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Large language models (LLMs) have brought significant and transformative changes in human society. These models have demonstrated remarkable capabilities in natural language understanding and generation, leading to various advancements and…

Machine Learning · Computer Science 2023-07-06 Yeqi Gao , Zhao Song , Shenghao Xie

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer…

Computation and Language · Computer Science 2023-04-27 Shuai Li , Zhao Song , Yu Xia , Tong Yu , Tianyi Zhou

Large language models (LLMs) have numerous real-life applications across various domains, such as natural language translation, sentiment analysis, language modeling, chatbots and conversational agents, creative writing, text…

Machine Learning · Computer Science 2025-02-18 Yeqi Gao , Zhao Song , Junze Yin

Large language models (LLMs) have brought significant changes to human society. Softmax regression and residual neural networks (ResNet) are two important techniques in deep learning: they not only serve as significant theoretical…

Machine Learning · Computer Science 2023-09-26 Zhao Song , Weixin Wang , Junze Yin

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

Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the…

Machine Learning · Statistics 2025-06-02 Yuzhou Gu , Zhao Song , Junze Yin

Large language models (LLMs) and generative AI have played a transformative role in computer research and applications. Controversy has arisen as to whether these models output copyrighted data, which can occur if the data the models are…

Machine Learning · Computer Science 2023-08-24 Timothy Chu , Zhao Song , Chiwun Yang

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

Neural language models have been widely used in various NLP tasks, including machine translation, next word prediction and conversational agents. However, it is challenging to deploy these models on mobile devices due to their slow…

Machine Learning · Computer Science 2018-10-31 Patrick H. Chen , Si Si , Sanjiv Kumar , Yang Li , Cho-Jui Hsieh

There have been significant advancements made by large language models (LLMs) in various aspects of our daily lives. LLMs serve as a transformative force in natural language processing, finding applications in text generation, translation,…

Machine Learning · Computer Science 2023-11-28 Zhihang Li , Zhao Song , Zifan Wang , Junze Yin

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 problem of rare and unknown words is an important issue that can potentially influence the performance of many NLP systems, including both the traditional count-based and the deep learning models. We propose a novel way to deal with the…

Computation and Language · Computer Science 2016-08-23 Caglar Gulcehre , Sungjin Ahn , Ramesh Nallapati , Bowen Zhou , Yoshua Bengio

To encourage intra-class compactness and inter-class separability among trainable feature vectors, large-margin softmax methods are developed and widely applied in the face recognition community. The introduction of the large-margin concept…

Audio and Speech Processing · Electrical Eng. & Systems 2021-04-22 Jingjing Huo , Yingbo Gao , Weiyue Wang , Ralf Schlüter , Hermann Ney

Large language models (LLMs), such as ChatGPT and GPT4, have shown outstanding performance in many human life task. Attention computation plays an important role in training LLMs. Softmax unit and ReLU unit are the key structure in…

Machine Learning · Computer Science 2023-08-17 Yichuan Deng , Zhao Song , Shenghao Xie

Large Language Models (LLMs) have shown immense potential in enhancing various aspects of our daily lives, from conversational AI to search and AI assistants. However, their growing capabilities come at the cost of extremely large model…

Machine Learning · Computer Science 2025-02-27 Yingyu Liang , Jiangxuan Long , Zhenmei Shi , Zhao Song , Yufa Zhou

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 Softmax function on top of a final linear layer is the de facto method to output probability distributions in neural networks. In many applications such as language models or text generation, this model has to produce distributions over…

Machine Learning · Computer Science 2019-05-15 Octavian-Eugen Ganea , Sylvain Gelly , Gary Bécigneul , Aliaksei Severyn

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

Softmax is the most commonly used output function for multiclass problems and is widely used in areas such as vision, natural language processing, and recommendation. A softmax model has linear costs in the number of classes which makes it…

Machine Learning · Computer Science 2018-08-03 Guy Blanc , Steffen Rendle

The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation. However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent…

Computation and Language · Computer Science 2019-03-25 Sachin Kumar , Yulia Tsvetkov
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