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We present a mechanism for detecting adversarial examples based on data representations taken from the hidden layers of the target network. For this purpose, we train individual autoencoders at intermediate layers of the target network.…

Machine Learning · Computer Science 2020-06-18 Bartosz Wójcik , Paweł Morawiecki , Marek Śmieja , Tomasz Krzyżek , Przemysław Spurek , Jacek Tabor

Deep Neural Networks (DNNs) have often supplied state-of-the-art results in pattern recognition tasks. Despite their advances, however, the existence of adversarial examples have caught the attention of the community. Many existing works…

Machine Learning · Computer Science 2021-01-25 Jay Morgan , Adeline Paiement , Arno Pauly , Monika Seisenberger

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

Computer Vision and Pattern Recognition · Computer Science 2018-04-17 Simant Dube

Deep neural networks obtain state-of-the-art performance on a series of tasks. However, they are easily fooled by adding a small adversarial perturbation to input. The perturbation is often human imperceptible on image data. We observe a…

Machine Learning · Computer Science 2019-06-11 Puyudi Yang , Jianbo Chen , Cho-Jui Hsieh , Jane-Ling Wang , Michael I. Jordan

Despite remarkable performance on a variety of tasks, many properties of deep neural networks are not yet theoretically understood. One such mystery is the depth degeneracy phenomenon: the deeper you make your network, the closer your…

Machine Learning · Statistics 2025-11-18 Cameron Jakub , Mihai Nica

State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the perturbations can \textit{transfer across models}:…

Machine Learning · Statistics 2018-02-28 Lei Wu , Zhanxing Zhu , Cheng Tai , Weinan E

While classic studies proved that wide networks allow universal approximation, recent research and successes of deep learning demonstrate the power of deep networks. Based on a symmetric consideration, we investigate if the design of…

Machine Learning · Computer Science 2022-05-25 Feng-Lei Fan , Rongjie Lai , Ge Wang

Neural networks are known to be highly sensitive to adversarial examples. These may arise due to different factors, such as random initialization, or spurious correlations in the learning problem. To better understand these factors, we…

Machine Learning · Statistics 2022-07-05 Elvis Dohmatob , Alberto Bietti

Adversarial examples have raised several open questions, such as why they can deceive classifiers and transfer between different models. A prevailing hypothesis to explain these phenomena suggests that adversarial perturbations appear as…

Machine Learning · Computer Science 2025-01-22 Soichiro Kumano , Hiroshi Kera , Toshihiko Yamasaki

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

Modern classification algorithms are susceptible to adversarial examples--perturbations to inputs that cause the algorithm to produce undesirable behavior. In this work, we seek to understand and extend adversarial examples across domains…

Machine Learning · Computer Science 2021-12-14 Volodymyr Kuleshov , Evgenii Nikishin , Shantanu Thakoor , Tingfung Lau , Stefano Ermon

In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing…

Machine Learning · Computer Science 2020-12-29 Gal Vardi , Ohad Shamir

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed…

Machine Learning · Statistics 2015-03-24 Ian J. Goodfellow , Jonathon Shlens , Christian Szegedy

State-of-the-art machine learning models frequently misclassify inputs that have been perturbed in an adversarial manner. Adversarial perturbations generated for a given input and a specific classifier often seem to be effective on other…

Machine Learning · Computer Science 2018-11-09 Zachary Charles , Harrison Rosenberg , Dimitris Papailiopoulos

Adversarial attacks in the form of imperceptible perturbations of normal images have been extensively studied, and for every new defense methodology created, multiple adversarial attacks are found to counteract it. In particular, a popular…

Computer Vision and Pattern Recognition · Computer Science 2020-06-09 Carl Cheng , Evan Hu

Neural networks are known to be vulnerable to adversarial examples: inputs that are close to natural inputs but classified incorrectly. In order to better understand the space of adversarial examples, we survey ten recent proposals that are…

Machine Learning · Computer Science 2017-11-02 Nicholas Carlini , David Wagner

The increasing use of deep neural networks (DNNs) has motivated a parallel endeavor: the design of adversaries that profit from successful misclassifications. However, not all adversarial examples are crafted for malicious purposes. For…

Computer Vision and Pattern Recognition · Computer Science 2024-09-18 Pk Douglas , Farzad Vasheghani Farahani

Adversarial training is a widely-applied approach to training deep neural networks to be robust against adversarial perturbation. However, although adversarial training has achieved empirical success in practice, it still remains unclear…

Machine Learning · Computer Science 2025-02-10 Binghui Li , Yuanzhi Li

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Machine Learning · Statistics 2020-10-26 Andrew Y. K. Foong , David R. Burt , Yingzhen Li , Richard E. Turner

Despite their impressive performance, deep neural networks exhibit striking failures on out-of-distribution inputs. One core idea of adversarial example research is to reveal neural network errors under such distribution shifts. We…

Machine Learning · Computer Science 2020-07-14 Jörn-Henrik Jacobsen , Jens Behrmann , Richard Zemel , Matthias Bethge