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We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles,…

Machine Learning · Statistics 2018-05-23 Kevin Roth , Aurelien Lucchi , Sebastian Nowozin , Thomas Hofmann

The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…

Optimization and Control · Mathematics 2020-05-05 Jacob H. Seidman , Mahyar Fazlyab , Victor M. Preciado , George J. Pappas

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…

Machine Learning · Statistics 2019-01-25 Zhuozhuo Tu , Jingwei Zhang , Dacheng Tao

Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making…

Machine Learning · Statistics 2021-11-17 Takeru Miyato , Andrew M. Dai , Ian Goodfellow

Deep reinforcement learning models are vulnerable to adversarial attacks that can decrease a victim's cumulative expected reward by manipulating the victim's observations. Despite the efficiency of previous optimization-based methods for…

Machine Learning · Computer Science 2023-02-28 You Qiaoben , Chengyang Ying , Xinning Zhou , Hang Su , Jun Zhu , Bo Zhang

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake image generation, where security methods…

Machine Learning · Computer Science 2025-10-07 David Benfield , Stefano Coniglio , Phan Tu Vuong , Alain Zemkoho

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Numerical Analysis · Mathematics 2025-12-10 Martin Burger , Samira Kabri , Gitta Kutyniok , Yunseok Lee , Lukas Weigand

Adversarial robustness has become a central goal in deep learning, both in the theory and the practice. However, successful methods to improve the adversarial robustness (such as adversarial training) greatly hurt generalization performance…

Machine Learning · Statistics 2022-10-20 Alex Lamb , Vikas Verma , Kenji Kawaguchi , Alexander Matyasko , Savya Khosla , Juho Kannala , Yoshua Bengio

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

Machine Learning · Computer Science 2024-08-23 Jie Wang , Rui Gao , Yao Xie

Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper…

Machine Learning · Computer Science 2023-05-25 Haotian Gu , Xin Guo , Xinyu Li

This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…

Optimization and Control · Mathematics 2024-07-08 Gang Bao , Dong Wang , Boyi Zou

A central concern in classification is the vulnerability of machine learning models to adversarial attacks. Adversarial training is one of the most popular techniques for training robust classifiers, which involves minimizing an adversarial…

Machine Learning · Computer Science 2025-10-09 Natalie S. Frank

We study the model robustness against adversarial examples, referred to as small perturbed input data that may however fool many state-of-the-art deep learning models. Unlike previous research, we establish a novel theory addressing the…

Machine Learning · Computer Science 2020-06-11 Shufei Zhang , Kaizhu Huang , Zenglin Xu

Adversarial Training is proved to be an efficient method to defend against adversarial examples, being one of the few defenses that withstand strong attacks. However, traditional defense mechanisms assume a uniform attack over the examples…

Machine Learning · Computer Science 2020-10-27 Huimin Zeng , Chen Zhu , Tom Goldstein , Furong Huang

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower…

Machine Learning · Computer Science 2023-04-07 Dimitris Bertsimas , Xavier Boix , Kimberly Villalobos Carballo , Dick den Hertog

Although adversarial training is known to be effective against adversarial examples, training dynamics are not well understood. In this study, we present the first theoretical analysis of adversarial training in random deep neural networks…

Machine Learning · Computer Science 2025-05-21 Soichiro Kumano , Hiroshi Kera , Toshihiko Yamasaki

Adversarial training is extensively utilized to improve the adversarial robustness of deep neural networks. Yet, mitigating the degradation of standard generalization performance in adversarial-trained models remains an open problem. This…

Machine Learning · Computer Science 2024-03-27 Xiangyu Yin , Wenjie Ruan

Adversarial training is an effective method to train deep learning models that are resilient to norm-bounded perturbations, with the cost of nominal performance drop. While adversarial training appears to enhance the robustness and safety…

Machine Learning · Computer Science 2021-03-16 Mathias Lechner , Ramin Hasani , Radu Grosu , Daniela Rus , Thomas A. Henzinger

In practice, there are often explicit constraints on what representations or decisions are acceptable in an application of machine learning. For example it may be a legal requirement that a decision must not favour a particular group.…

Machine Learning · Computer Science 2016-03-09 Harrison Edwards , Amos Storkey

While adversarial training can improve robust accuracy (against an adversary), it sometimes hurts standard accuracy (when there is no adversary). Previous work has studied this tradeoff between standard and robust accuracy, but only in the…

Machine Learning · Computer Science 2019-08-28 Aditi Raghunathan , Sang Michael Xie , Fanny Yang , John C. Duchi , Percy Liang