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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

Looped Transformers (LT) have emerged as a powerful architecture by iterating their layers multiple times before decoding the final token. However, pairing them with full attention retains quadratic complexity, making them computationally…

Machine Learning · Computer Science 2026-05-26 Chunyuan Deng , Yizhe Zhang , Rui-Jie Zhu , Yuanyuan Xu , Jiarui Liu , T. S. Eugene Ng , Hanjie Chen

Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Shulun Wang , Bin Liu , Feng Liu

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns:…

Machine Learning · Computer Science 2025-05-29 Jianliang He , Xintian Pan , Siyu Chen , Zhuoran Yang

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

We propose Lizard, a linearization framework that transforms pretrained Transformer-based Large Language Models (LLMs) into subquadratic architectures. Transformers faces severe computational and memory bottlenecks with long sequences due…

Attention based models have achieved many remarkable breakthroughs in numerous applications. However, the quadratic complexity of Attention makes the vanilla Attention based models hard to apply to long sequence tasks. Various improved…

Machine Learning · Computer Science 2024-09-18 Xue Wang , Tian Zhou , Jianqing Zhu , Jialin Liu , Kun Yuan , Tao Yao , Wotao Yin , Rong Jin , HanQin Cai

Attention-based deep networks have been successfully applied on textual data in the field of NLP. However, their application on protein sequences poses additional challenges due to the weak semantics of the protein words, unlike the plain…

Machine Learning · Computer Science 2022-08-29 Ashish Ranjan , Md Shah Fahad , Akshay Deepak

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform…

Machine Learning · Computer Science 2025-01-16 Songlin Yang , Bailin Wang , Yu Zhang , Yikang Shen , Yoon Kim

Many NLP tasks require processing long contexts beyond the length limit of pretrained models. In order to scale these models to longer text sequences, many efficient long-range attention variants have been proposed. Despite the abundance of…

Computation and Language · Computer Science 2022-05-05 Wenhan Xiong , Barlas Oğuz , Anchit Gupta , Xilun Chen , Diana Liskovich , Omer Levy , Wen-tau Yih , Yashar Mehdad

Attention modules, as simple and effective tools, have not only enabled deep neural networks to achieve state-of-the-art results in many domains, but also enhanced their interpretability. Most current models use deterministic attention…

Machine Learning · Statistics 2020-10-22 Xinjie Fan , Shujian Zhang , Bo Chen , Mingyuan Zhou

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading…

Computation and Language · Computer Science 2025-07-10 Dustin Wang , Rui-Jie Zhu , Steven Abreu , Yong Shan , Taylor Kergan , Yuqi Pan , Yuhong Chou , Zheng Li , Ge Zhang , Wenhao Huang , Jason Eshraghian

Transformers excel at sequence modeling but face quadratic complexity, while linear attention offers improved efficiency but often compromises recall accuracy over long contexts. In this work, we introduce Native Hybrid Attention (NHA), a…

Computation and Language · Computer Science 2026-04-16 Jusen Du , Jiaxi Hu , Tao Zhang , Weigao Sun , Yu Cheng

The Transformer model architecture has become one of the most widely used in deep learning and the attention mechanism is at its core. The standard attention formulation uses a softmax operation applied to a scaled dot product between query…

Machine Learning · Computer Science 2026-04-02 Hariprasath Govindarajan , Per Sidén , Jacob Roll , Fredrik Lindsten

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation…

Computation and Language · Computer Science 2024-06-25 Xuyang Shen , Dong Li , Ruitao Leng , Zhen Qin , Weigao Sun , Yiran Zhong

Current high-resolution vision-language models encode images as high-resolution image tokens and exhaustively take all these tokens to compute attention, which significantly increases the computational cost. To address this problem, we…

Computer Vision and Pattern Recognition · Computer Science 2024-07-30 Junyan Li , Delin Chen , Tianle Cai , Peihao Chen , Yining Hong , Zhenfang Chen , Yikang Shen , Chuang Gan

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

Neural operators offer a powerful data-driven framework for learning mappings between function spaces, in which the transformer-based neural operator architecture faces a fundamental scalability-accuracy trade-off: softmax attention…

Machine Learning · Computer Science 2025-10-21 Ming Zhong , Zhenya Yan

Scaling sequence length has become a critical demand in the era of large language models. However, existing methods struggle with either computational complexity or model expressivity, rendering the maximum sequence length restricted. To…

Computation and Language · Computer Science 2023-07-20 Jiayu Ding , Shuming Ma , Li Dong , Xingxing Zhang , Shaohan Huang , Wenhui Wang , Nanning Zheng , Furu Wei

Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does…

Machine Learning · Statistics 2018-11-09 Yuntian Deng , Yoon Kim , Justin Chiu , Demi Guo , Alexander M. Rush