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In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a…

Machine Learning · Computer Science 2025-11-05 Jingchao Gao , Ziqing Lu , Raghu Mudumbai , Xiaodong Wu , Jirong Yi , Myung Cho , Catherine Xu , Hui Xie , Weiyu Xu

In Federated Learning (FL), models are as fragile as centrally trained models against adversarial examples. However, the adversarial robustness of federated learning remains largely unexplored. This paper casts light on the challenge of…

Machine Learning · Computer Science 2023-02-21 Jie Zhang , Bo Li , Chen Chen , Lingjuan Lyu , Shuang Wu , Shouhong Ding , Chao Wu

Deep neural networks have proven remarkably effective at solving many classification problems, but have been criticized recently for two major weaknesses: the reasons behind their predictions are uninterpretable, and the predictions…

Machine Learning · Computer Science 2017-11-28 Andrew Slavin Ross , Finale Doshi-Velez

We study the robustness of machine learning approaches to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial…

Disordered Systems and Neural Networks · Physics 2024-01-26 Si Jiang , Sirui Lu , Dong-Ling Deng

Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous…

Machine Learning · Computer Science 2021-06-21 Hossein Aboutalebi , Mohammad Javad Shafiee , Michelle Karg , Christian Scharfenberger , Alexander Wong

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

Machine Learning · Statistics 2025-10-27 Antônio H. Ribeiro , David Vävinggren , Dave Zachariah , Thomas B. Schön , Francis Bach

Adversarial examples are malicious inputs crafted to cause a model to misclassify them. Their most common instantiation, "perturbation-based" adversarial examples introduce changes to the input that leave its true label unchanged, yet…

Machine Learning · Computer Science 2019-03-26 Jörn-Henrik Jacobsen , Jens Behrmannn , Nicholas Carlini , Florian Tramèr , Nicolas Papernot

Motivated by safety-critical classification problems, we investigate adversarial attacks against cost-sensitive classifiers. We use current state-of-the-art adversarially-resistant neural network classifiers [1] as the underlying models.…

Machine Learning · Statistics 2019-10-08 Gavin S. Hartnett , Andrew J. Lohn , Alexander P. Sedlack

Deep neural networks are vulnerable to adversarial attacks, where a small perturbation to an input alters the model prediction. In many cases, malicious inputs intentionally crafted for one model can fool another model. In this paper, we…

Machine Learning · Computer Science 2021-09-23 Liping Yuan , Xiaoqing Zheng , Yi Zhou , Cho-Jui Hsieh , Kai-wei Chang

This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of…

Machine Learning · Computer Science 2021-02-23 Rafael Pinot , Laurent Meunier , Florian Yger , Cédric Gouy-Pailler , Yann Chevaleyre , Jamal Atif

We derive a fundamental trade-off between standard and adversarial risk in a rather general situation that formalizes the following simple intuition: "If no (nearly) optimal predictor is smooth, adversarial robustness comes at the cost of…

Machine Learning · Statistics 2025-07-01 Sohail Bahmani

Adversarial training of binary classifiers can be reformulated as regularized risk minimization involving a nonlocal total variation. Building on this perspective, we establish a characterization of the subdifferential of this total…

Analysis of PDEs · Mathematics 2026-04-21 Leon Bungert , Lucas Schmitt

The study of adversarial robustness has so far largely focused on perturbations bound in p-norms. However, state-of-the-art models turn out to be also vulnerable to other, more natural classes of perturbations such as translations and…

Machine Learning · Computer Science 2019-09-17 Logan Engstrom , Brandon Tran , Dimitris Tsipras , Ludwig Schmidt , Aleksander Madry

Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…

Machine Learning · Statistics 2018-05-28 Sébastien Bubeck , Eric Price , Ilya Razenshteyn

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

Optimization and Control · Mathematics 2022-03-29 Camilo Garcia Trillos , Nicolas Garcia Trillos

Adversarial training is a principled approach for training robust neural networks. Despite of tremendous successes in practice, its theoretical properties still remain largely unexplored. In this paper, we provide new theoretical insights…

Machine Learning · Computer Science 2019-07-29 Yan Li , Ethan X. Fang , Huan Xu , Tuo Zhao

Adversarial examples, or nearly indistinguishable inputs created by an attacker, significantly reduce machine learning accuracy. Theoretical evidence has shown that the high intrinsic dimensionality of datasets facilitates an adversary's…

Machine Learning · Computer Science 2021-12-13 Sheila Alemany , Niki Pissinou

Although deep networks achieve strong accuracy on a range of computer vision benchmarks, they remain vulnerable to adversarial attacks, where imperceptible input perturbations fool the network. We present both theoretical and empirical…

Computer Vision and Pattern Recognition · Computer Science 2020-09-14 Chengzhi Mao , Amogh Gupta , Vikram Nitin , Baishakhi Ray , Shuran Song , Junfeng Yang , Carl Vondrick

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

State-of-the-art neural networks are vulnerable to adversarial examples; they can easily misclassify inputs that are imperceptibly different than their training and test data. In this work, we establish that the use of cross-entropy loss…

Machine Learning · Computer Science 2019-01-25 Kamil Nar , Orhan Ocal , S. Shankar Sastry , Kannan Ramchandran