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Two things seem to be indisputable in the contemporary deep learning discourse: 1. The categorical cross-entropy loss after softmax activation is the method of choice for classification. 2. Training a CNN classifier from scratch on small…

Machine Learning · Computer Science 2019-12-12 Björn Barz , Joachim Denzler

Modern deep learning is primarily an experimental science, in which empirical advances occasionally come at the expense of probabilistic rigor. Here we focus on one such example; namely the use of the categorical cross-entropy loss to model…

Machine Learning · Statistics 2020-11-11 Elliott Gordon-Rodriguez , Gabriel Loaiza-Ganem , Geoff Pleiss , John P. Cunningham

Intra-class compactness and inter-class separability are crucial indicators to measure the effectiveness of a model to produce discriminative features, where intra-class compactness indicates how close the features with the same label are…

Computer Vision and Pattern Recognition · Computer Science 2019-07-16 Yan Luo , Yongkang Wong , Mohan Kankanhalli , Qi Zhao

The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational…

Information Retrieval · Computer Science 2023-12-20 Jiancan Wu , Xiang Wang , Xingyu Gao , Jiawei Chen , Hongcheng Fu , Tianyu Qiu

Cosine similarity is often used to measure the similarity of vectors. These vectors might be the representations of neural network models. However, it is not guaranteed that cosine similarity of model representations will tell us anything…

Machine Learning · Computer Science 2026-04-01 Beatrix M. G. Nielsen

Recent state-of-the-art image segmentation algorithms are mostly based on deep neural networks, thanks to their high performance and fast computation time. However, these methods are usually trained in a supervised manner, which requires…

Computer Vision and Pattern Recognition · Computer Science 2020-01-08 Boah Kim , Jong Chul Ye

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

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

This paper revisits the special type of a neural network known under two names. In the statistics and machine learning community it is known as a multi-class logistic regression neural network. In the neural network community, it is simply…

Machine Learning · Statistics 2021-01-29 Marek Rychlik

The widely used ChestX-ray14 dataset addresses an important medical image classification problem and has the following caveats: 1) many lung pathologies are visually similar, 2) a variant of diseases including lung cancer, tuberculosis, and…

Computer Vision and Pattern Recognition · Computer Science 2018-07-26 Zongyuan Ge , Dwarikanath Mahapatra , Suman Sedai , Rahil Garnavi , Rajib Chakravorty

While semi-supervised learning (SSL) has yielded promising results, the more realistic SSL scenario remains to be explored, in which the unlabeled data exhibits extremely high recognition difficulty, e.g., fine-grained visual classification…

Machine Learning · Computer Science 2023-12-20 Yue Duan , Zhen Zhao , Lei Qi , Luping Zhou , Lei Wang , Yinghuan Shi

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

Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates a metric or cost between…

Machine Learning · Statistics 2019-05-16 Arthur Mensch , Mathieu Blondel , Gabriel Peyré

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

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

Graph neural networks (GNNs) have exhibited prominent performance in learning graph-structured data. Considering node classification task, based on the i.i.d assumption among node labels, the traditional supervised learning simply sums up…

Machine Learning · Computer Science 2024-05-28 Rui Miao , Kaixiong Zhou , Yili Wang , Ninghao Liu , Ying Wang , Xin Wang

Softmax Loss (SL) is being increasingly adopted for recommender systems (RS) as it has demonstrated better performance, robustness and fairness. Yet in implicit-feedback, a single global temperature and equal treatment of uniformly sampled…

Machine Learning · Computer Science 2026-02-10 Bucher Sahyouni , Matthew Vowels , Liqun Chen , Simon Hadfield

Labeling a training set is often expensive and susceptible to errors, making the design of robust loss functions for label noise an important problem. The symmetry condition provides theoretical guarantees for robustness to such noise. In…

Machine Learning · Computer Science 2026-05-21 Alexandre Lemire Paquin , Brahim Chaib-Draa , Philippe Giguère

The problem of devising learning strategies for discrete losses (e.g., multilabeling, ranking) is currently addressed with methods and theoretical analyses ad-hoc for each loss. In this paper we study a least-squares framework to…

Machine Learning · Computer Science 2018-10-17 Alex Nowak-Vila , Francis Bach , Alessandro Rudi

Deep neural networks trained with standard cross-entropy loss are more prone to memorize noisy labels, which degrades their performance. Negative learning using complementary labels is more robust when noisy labels intervene but with an…

Machine Learning · Computer Science 2022-09-07 Chen-Chen Zong , Zheng-Tao Cao , Hong-Tao Guo , Yun Du , Ming-Kun Xie , Shao-Yuan Li , Sheng-Jun Huang