2022-06-02 Jiuk Hong , Chaehyeon Lee , Soyoun Bang , Heechul Jung

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear…

Computer Vision and Pattern Recognition · Computer Science 2023-09-04 Dongchen Han , Xuran Pan , Yizeng Han , Shiji Song , Gao Huang

In both Computer Vision and the wider Deep Learning field, the Transformer architecture is well-established as state-of-the-art for many applications. For Multitask Learning, however, where there may be many more queries necessary compared…

Computer Vision and Pattern Recognition · Computer Science 2025-08-07 Christian Bohn , Thomas Kurbiel , Klaus Friedrichs , Hasan Tercan , Tobias Meisen

Scaling Transformers to ultra-long contexts is bottlenecked by the $O(n^2 d)$ cost of self-attention. Existing methods reduce this cost along the sequence axis through local windows, kernel approximations, or token-level sparsity, but these…

Machine Learning · Computer Science 2026-03-31 Yan Xie , Tiansheng Wen , Tangda Huang , Bo Chen , Chenyu You , Stefanie Jegelka , Yifei Wang

Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as the softmax of dot products between…

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