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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

High cost of training time caused by multi-step adversarial example generation is a major challenge in adversarial training. Previous methods try to reduce the computational burden of adversarial training using single-step adversarial…

Machine Learning · Computer Science 2021-02-09 Lehui Xie , Yaopeng Wang , Jia-Li Yin , Ximeng Liu

Adversarial attacks have been shown to be highly effective at degrading the performance of deep neural networks (DNNs). The most prominent defense is adversarial training, a method for learning a robust model. Nevertheless, adversarial…

Computer Vision and Pattern Recognition · Computer Science 2021-09-07 Uriya Pesso , Koby Bibas , Meir Feder

Sparse attacks are to optimize the magnitude of adversarial perturbations for fooling deep neural networks (DNNs) involving only a few perturbed pixels (i.e., under the l0 constraint), suitable for interpreting the vulnerability of DNNs.…

Machine Learning · Computer Science 2025-06-24 Fudong Lin , Jiadong Lou , Hao Wang , Brian Jalaian , Xu Yuan

Neural networks are vulnerable to adversarial attacks -- small visually imperceptible crafted noise which when added to the input drastically changes the output. The most effective method of defending against these adversarial attacks is to…

Deep Neural Networks (DNNs) have revolutionized a wide range of industries, from healthcare and finance to automotive, by offering unparalleled capabilities in data analysis and decision-making. Despite their transforming impact, DNNs face…

Machine Learning · Computer Science 2024-02-08 Zhenyu Liu , Garrett Gagnon , Swagath Venkataramani , Liu Liu

The evaluation of robustness against adversarial manipulation of neural networks-based classifiers is mainly tested with empirical attacks as methods for the exact computation, even when available, do not scale to large networks. We propose…

Machine Learning · Computer Science 2020-07-21 Francesco Croce , Matthias Hein

Throughout the past five years, the susceptibility of neural networks to minimal adversarial perturbations has moved from a peculiar phenomenon to a core issue in Deep Learning. Despite much attention, however, progress towards more robust…

Machine Learning · Statistics 2019-12-13 Wieland Brendel , Jonas Rauber , Matthias Kümmerer , Ivan Ustyuzhaninov , Matthias Bethge

Despite much effort, deep neural networks remain highly susceptible to tiny input perturbations and even for MNIST, one of the most common toy datasets in computer vision, no neural network model exists for which adversarial perturbations…

Computer Vision and Pattern Recognition · Computer Science 2018-09-21 Lukas Schott , Jonas Rauber , Matthias Bethge , Wieland Brendel

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…

Machine Learning · Computer Science 2019-10-09 Matteo Terzi , Gian Antonio Susto , Pratik Chaudhari

Deep Neural Networks, despite their great success in diverse domains, are provably sensitive to small perturbations on correctly classified examples and lead to erroneous predictions. Recently, it was proposed that this behavior can be…

Machine Learning · Computer Science 2020-09-29 Nan Xu , Oluwaseyi Feyisetan , Abhinav Aggarwal , Zekun Xu , Nathanael Teissier

Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with…

Cryptography and Security · Computer Science 2023-06-06 Chen Wan , Fangjun Huang

Deep neural networks have achieved remarkable success in a wide range of classification tasks. However, they remain highly susceptible to adversarial examples - inputs that are subtly perturbed to induce misclassification while appearing…

Machine Learning · Computer Science 2025-10-20 Virendra Nishad , Bhaskar Mukhoty , Hilal AlQuabeh , Sandeep K. Shukla , Sayak Ray Chowdhury

We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves…

Numerical Analysis · Mathematics 2026-05-26 Shu Liu , Stanley Osher , Wuchen Li

Adversarial examples have shown a powerful ability to make a well-trained model misclassified. Current mainstream adversarial attack methods only consider one of the distortions among $L_0$-norm, $L_2$-norm, and $L_\infty$-norm. $L_0$-norm…

Computer Vision and Pattern Recognition · Computer Science 2024-07-04 Chao Zhou , Yuan-Gen Wang , Zi-jia Wang , Xiangui Kang

After the discovery of adversarial examples and their adverse effects on deep learning models, many studies focused on finding more diverse methods to generate these carefully crafted samples. Although empirical results on the effectiveness…

Machine Learning · Computer Science 2020-06-03 Utku Ozbulak , Manvel Gasparyan , Wesley De Neve , Arnout Van Messem

We study the problem of defending deep neural network approaches for image classification from physically realizable attacks. First, we demonstrate that the two most scalable and effective methods for learning robust models, adversarial…

Machine Learning · Computer Science 2020-02-18 Tong Wu , Liang Tong , Yevgeniy Vorobeychik

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation…

Optimization and Control · Mathematics 2024-01-18 Dongsheng Ding , Chen-Yu Wei , Kaiqing Zhang , Alejandro Ribeiro

Research on adversarial examples in computer vision tasks has shown that small, often imperceptible changes to an image can induce misclassification, which has security implications for a wide range of image processing systems. Considering…

Computer Vision and Pattern Recognition · Computer Science 2019-04-05 Jérôme Rony , Luiz G. Hafemann , Luiz S. Oliveira , Ismail Ben Ayed , Robert Sabourin , Eric Granger

This work uses adversarial perturbations to enhance deepfake images and fool common deepfake detectors. We created adversarial perturbations using the Fast Gradient Sign Method and the Carlini and Wagner L2 norm attack in both blackbox and…

Computer Vision and Pattern Recognition · Computer Science 2020-05-18 Apurva Gandhi , Shomik Jain