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Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token…

Computation and Language · Computer Science 2026-03-16 Yichuan Deng , Zhao Song , Kaijun Yuan , Tianyi Zhou

The self-attention mechanism distinguishes transformer-based large language models (LLMs) apart from convolutional and recurrent neural networks. Despite the performance improvement, achieving real-time LLM inference on silicon remains…

Hardware Architecture · Computer Science 2024-11-18 Shiwei Liu , Guanchen Tao , Yifei Zou , Derek Chow , Zichen Fan , Kauna Lei , Bangfei Pan , Dennis Sylvester , Gregory Kielian , Mehdi Saligane

Transformer networks have emerged as the state-of-the-art approach for natural language processing tasks and are gaining popularity in other domains such as computer vision and audio processing. However, the efficient hardware acceleration…

Hardware Architecture · Computer Science 2024-07-29 Gamze İslamoğlu , Moritz Scherer , Gianna Paulin , Tim Fischer , Victor J. B. Jung , Angelo Garofalo , Luca Benini

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

Mathematical Software · Computer Science 2019-05-28 Jacek Czaja , Michal Gallus , Tomasz Patejko , Jian Tang

Softmax is the de facto standard in modern neural networks for language processing when it comes to normalizing logits. However, by producing a dense probability distribution each token in the vocabulary has a nonzero chance of being…

Computation and Language · Computer Science 2022-05-20 Maxat Tezekbayev , Vassilina Nikoulina , Matthias Gallé , Zhenisbek Assylbekov

The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reduction…

Performance · Computer Science 2018-07-31 Maxim Milakov , Natalia Gimelshein

Transformer has shown great successes in natural language processing, computer vision, and audio processing. As one of its core components, the softmax attention helps to capture long-range dependencies yet prohibits its scale-up due to the…

Computation and Language · Computer Science 2022-02-18 Zhen Qin , Weixuan Sun , Hui Deng , Dongxu Li , Yunshen Wei , Baohong Lv , Junjie Yan , Lingpeng Kong , Yiran Zhong

Transformers have improved drastically the performance of natural language processing (NLP) and computer vision applications. The computation of transformers involves matrix multiplications and non-linear activation functions such as…

Hardware Architecture · Computer Science 2024-02-19 Christodoulos Peltekis , Kosmas Alexandridis , Giorgos Dimitrakopoulos

Transformers have shown remarkable performance in both natural language processing (NLP) and computer vision (CV) tasks. However, their real-time inference speed and efficiency are limited due to the inefficiency in Softmax and Layer…

Machine Learning · Computer Science 2025-10-21 Wenxun Wang , Shuchang Zhou , Wenyu Sun , Peiqin Sun , Yongpan Liu

We propose an approximate strategy to efficiently train neural network based language models over very large vocabularies. Our approach, called adaptive softmax, circumvents the linear dependency on the vocabulary size by exploiting the…

Computation and Language · Computer Science 2017-06-20 Edouard Grave , Armand Joulin , Moustapha Cissé , David Grangier , Hervé Jégou

In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. To address this, previous approximation…

Hardware Architecture · Computer Science 2026-04-28 Dawon Choi , Hana Kim , Ji-Hoon Kim

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

Machine Learning · Computer Science 2021-12-24 Shaoshi Sun , Zhenyuan Zhang , BoCheng Huang , Pengbin Lei , Jianlin Su , Shengfeng Pan , Jiarun Cao

The Transformer model has been pivotal in advancing fields such as natural language processing, speech recognition, and computer vision. However, a critical limitation of this model is its quadratic computational and memory complexity…

Computer Vision and Pattern Recognition · Computer Science 2024-06-04 Firas Khader , Omar S. M. El Nahhas , Tianyu Han , Gustav Müller-Franzes , Sven Nebelung , Jakob Nikolas Kather , Daniel Truhn

The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to…

Computation and Language · Computer Science 2025-02-03 Ken M. Nakanishi

The softmax function is crucial in Transformer attention, which normalizes each row of the attention scores with summation to one, achieving superior performances over other alternative functions. However, the softmax function can face a…

Computation and Language · Computer Science 2025-02-26 Chuanyang Zheng , Yihang Gao , Guoxuan Chen , Han Shi , Jing Xiong , Xiaozhe Ren , Chao Huang , Xin Jiang , Zhenguo Li , Yu Li

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

The attention mechanism is a pivotal element within the transformer architecture, making a substantial contribution to its exceptional performance. Within this attention mechanism, Softmax is an imperative component that enables the model…

Hardware Architecture · Computer Science 2024-09-05 Tianhua Xia , Sai Qian Zhang

Transformer model has gained prominence as a popular deep neural network architecture for neural language processing (NLP) and computer vision (CV) applications. However, the extensive use of nonlinear operations, like softmax, poses a…

Hardware Architecture · Computer Science 2024-11-21 Shuai Dong , Junyi Yang , Xiaoqi Peng , Hongyang Shang , Ye Ke , Xiaofeng Yang , Hongjie Liu , Arindam Basu

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

The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

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