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Making classifiers robust to adversarial examples is hard. Thus, many defenses tackle the seemingly easier task of detecting perturbed inputs. We show a barrier towards this goal. We prove a general hardness reduction between detection and…

Machine Learning · Computer Science 2022-06-17 Florian Tramèr

The robustness of neural networks to intended perturbations has recently attracted significant attention. In this paper, we propose a new method, \emph{learning with a strong adversary}, that learns robust classifiers from supervised data.…

Machine Learning · Computer Science 2016-01-19 Ruitong Huang , Bing Xu , Dale Schuurmans , Csaba Szepesvari

Modern machine learning systems have been applied successfully to a variety of tasks in recent years but making such systems robust against adversarially chosen modifications of input instances seems to be a much harder problem. It is…

Quantum Physics · Physics 2021-12-20 Khashayar Barooti , Grzegorz Głuch , Ruediger Urbanke

Despite extraordinary progress, current machine learning systems have been shown to be brittle against adversarial examples: seemingly innocuous but carefully crafted perturbations of test examples that cause machine learning predictors to…

Machine Learning · Computer Science 2023-06-14 Omar Montasser

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

Computational Complexity · Computer Science 2025-12-02 Guy Blanc , Caleb Koch , Jane Lange , Carmen Strassle , Li-Yang Tan

A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…

Machine Learning · Computer Science 2022-05-13 Pascale Gourdeau , Varun Kanade , Marta Kwiatkowska , James Worrell

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 our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary…

Machine Learning · Computer Science 2018-11-16 Sébastien Bubeck , Yin Tat Lee , Eric Price , Ilya Razenshteyn

We study the problem of reducing adversarially robust learning to standard PAC learning, i.e. the complexity of learning adversarially robust predictors using access to only a black-box non-robust learner. We give a reduction that can…

Machine Learning · Computer Science 2020-10-26 Omar Montasser , Steve Hanneke , Nathan Srebro

We study the problem of learning an adversarially robust predictor to test time attacks in the semi-supervised PAC model. We address the question of how many labeled and unlabeled examples are required to ensure learning. We show that…

Machine Learning · Computer Science 2024-05-07 Idan Attias , Steve Hanneke , Yishay Mansour

We initiate the study of a new notion of adversarial loss which we call distributional adversarial loss. In this notion, we assume for each original example, the allowed adversarial perturbation set is a family of distributions, and the…

Machine Learning · Computer Science 2025-06-23 Saba Ahmadi , Siddharth Bhandari , Avrim Blum , Chen Dan , Prabhav Jain

Contrastive learning (CL) has recently emerged as an effective approach to learning representation in a range of downstream tasks. Central to this approach is the selection of positive (similar) and negative (dissimilar) sets to provide the…

Machine Learning · Computer Science 2021-10-25 Anh Bui , Trung Le , He Zhao , Paul Montague , Seyit Camtepe , Dinh Phung

A new understanding of adversarial examples and adversarial robustness is proposed by decoupling the data generator and the label generator (which we call the teacher). In our framework, adversarial robustness is a conditional concept---the…

Machine Learning · Computer Science 2020-12-15 Chao Ma , Lexing Ying

Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test…

Machine Learning · Computer Science 2019-12-20 Sanjam Garg , Somesh Jha , Saeed Mahloujifar , Mohammad Mahmoody

Most machine learning classifiers, including deep neural networks, are vulnerable to adversarial examples. Such inputs are typically generated by adding small but purposeful modifications that lead to incorrect outputs while imperceptible…

Machine Learning · Computer Science 2017-09-28 Beilun Wang , Ji Gao , Yanjun Qi

Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high…

Machine Learning · Computer Science 2018-05-03 Ludwig Schmidt , Shibani Santurkar , Dimitris Tsipras , Kunal Talwar , Aleksander Mądry

Ideally, what confuses neural network should be confusing to humans. However, recent experiments have shown that small, imperceptible perturbations can change the network prediction. To address this gap in perception, we propose a novel…

Machine Learning · Computer Science 2018-10-31 Alexander Matyasko , Lap-Pui Chau

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

Machine Learning · Computer Science 2023-01-19 Robi Bhattacharjee , Somesh Jha , Kamalika Chaudhuri

As deep learning applications, especially programs of computer vision, are increasingly deployed in our lives, we have to think more urgently about the security of these applications.One effective way to improve the security of deep…

Computer Vision and Pattern Recognition · Computer Science 2022-06-02 Xiao Tan , Jingbo Gao , Ruolin Li

Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…

Machine Learning · Computer Science 2025-02-12 Hassan Ashtiani , Vinayak Pathak , Ruth Urner
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