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We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…

Machine Learning · Statistics 2018-12-05 Gamaleldin F. Elsayed , Dilip Krishnan , Hossein Mobahi , Kevin Regan , Samy Bengio

This paper studies the unsupervised embedding learning problem, which requires an effective similarity measurement between samples in low-dimensional embedding space. Motivated by the positive concentrated and negative separated properties…

Computer Vision and Pattern Recognition · Computer Science 2019-04-09 Mang Ye , Xu Zhang , Pong C. Yuen , Shih-Fu Chang

The extraction of useful deep features is important for many computer vision tasks. Deep features extracted from classification networks have proved to perform well in those tasks. To obtain features of greater usefulness, end-to-end…

Computer Vision and Pattern Recognition · Computer Science 2023-05-26 Shota Horiguchi , Daiki Ikami , Kiyoharu Aizawa

In face recognition, designing margin-based (e.g., angular, additive, additive angular margins) softmax loss functions plays an important role in learning discriminative features. However, these hand-crafted heuristic methods are…

Computer Vision and Pattern Recognition · Computer Science 2020-07-14 Xiaobo Wang , Shuo Wang , Cheng Chi , Shifeng Zhang , Tao Mei

The key task of machine learning is to minimize the loss function that measures the model fit to the training data. The numerical methods to do this efficiently depend on the properties of the loss function. The most decisive among these…

Machine Learning · Computer Science 2025-10-31 Tomas Hrycej , Bernhard Bermeitinger , Massimo Pavone , Götz-Henrik Wiegand , Siegfried Handschuh

Prediction under uncertainty is a critical requirement for the deep neural network to succeed responsibly. This paper focuses on selective prediction, which allows DNNs to make informed decisions about when to predict or abstain based on…

Computer Vision and Pattern Recognition · Computer Science 2026-02-13 Ishan Mishra , Jiajie Li , Deepak Mishra , Jinjun Xiong

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

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Kanchana Ranasinghe , Muzammal Naseer , Munawar Hayat , Salman Khan , Fahad Shahbaz Khan

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

This work develops a novel end-to-end deep unsupervised learning method based on convolutional neural network (CNN) with pseudo-classes for remote sensing scene representation. First, we introduce center points as the centers of the pseudo…

Computer Vision and Pattern Recognition · Computer Science 2019-03-19 Zhiqiang Gong , Ping Zhong , Weidong Hu , Fang Liu , Bingwei Hui

Few-shot classification algorithms can alleviate the data scarceness issue, which is vital in many real-world problems, by adopting models pre-trained from abundant data in other domains. However, the pre-training process was commonly…

Machine Learning · Computer Science 2020-03-03 Chao Wang , Ruo-Ze Liu , Han-Jia Ye , Yang Yu

Convolutional Neural Networks (CNNs) have been widely used in computer vision tasks, such as face recognition and verification, and have achieved state-of-the-art results due to their ability to capture discriminative deep features.…

Computer Vision and Pattern Recognition · Computer Science 2018-07-31 Alessandro Calefati , Muhammad Kamran Janjua , Shah Nawaz , Ignazio Gallo

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

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

Computer Vision and Pattern Recognition · Computer Science 2020-07-21 Ismail Elezi , Sebastiano Vascon , Alessandro Torcinovich , Marcello Pelillo , Laura Leal-Taixe

The top-k error is a common measure of performance in machine learning and computer vision. In practice, top-k classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed…

Machine Learning · Computer Science 2018-02-22 Leonard Berrada , Andrew Zisserman , M. Pawan Kumar

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

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Computer Vision and Pattern Recognition · Computer Science 2023-12-19 Deen Dayal Mohan , Bhavin Jawade , Srirangaraj Setlur , Venu Govindaraj

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

Machine Learning · Computer Science 2025-12-23 Francis Bach

We present a simple yet effective progressive self-guided loss function to facilitate deep learning-based salient object detection (SOD) in images. The saliency maps produced by the most relevant works still suffer from incomplete…

Computer Vision and Pattern Recognition · Computer Science 2021-09-08 Sheng Yang , Weisi Lin , Guosheng Lin , Qiuping Jiang , Zichuan Liu

The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

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