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We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first…

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

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This…

Machine Learning · Computer Science 2024-02-27 Yury Nahshan , Joseph Kampeas , Emir Haleva

Transformer-based architectures have become the prevailing backbone of large language models. However, the quadratic time and memory complexity of self-attention remains a fundamental obstacle to efficient long-context modeling. To address…

Computation and Language · Computer Science 2026-02-10 Yutao Sun , Zhenyu Li , Yike Zhang , Tengyu Pan , Bowen Dong , Yuyi Guo , Jianyong Wang

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

The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale inference. This has motivated a rapidly growing body of work…

Multi-head, key-value attention is the backbone of the widely successful Transformer model and its variants. This attention mechanism uses multiple parallel key-value attention blocks (called heads), each performing two fundamental…

Machine Learning · Computer Science 2022-02-15 Sarthak Mittal , Sharath Chandra Raparthy , Irina Rish , Yoshua Bengio , Guillaume Lajoie

The Transformer translation model is based on the multi-head attention mechanism, which can be parallelized easily. The multi-head attention network performs the scaled dot-product attention function in parallel, empowering the model by…

Computation and Language · Computer Science 2021-09-13 Hongfei Xu , Qiuhui Liu , Josef van Genabith , Deyi Xiong

In the Transformer model, "self-attention" combines information from attended embeddings into the representation of the focal embedding in the next layer. Thus, across layers of the Transformer, information originating from different tokens…

Machine Learning · Computer Science 2020-06-02 Samira Abnar , Willem Zuidema

The key to a Transformer model is the self-attention mechanism, which allows the model to analyze an entire sequence in a computationally efficient manner. Recent work has suggested the possibility that general attention mechanisms used by…

Machine Learning · Computer Science 2020-01-01 Thomas Dowdell , Hongyu Zhang

The use of deep pre-trained bidirectional transformers has led to remarkable progress in a number of applications (Devlin et al., 2018). For tasks that make pairwise comparisons between sequences, matching a given input with a corresponding…

Computation and Language · Computer Science 2020-03-27 Samuel Humeau , Kurt Shuster , Marie-Anne Lachaux , Jason Weston

The self-attention mechanism has been a key factor in the advancement of vision Transformers. However, its quadratic complexity imposes a heavy computational burden in high-resolution scenarios, restricting the practical application.…

Computer Vision and Pattern Recognition · Computer Science 2025-12-29 Dongchen Han , Tianyu Li , Ziyi Wang , Gao Huang

The Transformer architecture has shown to be a powerful tool for a wide range of tasks. It is based on the self-attention mechanism, which is an inherently computationally expensive operation with quadratic computational complexity: memory…

Machine Learning · Computer Science 2024-02-07 Adjorn van Engelenhoven , Nicola Strisciuglio , Estefanía Talavera

Latest development of neural models has connected the encoder and decoder through a self-attention mechanism. In particular, Transformer, which is solely based on self-attention, has led to breakthroughs in Natural Language Processing (NLP)…

Computation and Language · Computer Science 2019-11-07 Xindian Ma , Peng Zhang , Shuai Zhang , Nan Duan , Yuexian Hou , Dawei Song , Ming Zhou

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…

Machine Learning · Computer Science 2020-06-16 Sinong Wang , Belinda Z. Li , Madian Khabsa , Han Fang , Hao Ma

The Transformer architecture is widely deployed in many popular and impactful Large Language Models. At its core is the attention mechanism for calculating correlations between pairs of tokens. Performing an attention computation takes…

Machine Learning · Computer Science 2025-05-26 Josh Alman , Hantao Yu

Transformers have achieved significant success across various domains, relying on self-attention to capture dependencies. However, the standard first-order attention mechanism is often limited by a low-rank bottleneck, struggling to capture…

Computation and Language · Computer Science 2025-12-05 Hanting Chen , Chong Zhu , Kai Han , Yuchuan Tian , Yuchen Liang , Tianyu Guo , Xinghao Chen , Dacheng Tao , Yunhe Wang

Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the…

Machine Learning · Computer Science 2024-02-13 Armin Gerami , Monte Hoover , Pranav S. Dulepet , Ramani Duraiswami

The most widely used artificial intelligence (AI) models today are Transformers employing self-attention. In its standard form, self-attention incurs costs that increase with context length, driving demand for storage, compute, and energy…

Machine Learning · Computer Science 2026-02-03 Franz A. Heinsen , Leo Kozachkov

Transformers are increasingly dominating multi-modal reasoning tasks, such as visual question answering, achieving state-of-the-art results thanks to their ability to contextualize information using the self-attention and co-attention…

Computer Vision and Pattern Recognition · Computer Science 2021-03-30 Hila Chefer , Shir Gur , Lior Wolf
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