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We consider adversarial training of deep neural networks through the lens of Bayesian learning, and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on…

Machine Learning · Computer Science 2021-02-24 Matthew Wicker , Luca Laurenti , Andrea Patane , Zhoutong Chen , Zheng Zhang , Marta Kwiatkowska

We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three…

Machine Learning · Computer Science 2022-02-23 Zhiyu Zhang , Ashok Cutkosky , Ioannis Ch. Paschalidis

The vulnerability of Deep Neural Networks to Adversarial Attacks has fuelled research towards building robust models. While most Adversarial Training algorithms aim at defending attacks constrained within low magnitude Lp norm bounds,…

Machine Learning · Computer Science 2022-10-19 Sravanti Addepalli , Samyak Jain , Gaurang Sriramanan , R. Venkatesh Babu

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

Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest…

Machine Learning · Computer Science 2018-10-17 Laurent Lessard , Xuezhou Zhang , Xiaojin Zhu

Current machine learning models achieve super-human performance in many real-world applications. Still, they are susceptible against imperceptible adversarial perturbations. The most effective solution for this problem is adversarial…

Machine Learning · Computer Science 2023-01-26 Mohammad Azizmalayeri , Arman Zarei , Alireza Isavand , Mohammad Taghi Manzuri , Mohammad Hossein Rohban

Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…

Machine Learning · Computer Science 2024-01-18 Nicolas Garcia Trillos , Matt Jacobs , Jakwang Kim , Matthew Werenski

Adversarial training based on the minimax formulation is necessary for obtaining adversarial robustness of trained models. However, it is conservative or even pessimistic so that it sometimes hurts the natural generalization. In this paper,…

Machine Learning · Computer Science 2020-09-08 Jingfeng Zhang , Xilie Xu , Bo Han , Gang Niu , Lizhen Cui , Masashi Sugiyama , Mohan Kankanhalli

The vulnerability of deep neural networks (DNNs) to adversarial examples has attracted great attention in the machine learning community. The problem is related to non-flatness and non-smoothness of normally obtained loss landscapes.…

Machine Learning · Computer Science 2023-02-13 Qizhang Li , Yiwen Guo , Wangmeng Zuo , Hao Chen

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

Neural and Evolutionary Computing · Computer Science 2019-09-09 Stefano Massaroli , Michael Poli , Federico Califano , Angela Faragasso , Jinkyoo Park , Atsushi Yamashita , Hajime Asama

Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods such as adversarial training can defend against particular…

Machine Learning · Computer Science 2026-03-10 Kuo Gai , Sicong Wang , Shihua Zhang

Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…

Machine Learning · Statistics 2025-03-20 Antônio H. RIbeiro , Thomas B. Schön , Dave Zahariah , Francis Bach

The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…

Machine Learning · Computer Science 2020-07-13 Anh Bui , Trung Le , He Zhao , Paul Montague , Olivier deVel , Tamas Abraham , Dinh Phung

Adversarial training has been proven to be an effective technique for improving the adversarial robustness of models. However, there seems to be an inherent trade-off between optimizing the model for accuracy and robustness. To this end, we…

Computer Vision and Pattern Recognition · Computer Science 2020-08-20 Elahe Arani , Fahad Sarfraz , Bahram Zonooz

Adversarial training has proven to be effective in hardening networks against adversarial examples. However, the gained robustness is limited by network capacity and number of training samples. Consequently, to build more robust models, it…

Machine Learning · Computer Science 2020-06-02 Zheng Xu , Ali Shafahi , Tom Goldstein

An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs. To improve the robustness of these models, one of the most popular defense mechanisms is to alternatively maximize the loss over…

Machine Learning · Computer Science 2020-10-22 Zhun Deng , Hangfeng He , Jiaoyang Huang , Weijie J. Su

Adversarial training has emerged as an effective approach to train robust neural network models that are resistant to adversarial attacks, even in low-label regimes where labeled data is scarce. In this paper, we introduce a novel…

Machine Learning · Computer Science 2024-11-28 Tian Ye , Rajgopal Kannan , Viktor Prasanna

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

Optimization and Control · Mathematics 2025-01-30 Anran Li , John P. Swensen , Mehdi Hosseinzadeh

The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…

Optimization and Control · Mathematics 2021-03-02 Jelena Diakonikolas , Constantinos Daskalakis , Michael I. Jordan

Machine learning systems based on deep neural networks, being able to produce state-of-the-art results on various perception tasks, have gained mainstream adoption in many applications. However, they are shown to be vulnerable to…

Machine Learning · Computer Science 2018-01-16 Bo Luo , Yannan Liu , Lingxiao Wei , Qiang Xu