English
Related papers

Related papers: Sparse-softmax: A Simpler and Faster Alternative S…

200 papers

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

The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in…

Performance · Computer Science 2020-01-14 Marat Dukhan , Artsiom Ablavatski

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 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

In order to push the performance on realistic computer vision tasks, the number of classes in modern benchmark datasets has significantly increased in recent years. This increase in the number of classes comes along with increased ambiguity…

Machine Learning · Statistics 2016-04-14 Maksim Lapin , Matthias Hein , Bernt Schiele

While transformer models exhibit strong in-context learning (ICL) abilities, they often fail to generalize under simple distribution shifts. We analyze these failures and identify Softmax, the scoring function in the attention mechanism, as…

Computation and Language · Computer Science 2026-05-12 Omar Naim , Swarnadeep Bhar , Jérôme Bolte , Nicholas Asher

Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Shulun Wang , Bin Liu , Feng Liu

A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to…

Artificial Intelligence · Computer Science 2017-06-15 Kavosh Asadi , Michael L. Littman

The popular softmax loss and its recent extensions have achieved great success in the deep learning-based image classification. However, the data for training image classifiers usually has different quality. Ignoring such problem, the…

Computer Vision and Pattern Recognition · Computer Science 2020-07-29 Weihua Liu , Xiabi Liu , Murong Wang , Ling Ma

Softmax is a standard final layer used in Neural Nets (NNs) to summarize information encoded in the trained NN and return a prediction. However, Softmax leverages only a subset of the class-specific structure encoded in the trained model…

Machine Learning · Computer Science 2019-12-09 Charles B. Delahunt , Courosh Mehanian , J. Nathan Kutz

The Softmax loss is one of the most widely employed surrogate objectives for classification and ranking tasks. To elucidate its theoretical properties, the Fenchel-Young framework situates it as a canonical instance within a broad family of…

Machine Learning · Computer Science 2026-02-02 Yuanhao Pu , Defu Lian , Enhong Chen

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

Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from…

Machine Learning · Computer Science 2020-01-01 A. Ali Heydari , Craig A. Thompson , Asif Mehmood

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric…

Computer Vision and Pattern Recognition · Computer Science 2018-05-31 Feng Wang , Weiyang Liu , Haijun Liu , Jian Cheng

Learning systems match predicted scores to observations over some domain. Often, it is critical to produce accurate predictions in some subset (or region) of the domain, yet less important to accurately predict in other regions. We…

Machine Learning · Computer Science 2025-06-11 Gil I. Shamir , Manfred K. Warmuth

Loss functions steer the optimization direction of recommendation models and are critical to model performance, but have received relatively little attention in recent recommendation research. Among various losses, we find Softmax loss (SL)…

Machine Learning · Computer Science 2023-12-21 Junkang Wu , Jiawei Chen , Jiancan Wu , Wentao Shi , Jizhi Zhang , Xiang Wang

Loss functions play a key role in training superior deep neural networks. In convolutional neural networks (CNNs), the popular cross entropy loss together with softmax does not explicitly guarantee minimization of intra-class variance or…

Computer Vision and Pattern Recognition · Computer Science 2019-04-26 XiaoBin Li , WeiQiang Wang

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

Machine Learning · Computer Science 2022-07-26 Yating Wang , Wing Tat Leung , Guang Lin

This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as…

Machine Learning · Computer Science 2012-07-03 Armand Joulin , Francis Bach

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size…

Machine Learning · Computer Science 2016-05-30 Alexandre de Brébisson , Pascal Vincent