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Despite the impressive performances reported by deep neural networks in different application domains, they remain largely vulnerable to adversarial examples, i.e., input samples that are carefully perturbed to cause misclassification at…

Computer Vision and Pattern Recognition · Computer Science 2020-04-20 Angelo Sotgiu , Ambra Demontis , Marco Melis , Battista Biggio , Giorgio Fumera , Xiaoyi Feng , Fabio Roli

We construct pairs of distributions $\mu_d, \nu_d$ on $\mathbb{R}^d$ such that the quantity $|\mathbb{E}_{x \sim \mu_d} [F(x)] - \mathbb{E}_{x \sim \nu_d} [F(x)]|$ decreases as $\Omega(1/d^2)$ for some three-layer ReLU network $F$ with…

Machine Learning · Computer Science 2021-12-30 Carles Domingo-Enrich

Convolutional Neural Networks have been shown to be vulnerable to adversarial examples, which are known to locate in subspaces close to where normal data lies but are not naturally occurring and of low probability. In this work, we…

Computer Vision and Pattern Recognition · Computer Science 2020-08-27 Fu Lin , Rohit Mittapalli , Prithvijit Chattopadhyay , Daniel Bolya , Judy Hoffman

Deep neural networks have achieved substantial achievements in several computer vision areas, but have vulnerabilities that are often fooled by adversarial examples that are not recognized by humans. This is an important issue for security…

Computer Vision and Pattern Recognition · Computer Science 2021-01-29 Hakmin Lee , Hong Joo Lee , Seong Tae Kim , Yong Man Ro

Adversarial examples have attracted significant attention over the years, yet understanding their frequency-based characteristics remains insufficient. In this paper, we investigate the intriguing properties of adversarial examples in the…

Computer Vision and Pattern Recognition · Computer Science 2025-06-17 Lu Chen , Han Yang , Hu Wang , Yuxin Cao , Shaofeng Li , Yuan Luo

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite…

Machine Learning · Computer Science 2023-08-01 Shijun Zhang , Jianfeng Lu , Hongkai Zhao

Gradient descent (GD) type optimization schemes are the standard instruments to train fully connected feedforward artificial neural networks (ANNs) with rectified linear unit (ReLU) activation and can be considered as temporal…

Optimization and Control · Mathematics 2022-02-24 Shokhrukh Ibragimov , Arnulf Jentzen , Timo Kröger , Adrian Riekert

Artificial neural networks have been successfully used for many different classification tasks including malware detection and distinguishing between malicious and non-malicious programs. Although artificial neural networks perform very…

Machine Learning · Computer Science 2019-09-12 Robert Podschwadt , Hassan Takabi

Adversarial examples are a key method to exploit deep neural networks. Using gradient information, such examples can be generated in an efficient way without altering the victim model. Recent frequency domain transformation has further…

Machine Learning · Computer Science 2024-08-26 Zhibo Jin , Jiayu Zhang , Zhiyu Zhu , Xinyi Wang , Yiyun Huang , Huaming Chen

In recent years, deep learning has shown performance breakthroughs in many applications, such as image detection, image segmentation, pose estimation, and speech recognition. However, this comes with a major concern: deep networks have been…

Machine Learning · Computer Science 2019-01-11 Felix Kreuk , Assi Barak , Shir Aviv-Reuven , Moran Baruch , Benny Pinkas , Joseph Keshet

In this article we study fully-connected feedforward deep ReLU ANNs with an arbitrarily large number of hidden layers and we prove convergence of the risk of the GD optimization method with random initializations in the training of such…

Optimization and Control · Mathematics 2022-07-14 Arnulf Jentzen , Adrian Riekert

Adversarial examples have been found for various deep as well as shallow learning models, and have at various times been suggested to be either fixable model-specific bugs, or else inherent dataset feature, or both. We present theoretical…

Machine Learning · Computer Science 2023-04-14 Benjamin L. Badger

It has been demonstrated that very simple attacks can fool highly-sophisticated neural network architectures. In particular, so-called adversarial examples, constructed from perturbations of input data that are small or imperceptible to…

Cryptography and Security · Computer Science 2019-04-09 N. Benjamin Erichson , Zhewei Yao , Michael W. Mahoney

Adversarial examples contain small perturbations that can remain imperceptible to human observers but alter the behavior of even the best performing deep learning models and yield incorrect outputs. Since their discovery, adversarial…

Computer Vision and Pattern Recognition · Computer Science 2019-08-08 Andras Rozsa , Terrance E. Boult

Deep neural networks (DNNs) have proven to be quite effective in a vast array of machine learning tasks, with recent examples in cyber security and autonomous vehicles. Despite the superior performance of DNNs in these applications, it has…

Machine Learning · Computer Science 2017-08-22 Qinglong Wang , Wenbo Guo , Kaixuan Zhang , Alexander G. Ororbia , Xinyu Xing , Xue Liu , C. Lee Giles

Fundamental questions remain about when and why adversarial examples arise in neural networks, with competing views characterising them either as artifacts of the irregularities in the decision landscape or as products of sensitivity to…

Machine Learning · Computer Science 2025-10-14 Edward Stevinson , Lucas Prieto , Melih Barsbey , Tolga Birdal

Most previous works usually explained adversarial examples from several specific perspectives, lacking relatively integral comprehension about this problem. In this paper, we present a systematic study on adversarial examples from three…

Machine Learning · Computer Science 2019-03-01 Ke Sun , Zhanxing Zhu , Zhouchen Lin

Deep neural networks are vulnerable to adversarial examples, which are crafted by adding small, human-imperceptible perturbations to the original images, but make the model output inaccurate predictions. Before deep neural networks are…

Computer Vision and Pattern Recognition · Computer Science 2021-01-13 Bo Yang , Kaiyong Xu , Hengjun Wang , Hengwei Zhang

A counter-intuitive property of convolutional neural networks (CNNs) is their inherent susceptibility to adversarial examples, which severely hinders the application of CNNs in security-critical fields. Adversarial examples are similar to…

Machine Learning · Computer Science 2022-07-27 Jiebao Zhang , Wenhua Qian , Rencan Nie , Jinde Cao , Dan Xu

Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-11 David Stutz , Matthias Hein , Bernt Schiele
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