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Emerging Large Language Model (LLM) applications require long input context in order to perform complex tasks like document analysis and code generation. For these long context length applications, the length of the input prompt poses a…

Transformer architectures have led to remarkable progress in many state-of-art applications. However, despite their successes, modern transformers rely on the self-attention mechanism, whose time- and space-complexity is quadratic in the…

Machine Learning · Computer Science 2022-09-13 Feyza Duman Keles , Pruthuvi Mahesakya Wijewardena , Chinmay Hegde

Deploying Transformer models on edge devices is limited by latency and energy budgets. While INT8 quantization effectively accelerates the primary matrix multiplications, it exposes the softmax as the dominant bottleneck. This stage incurs…

Machine Learning · Computer Science 2025-11-27 Wanli Zhong , Haibo Feng , Zirui Zhou , Hanyang Peng , Shiqi Yu

Quaternion neural networks are parameter-efficient and model multidimensional dependencies by representing four related features as a single entity. However, existing quaternion self-attention computes component-wise scores and applies…

Machine Learning · Computer Science 2026-05-26 Shogo Yamauchi , Tohru Nitta , Hideaki Tamori

The advent of foundation models have revolutionized various fields, enabling unprecedented task accuracy and flexibility in computational linguistics, computer vision and other domains. Attention mechanism has become an essential component…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-19 Mohammadali Shakerdargah , Shan Lu , Chao Gao , Di Niu

Large language models (LLMs) have made fundamental changes in human life. The attention scheme is one of the key components over all the LLMs, such as BERT, GPT-1, Transformers, GPT-2, 3, 3.5 and 4. Inspired by previous theoretical study of…

Data Structures and Algorithms · Computer Science 2023-04-06 Jan van den Brand , Zhao Song , Tianyi Zhou

Transformer-based models have emerged as a leading architecture for natural language processing, natural language generation, and image generation tasks. A fundamental element of the transformer architecture is self-attention, which allows…

Machine Learning · Computer Science 2025-07-01 Venmugil Elango

In the realm of deep learning, the self-attention mechanism has substantiated its pivotal role across a myriad of tasks, encompassing natural language processing and computer vision. Despite achieving success across diverse applications,…

Computation and Language · Computer Science 2023-10-25 Muhan Zhang

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 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

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

Transformer is a powerful tool for many natural language tasks which is based on self-attention, a mechanism that encodes the dependence of other tokens on each specific token, but the computation of self-attention is a bottleneck due to…

Machine Learning · Computer Science 2021-03-11 Madhusudan Verma

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

The quadratic complexity of standard attention mechanisms poses a significant scalability bottleneck for large language models (LLMs) in long-context scenarios. While hybrid attention strategies that combine sparse and full attention within…

Computation and Language · Computer Science 2026-01-29 Zecheng Tang , Quantong Qiu , Yi Yang , Zhiyi Hong , Haiya Xiang , Kebin Liu , Qingqing Dang , Juntao Li , Min Zhang

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

The size of the key-value (KV) cache plays a critical role in determining both the maximum context length and the number of concurrent requests supported during inference in modern language models. The KV cache size grows proportionally…

Computation and Language · Computer Science 2024-09-24 Shashank Rajput , Ying Sheng , Sean Owen , Vitaliy Chiley

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 quadratic complexity of self-attention in Transformer models remains a significant bottleneck for processing long sequences and deploying large language models efficiently. For this approach, there has been significant research into…

Computation and Language · Computer Science 2026-05-26 Spandan Pratyush

The attention mechanism is the key to the success of transformers in different machine learning tasks. However, the quadratic complexity with respect to the sequence length of the vanilla softmax-based attention mechanism becomes the major…

Image and Video Processing · Electrical Eng. & Systems 2025-08-05 Chong Wu , Maolin Che , Renjie Xu , Zhuoheng Ran , Hong Yan

A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…

Computational Complexity · Computer Science 2019-02-07 Tyler Michael Smith , Bradley Lowery , Julien Langou , Robert A. van de Geijn