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The softmax attention mechanism has emerged as a noteworthy development in the field of Artificial Intelligence research, building on the successes of Transformer-based architectures. However, their ever increasing sizes necessitate ever…

Computation and Language · Computer Science 2023-05-19 Luca Herranz-Celotti , Ermal Rrapaj

An efficient attention implementation is essential for large models due to its quadratic time complexity. Fortunately, attention commonly exhibits sparsity, i.e., many values in the attention map are near zero, allowing for the omission of…

Machine Learning · Computer Science 2025-11-20 Jintao Zhang , Chendong Xiang , Haofeng Huang , Jia Wei , Haocheng Xi , Jun Zhu , Jianfei Chen

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates \emph{global competition}, a…

Machine Learning · Computer Science 2026-02-03 Mingwei Xu , Xuan Lin , Xinnan Guo , Wanqing Xu , Wanyun Cui

Despite powering modern AI, transformers remain mysteriously brittle to train. We develop a stability theory that explains why pre-LayerNorm works, why DeepNorm uses $N^{-1/4}$ scaling, and why warmup is necessary, all from first…

Machine Learning · Computer Science 2026-02-24 Seyed Morteza Emadi

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. However, the employment of self-attention modules results in a quadratic…

Computer Vision and Pattern Recognition · Computer Science 2022-05-03 Jiachen Lu , Jinghan Yao , Junge Zhang , Xiatian Zhu , Hang Xu , Weiguo Gao , Chunjing Xu , Tao Xiang , Li Zhang

We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm can converge to the globally optimal self-attention…

Machine Learning · Computer Science 2026-03-03 Gautam Goel , Mahdi Soltanolkotabi , Peter Bartlett

The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…

Artificial Intelligence · Computer Science 2026-02-13 Hanno Ackermann , Hong Cai , Mohsen Ghafoorian , Amirhossein Habibian

Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the…

Computer Vision and Pattern Recognition · Computer Science 2024-03-18 Jiachen Lu , Junge Zhang , Xiatian Zhu , Jianfeng Feng , Tao Xiang , Li Zhang

The attention module is the key component in Transformers. While the global attention mechanism offers high expressiveness, its excessive computational cost restricts its applicability in various scenarios. In this paper, we propose a novel…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Dongchen Han , Tianzhu Ye , Yizeng Han , Zhuofan Xia , Siyuan Pan , Pengfei Wan , Shiji Song , Gao Huang

Transformers have become prevalent in computer vision due to their performance and flexibility in modelling complex operations. Of particular significance is the 'cross-attention' operation, which allows a vector representation (e.g. of an…

Computer Vision and Pattern Recognition · Computer Science 2022-08-08 Ali Athar , Jonathon Luiten , Alexander Hermans , Deva Ramanan , Bastian Leibe

Attention accounts for an increasingly dominant fraction of total computation during inference for mixture-of-experts (MoE) models, making efficient acceleration critical. Emerging domain-specific accelerators for large model inference are…

Hardware Architecture · Computer Science 2026-04-03 Chi Zhang , Luca Colagrande , Renzo Andri , Luca Benini

Softmax attention is the cornerstone of modern large language models, but its memory scales linearly and compute quadratically with sequence length. Linear recurrent models, such as linear attention and state space models, have become…

Machine Learning · Computer Science 2026-05-28 Kevin Y. Li , Asher Trockman , Ananda Theertha Suresh , Ziteng Sun

Self-attention is a useful mechanism to build generative models for language and images. It determines the importance of context elements by comparing each element to the current time step. In this paper, we show that a very lightweight…

Computation and Language · Computer Science 2019-02-26 Felix Wu , Angela Fan , Alexei Baevski , Yann N. Dauphin , Michael Auli

The quadratic time and memory complexity inherent to self-attention mechanisms, with respect to sequence length, presents a critical computational bottleneck in the training and deployment of large-scale Transformer-based language models.…

Machine Learning · Computer Science 2024-03-19 Praneeth Kacham , Vahab Mirrokni , Peilin Zhong

Attention architectures are widely used; they recently gained renewed popularity with Transformers yielding a streak of state of the art results. Yet, the geometrical implications of softmax-attention remain largely unexplored. In this work…

Machine Learning · Computer Science 2020-05-20 Oliver Richter , Roger Wattenhofer

Learned Indexes (LIs) represent a paradigm shift from traditional index structures by employing machine learning models to approximate the cumulative distribution function (CDF) of sorted data. While LIs achieve remarkable efficiency for…

Machine Learning · Computer Science 2025-09-26 Alireza Heidari , Amirhossein Ahmad , Wei Zhang , Ying Xiong

Local-global attention models have recently emerged as compelling alternatives to standard Transformers, promising improvements in both training and inference efficiency. However, the crucial choice of window size presents a Pareto…

Computation and Language · Computer Science 2025-11-18 Bailin Wang , Chang Lan , Chong Wang , Ruoming Pang

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the…

Machine Learning · Computer Science 2025-04-02 Zhixuan Lin , Evgenii Nikishin , Xu Owen He , Aaron Courville

Recent advances in transformer-based Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their quadratic computational complexity concerning sequence length remains a significant bottleneck…

Computation and Language · Computer Science 2025-06-05 Zichuan Fu , Wentao Song , Yejing Wang , Xian Wu , Yefeng Zheng , Yingying Zhang , Derong Xu , Xuetao Wei , Tong Xu , Xiangyu Zhao

Deep neural networks are increasingly bottlenecked by the cost of optimization, both in terms of GPU memory and compute time. Existing acceleration techniques, such as mixed precision, second-order methods, and batch size scaling, are…

Machine Learning · Computer Science 2025-09-03 Mohsen Sheibanian , Pouya Shaeri , Alimohammad Beigi , Ryan T. Woo , Aryan Keluskar
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