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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

Deep neural networks (DNNs) have achieved state-of-the-art results in various pattern recognition tasks. However, they perform poorly on out-of-distribution adversarial examples i.e. inputs that are specifically crafted by an adversary to…

Cryptography and Security · Computer Science 2019-05-09 Chirag Agarwal , Anh Nguyen , Dan Schonfeld

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

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

Scalability issue plays a crucial role in productionizing modern recommender systems. Even lightweight architectures may suffer from high computational overload due to intermediate calculations, limiting their practicality in real-world…

Information Retrieval · Computer Science 2024-12-03 Gleb Mezentsev , Danil Gusak , Ivan Oseledets , Evgeny Frolov

In the context of adversarial robustness, a single model does not usually have enough power to defend against all possible adversarial attacks, and as a result, has sub-optimal robustness. Consequently, an emerging line of work has focused…

Machine Learning · Computer Science 2022-06-08 Dinghuai Zhang , Hongyang Zhang , Aaron Courville , Yoshua Bengio , Pradeep Ravikumar , Arun Sai Suggala

This study presents a comparative analysis of two objective functions, Mean Squared Error (MSE) and Softmax Cross-Entropy (SCE) for neural network classification tasks. While SCE combined with softmax activation is the conventional choice…

Machine Learning · Computer Science 2024-11-19 Kanishka Tyagi , Chinmay Rane , Ketaki Vaidya , Jeshwanth Challgundla , Soumitro Swapan Auddy , Michael Manry

The softmax cross-entropy loss function has been widely used to train deep models for various tasks. In this work, we propose a Gaussian mixture (GM) loss function for deep neural networks for visual classification. Unlike the softmax…

Computer Vision and Pattern Recognition · Computer Science 2020-11-19 Weitao Wan , Jiansheng Chen , Cheng Yu , Tong Wu , Yuanyi Zhong , Ming-Hsuan Yang

Researches using margin based comparison loss demonstrate the effectiveness of penalizing the distance between face feature and their corresponding class centers. Despite their popularity and excellent performance, they do not explicitly…

Computer Vision and Pattern Recognition · Computer Science 2020-06-12 Ying Huang , Shangfeng Qiu , Wenwei Zhang , Xianghui Luo , Jinzhuo Wang

Softmax loss is arguably one of the most popular losses to train CNN models for image classification. However, recent works have exposed its limitation on feature discriminability. This paper casts a new viewpoint on the weakness of softmax…

Computer Vision and Pattern Recognition · Computer Science 2018-05-11 Xiaobo Wang , Shifeng Zhang , Zhen Lei , Si Liu , Xiaojie Guo , Stan Z. Li

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

The inability to guarantee robustness is one of the major obstacles to the application of deep learning models in security-demanding domains. We identify that the most commonly used cross-entropy (CE) loss does not guarantee robust boundary…

Machine Learning · Computer Science 2023-02-21 Weiwei Gao , Dazhi Zhang , Yao Li , Zhichang Guo , Ovanes Petrosian

Owing to security implications of adversarial vulnerability, adversarial robustness of deep metric learning models has to be improved. In order to avoid model collapse due to excessively hard examples, the existing defenses dismiss the…

Machine Learning · Computer Science 2022-03-04 Mo Zhou , Vishal M. Patel

The learning objective is integral to collaborative filtering systems, where the Bayesian Personalized Ranking (BPR) loss is widely used for learning informative backbones. However, BPR often experiences slow convergence and suboptimal…

Information Retrieval · Computer Science 2024-06-25 Xiaodong Yang , Huiyuan Chen , Yuchen Yan , Yuxin Tang , Yuying Zhao , Eric Xu , Yiwei Cai , Hanghang Tong

Cross-entropy (CE) training loss dominates deep learning practice, yet existing theory often relies on simplifications, either replacing it with squared loss or restricting to convex models, that miss essential behavior. CE and squared loss…

Machine Learning · Computer Science 2025-12-04 Connall Garrod , Jonathan P. Keating , Christos Thrampoulidis

The cross-entropy softmax loss is the primary loss function used to train deep neural networks. On the other hand, the focal loss function has been demonstrated to provide improved performance when there is an imbalance in the number of…

Computer Vision and Pattern Recognition · Computer Science 2022-06-17 Leslie N. Smith

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

Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the…

Machine Learning · Computer Science 2026-04-13 Matheus Vinícius Todescato , Joel Luís Carbonera

Large language models (LLMs) have been garnering increasing attention in the recommendation community. Some studies have observed that LLMs, when fine-tuned by the cross-entropy (CE) loss with a full softmax, could achieve…

Information Retrieval · Computer Science 2024-08-27 Cong Xu , Zhangchi Zhu , Mo Yu , Jun Wang , Jianyong Wang , Wei Zhang

The adversarial vulnerability of deep neural networks (DNNs) has been actively investigated in the past several years. This paper investigates the scale-variant property of cross-entropy loss, which is the most commonly used loss function…

Machine Learning · Computer Science 2022-10-12 Ziquan Liu , Antoni B. Chan
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