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Various forms of sparse attention have been explored to mitigate the quadratic computational and memory cost of the attention mechanism in transformers. We study sparse transformers not through a lens of efficiency but rather in terms of…

Machine Learning · Computer Science 2025-06-19 Parikshit Ram , Kenneth L. Clarkson , Tim Klinger , Shashanka Ubaru , Alexander G. Gray

Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention…

Machine Learning · Computer Science 2025-10-07 Ruoxi Yu , Haotian Jiang , Jingpu Cheng , Penghao Yu , Qianxiao Li , Zhong Li

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens $X$ and makes them interact through…

Machine Learning · Computer Science 2024-02-23 Davoud Ataee Tarzanagh , Yingcong Li , Christos Thrampoulidis , Samet Oymak

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

Vision Transformers have achieved impressive performance in video classification, while suffering from the quadratic complexity caused by the Softmax attention mechanism. Some studies alleviate the computational costs by reducing the number…

Computer Vision and Pattern Recognition · Computer Science 2022-10-18 Kaiyue Lu , Zexiang Liu , Jianyuan Wang , Weixuan Sun , Zhen Qin , Dong Li , Xuyang Shen , Hui Deng , Xiaodong Han , Yuchao Dai , Yiran Zhong

Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…

Machine Learning · Computer Science 2021-08-19 Radostin Cholakov , Todor Kolev

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in…

Machine Learning · Computer Science 2024-10-31 Max Vladymyrov , Johannes von Oswald , Mark Sandler , Rong Ge

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear…

Computation and Language · Computer Science 2022-10-20 Zhen Qin , XiaoDong Han , Weixuan Sun , Dongxu Li , Lingpeng Kong , Nick Barnes , Yiran Zhong

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the…

Machine Learning · Computer Science 2026-02-27 O. Duranthon , P. Marion , C. Boyer , B. Loureiro , L. Zdeborová

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

Linear attention has attracted interest as a computationally efficient approximation to softmax attention, especially for long sequences. Recent studies have explored distilling softmax attention in pre-trained Transformers into linear…

Machine Learning · Computer Science 2025-07-08 Naoki Nishikawa , Rei Higuchi , Taiji Suzuki

Attention mechanisms represent a fundamental paradigm shift in neural network architectures, enabling models to selectively focus on relevant portions of input sequences through learned weighting functions. This monograph provides a…

Machine Learning · Computer Science 2026-01-08 Hasi Hays

Transformer-based models have demonstrated remarkable in-context learning capabilities, prompting extensive research into its underlying mechanisms. Recent studies have suggested that Transformers can implement first-order optimization…

Machine Learning · Computer Science 2024-03-06 Angeliki Giannou , Liu Yang , Tianhao Wang , Dimitris Papailiopoulos , Jason D. Lee

The dot product self-attention (DPSA) is a fundamental component of transformers. However, scaling them to long sequences, like documents or high-resolution images, becomes prohibitively expensive due to quadratic time and memory…

Computer Vision and Pattern Recognition · Computer Science 2024-01-09 Pourya Shamsolmoali , Masoumeh Zareapoor , Eric Granger , Michael Felsberg

While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically,…

Machine Learning · Computer Science 2025-10-28 Jonas A. Actor , Anthony Gruber , Eric C. Cyr

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from…

Machine Learning · Computer Science 2025-11-25 Jeffrey Willette , Heejun Lee , Sung Ju Hwang

Attention mechanism plays a dominant role in the sequence generation models and has been used to improve the performance of machine translation and abstractive text summarization. Different from neural machine translation, in the task of…

Computation and Language · Computer Science 2020-04-09 Piji Li , Lidong Bing , Zhongyu Wei , Wai Lam

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

Large Vision-Language Models (LVLMs) have advanced rapidly by aligning visual patches with the text embedding space, but a fixed visual-token budget forces images to be resized to a uniform pretraining resolution, often erasing fine-grained…

Computer Vision and Pattern Recognition · Computer Science 2026-02-05 Zipeng Zhu , Zhanghao Hu , Qinglin Zhu , Yuxi Hong , Yijun Liu , Jingyong Su , Yulan He , Lin Gui

This document provides a brief introduction to the attention mechanism used in modern language models based on the Transformer architecture. We first illustrate how text is encoded as vectors and how the attention mechanism processes these…

Numerical Analysis · Mathematics 2026-04-02 Michel Fabrice Serret