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While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…

Machine Learning · Computer Science 2022-03-18 Xiongjie Chen , Yongxin Yang , Yunpeng Li

Deep neural networks are known to be vulnerable to adversarial perturbations. The amount of these perturbations are generally quantified using $L_p$ metrics, such as $L_0$, $L_2$ and $L_\infty$. However, even when the measured perturbations…

Computer Vision and Pattern Recognition · Computer Science 2023-10-24 Ayberk Aydin , Alptekin Temizel

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Machine Learning · Statistics 2017-10-23 Nicolas Courty , Rémi Flamary , Mélanie Ducoffe

In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While data augmentation techniques…

Machine Learning · Statistics 2025-06-26 Jiaming Hu , Debarghya Mukherjee , Ioannis Ch. Paschalidis

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small…

Optimization and Control · Mathematics 2025-10-24 Guangyi He , Tobias Sutter , Lukas Gonon

In recent years, deep neural networks demonstrated state-of-the-art performance in a large variety of tasks and therefore have been adopted in many applications. On the other hand, the latest studies revealed that neural networks are…

Computer Vision and Pattern Recognition · Computer Science 2018-12-07 Jingyang Zhang , Hsin-Pai Cheng , Chunpeng Wu , Hai Li , Yiran Chen

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…

Machine Learning · Computer Science 2023-02-16 Alexander Cloninger , Keaton Hamm , Varun Khurana , Caroline Moosmüller

Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide…

Machine Learning · Computer Science 2019-02-12 Chenxiao Zhao , P. Thomas Fletcher , Mixue Yu , Yaxin Peng , Guixu Zhang , Chaomin Shen

Adversarial examples of deep neural networks are receiving ever increasing attention because they help in understanding and reducing the sensitivity to their input. This is natural given the increasing applications of deep neural networks…

Computer Vision and Pattern Recognition · Computer Science 2021-01-13 Hanwei Zhang , Yannis Avrithis , Teddy Furon , Laurent Amsaleg

As designers of artificial intelligence try to outwit hackers, both sides continue to hone in on AI's inherent vulnerabilities. Designed and trained from certain statistical distributions of data, AI's deep neural networks (DNNs) remain…

Computer Vision and Pattern Recognition · Computer Science 2022-04-25 Wenzhao Xiang , Hang Su , Chang Liu , Yandong Guo , Shibao Zheng

Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the…

Machine Learning · Computer Science 2021-06-21 Gérard Biau , Maxime Sangnier , Ugo Tanielian

Many machine learning adversarial attacks find adversarial samples of a victim model ${\mathcal M}$ by following the gradient of some attack objective functions, either explicitly or implicitly. To confuse and detect such attacks, we take…

Cryptography and Security · Computer Science 2021-03-09 Jiyi Zhang , Ee-Chien Chang , Hwee Kuan Lee

With the increasing attention to deep neural network (DNN) models, attacks are also upcoming for such models. For example, an attacker may carefully construct images in specific ways (also referred to as adversarial examples) aiming to…

Computer Vision and Pattern Recognition · Computer Science 2024-01-08 Yuexin Xiang , Tiantian Li , Wei Ren , Tianqing Zhu , Kim-Kwang Raymond Choo

Despite numerous attempts to defend deep learning based image classifiers, they remain susceptible to the adversarial attacks. This paper proposes a technique to identify susceptible classes, those classes that are more easily subverted. To…

Machine Learning · Computer Science 2019-06-03 Rangeet Pan , Md Johirul Islam , Shibbir Ahmed , Hridesh Rajan

Artificial neural networks are prone to being fooled by carefully perturbed inputs which cause an egregious misclassification. These \textit{adversarial} attacks have been the focus of extensive research. Likewise, there has been an…

Machine Learning · Computer Science 2023-10-11 Dwight Nwaigwe , Lucrezia Carboni , Martial Mermillod , Sophie Achard , Michel Dojat

The Frank-Wolfe algorithm has seen a resurgence in popularity due to its ability to efficiently solve constrained optimization problems in machine learning and high-dimensional statistics. As such, there is much interest in establishing…

Machine Learning · Statistics 2022-05-19 Suhas Vijaykumar

Given the ability to directly manipulate image pixels in the digital input space, an adversary can easily generate imperceptible perturbations to fool a Deep Neural Network (DNN) image classifier, as demonstrated in prior work. In this…

Computer Vision and Pattern Recognition · Computer Science 2019-05-02 Shang-Tse Chen , Cory Cornelius , Jason Martin , Duen Horng Chau

Adversarial attacks aim to confound machine learning systems, while remaining virtually imperceptible to humans. Attacks on image classification systems are typically gauged in terms of $p$-norm distortions in the pixel feature space. We…

Machine Learning · Computer Science 2019-06-07 Ayon Sen , Xiaojin Zhu , Liam Marshall , Robert Nowak

Deep neural networks are susceptible to small-but-specific adversarial perturbations capable of deceiving the network. This vulnerability can lead to potentially harmful consequences in security-critical applications. To address this…

Computer Vision and Pattern Recognition · Computer Science 2018-06-29 Jasjeet Dhaliwal , Saurabh Shintre

A popular method to perform adversarial attacks on neuronal networks is the so-called fast gradient sign method and its iterative variant. In this paper, we interpret this method as an explicit Euler discretization of a differential…

Machine Learning · Computer Science 2025-09-17 Lukas Weigand , Tim Roith , Martin Burger