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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

Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic…

Machine Learning · Computer Science 2019-10-16 Zhenyue Qin , Dongwoo Kim

We propose a method, called Label Embedding Network, which can learn label representation (label embedding) during the training process of deep networks. With the proposed method, the label embedding is adaptively and automatically learned…

Machine Learning · Computer Science 2017-10-31 Xu Sun , Bingzhen Wei , Xuancheng Ren , Shuming Ma

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

Machine Learning · Computer Science 2020-04-14 Biswajit Paria , Chih-Kuan Yeh , Ian E. H. Yen , Ning Xu , Pradeep Ravikumar , Barnabás Póczos

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…

Numerical Analysis · Mathematics 2026-02-25 Egor P. Berezin , Robert T. Zaks , German Z. Alekhin , Stanislav V. Morozov , Sergey A. Matveev

Over the past decade, recommender systems have experienced a surge in popularity. Despite notable progress, they grapple with challenging issues, such as high data dimensionality and sparseness. Representing users and items as…

Information Retrieval · Computer Science 2025-07-28 Pedro R. Pires , Tiago A. Almeida

Network embedding techniques inspired by word2vec represent an effective unsupervised relational learning model. Commonly, by means of a Skip-Gram procedure, these techniques learn low dimensional vector representations of the nodes in a…

Machine Learning · Computer Science 2019-07-23 Pedro Almagro-Blanco , Fernando Sancho-Caparrini

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 is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven…

Machine Learning · Computer Science 2025-06-03 Wojciech Masarczyk , Mateusz Ostaszewski , Tin Sum Cheng , Tomasz Trzciński , Aurelien Lucchi , Razvan Pascanu

Enabling machine learning classifiers to defer their decision to a downstream expert when the expert is more accurate will ensure improved safety and performance. This objective can be achieved with the learning-to-defer framework which…

Machine Learning · Computer Science 2023-11-03 Yuzhou Cao , Hussein Mozannar , Lei Feng , Hongxin Wei , Bo An

Recently, learning discriminative features to improve the recognition performances gradually becomes the primary goal of deep learning, and numerous remarkable works have emerged. In this paper, we propose a novel yet extremely simple…

Computer Vision and Pattern Recognition · Computer Science 2018-12-03 Binghui Chen , Weihong Deng , Haifeng Shen

Softmax loss is widely used in deep neural networks for multi-class classification, where each class is represented by a weight vector, a sample is represented as a feature vector, and the feature vector has the largest projection on the…

Computer Vision and Pattern Recognition · Computer Science 2017-05-30 Yuhui Yuan , Kuiyuan Yang , Chao Zhang

Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…

Machine Learning · Statistics 2016-03-03 Oren Rippel , Manohar Paluri , Piotr Dollar , Lubomir Bourdev

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…

Optimization and Control · Mathematics 2021-01-14 Dmitry Pasechnyuk , Anton Anikin , Vladislav Matyukhin

To date, the simulation of organ deformations for applications like therapy planning or image-guided interventions is calculated by solving the elastodynamics equations. While efficient solvers have been proposed for fast simulations,…

Quantitative Methods · Quantitative Biology 2018-12-18 Felix Meister , Tiziano Passerini , Viorel Mihalef , Ahmet Tuysuzoglu , Andreas Maier , Tommaso Mansi

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

Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. We show that optimising the parameters of classification neural…

Machine Learning · Computer Science 2020-09-18 Zhenyue Qin , Dongwoo Kim , Tom Gedeon

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…

Machine Learning · Statistics 2023-05-18 Andrew Davison , Morgane Austern

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

Machine Learning · Computer Science 2018-10-16 Yihan Gao , Chao Zhang , Jian Peng , Aditya Parameswaran

Over the recent years, various deep learning-based methods were proposed for extracting a fixed-dimensional embedding vector from speech signals. Although the deep learning-based embedding extraction methods have shown good performance in…

Audio and Speech Processing · Electrical Eng. & Systems 2021-12-08 Woo Hyun Kang , Jahangir Alam , Abderrahim Fathan