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We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles,…

Machine Learning · Statistics 2018-05-23 Kevin Roth , Aurelien Lucchi , Sebastian Nowozin , Thomas Hofmann

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack…

Computer Vision and Pattern Recognition · Computer Science 2022-12-07 Julia Grabinski , Paul Gavrikov , Janis Keuper , Margret Keuper

Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common…

Computer Vision and Pattern Recognition · Computer Science 2022-10-26 Paul Gavrikov , Janis Keuper

Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even…

Machine Learning · Computer Science 2019-10-21 Florian Tramèr , Dan Boneh

State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against it. Formulated as a min-max problem, it…

Machine Learning · Statistics 2023-10-18 Antônio H. Ribeiro , Dave Zachariah , Francis Bach , Thomas B. Schön

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

Machine Learning · Computer Science 2019-11-12 Bai Li , Changyou Chen , Wenlin Wang , Lawrence Carin

Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of ML models, often associated with their black-box operation and…

Machine Learning · Computer Science 2025-04-29 Elad Sofer , Tomer Shaked , Caroline Chaux , Nir Shlezinger

Several existing works study either adversarial or natural distributional robustness of deep neural networks separately. In practice, however, models need to enjoy both types of robustness to ensure reliability. In this work, we bridge this…

Machine Learning · Computer Science 2022-09-19 Mazda Moayeri , Kiarash Banihashem , Soheil Feizi

Deep neural networks are easily fooled by small perturbations known as adversarial attacks. Adversarial Training (AT) is a technique aimed at learning features robust to such attacks and is widely regarded as a very effective defense.…

Machine Learning · Computer Science 2020-09-11 Theodoros Tsiligkaridis , Jay Roberts

While existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real-world settings. In many such cases although test data might not be…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Tejas Gokhale , Rushil Anirudh , Bhavya Kailkhura , Jayaraman J. Thiagarajan , Chitta Baral , Yezhou Yang

Neural networks are vulnerable to small adversarial perturbations. Existing literature largely focused on understanding and mitigating the vulnerability of learned models. In this paper, we demonstrate an intriguing phenomenon about the…

Machine Learning · Computer Science 2019-02-25 Gavin Weiguang Ding , Kry Yik Chau Lui , Xiaomeng Jin , Luyu Wang , Ruitong Huang

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

Machine Learning · Computer Science 2025-09-24 Steffen Schotthöfer , H. Lexie Yang , Stefan Schnake

We consider adversarial training of deep neural networks through the lens of Bayesian learning, and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on…

Machine Learning · Computer Science 2021-02-24 Matthew Wicker , Luca Laurenti , Andrea Patane , Zhoutong Chen , Zheng Zhang , Marta Kwiatkowska

Neural networks are vulnerable to adversarial examples, i.e. inputs that are imperceptibly perturbed from natural data and yet incorrectly classified by the network. Adversarial training, a heuristic form of robust optimization that…

Machine Learning · Computer Science 2019-11-12 Ruiqi Gao , Tianle Cai , Haochuan Li , Liwei Wang , Cho-Jui Hsieh , Jason D. Lee

Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this…

Machine Learning · Computer Science 2018-11-26 Eric Wong , Frank R. Schmidt , Jan Hendrik Metzen , J. Zico Kolter

Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the…

Machine Learning · Computer Science 2020-04-28 Yuanhao Xiong , Cho-Jui Hsieh

Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with…

Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. In this paper we study how the…

Machine Learning · Computer Science 2020-02-11 Marc Khoury

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Adversarial training is a common approach to improving the robustness of deep neural networks against adversarial examples. In this work, we propose a novel regularization approach as an alternative. To derive the regularizer, we formulate…

Machine Learning · Computer Science 2021-02-09 Avery Ma , Fartash Faghri , Nicolas Papernot , Amir-massoud Farahmand