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The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation…

Machine Learning · Statistics 2016-11-01 Michalis K. Titsias

We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can…

Machine Learning · Computer Science 2023-07-04 Zsolt Zombori , Agapi Rissaki , Kristóf Szabó , Wolfgang Gatterbauer , Michael Benedikt

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

Recently, the robustness of deep learning models has received widespread attention, and various methods for improving model robustness have been proposed, including adversarial training, model architecture modification, design of loss…

Machine Learning · Computer Science 2023-03-23 Hao Wang , Chen Li , Jinzhe Jiang , Xin Zhang , Yaqian Zhao , Weifeng Gong

Speaker Recognition is a challenging task with essential applications such as authentication, automation, and security. The SincNet is a new deep learning based model which has produced promising results to tackle the mentioned task. To…

Audio and Speech Processing · Electrical Eng. & Systems 2019-10-15 João Antônio Chagas Nunes , David Macêdo , Cleber Zanchettin

In text generation, a large language model (LM) makes a choice of each new word based only on the former selection of its context using the softmax function. Nevertheless, the link statistics information of concurrent words based on a…

Computation and Language · Computer Science 2023-12-20 Liu Bin , Yin Guosheng

Cross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly…

Machine Learning · Statistics 2017-11-21 Weiyang Liu , Yandong Wen , Zhiding Yu , Meng Yang

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly…

Machine Learning · Computer Science 2025-08-05 Jialiang Wang , Xiong Zhou , Deming Zhai , Junjun Jiang , Xiangyang Ji , Xianming Liu

Classifiers in natural language processing (NLP) often have a large number of output classes. For example, neural language models (LMs) and machine translation (MT) models both predict tokens from a vocabulary of thousands. The Softmax…

Machine Learning · Computer Science 2022-03-22 Andreas Grivas , Nikolay Bogoychev , Adam Lopez

Deep convolutional neural networks (CNNs) trained with logistic and softmax losses have made significant advancement in visual recognition tasks in computer vision. When training data exhibit class imbalances, the class-wise reweighted…

Machine Learning · Computer Science 2020-03-06 Xiangrui Li , Xin Li , Deng Pan , Dongxiao Zhu

Neural Network Language Models (NNLMs) generate probability distributions by applying a softmax function to a distance metric formed by taking the dot product of a prediction vector with all word vectors in a high-dimensional embedding…

Machine Learning · Computer Science 2020-05-07 David Demeter , Gregory Kimmel , Doug Downey

Unsupervised neural grammar induction aims to learn interpretable hierarchical structures from language data. However, existing models face an expressiveness bottleneck, often resulting in unnecessarily large yet underperforming grammars.…

Computation and Language · Computer Science 2025-09-26 Jinwook Park , Kangil Kim

Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…

Machine Learning · Computer Science 2022-12-16 Xingchao Liu , Xing Han , Na Zhang , Qiang Liu

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

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

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

A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to…

Machine Learning · Computer Science 2019-10-31 Tyler Lee , Anthony Ndirango

Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing…

Machine Learning · Statistics 2018-03-26 Francois Fagan , Garud Iyengar

Neural machine translation (NMT) models are typically trained using a softmax cross-entropy loss where the softmax distribution is compared against smoothed gold labels. In low-resource scenarios, NMT models tend to over-fit because the…

Computation and Language · Computer Science 2020-09-22 Raj Dabre , Atsushi Fujita

The computational cost of training with softmax cross entropy loss grows linearly with the number of classes. For the settings where a large number of classes are involved, a common method to speed up training is to sample a subset of…

Machine Learning · Computer Science 2020-01-01 Ankit Singh Rawat , Jiecao Chen , Felix Yu , Ananda Theertha Suresh , Sanjiv Kumar