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We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed…

Machine Learning · Computer Science 2019-06-18 Jeremy M Cohen , Elan Rosenfeld , J. Zico Kolter

Randomized smoothing has become essential for achieving certified adversarial robustness in machine learning models. However, current methods primarily use isotropic noise distributions that are uniform across all data dimensions, such as…

Machine Learning · Computer Science 2025-10-24 Hanbin Hong , Ashish Kundu , Ali Payani , Binghui Wang , Yuan Hong

Randomized smoothing is a defensive technique to achieve enhanced robustness against adversarial examples which are small input perturbations that degrade the performance of neural network models. Conventional randomized smoothing adds…

Machine Learning · Computer Science 2024-07-17 Ryo Hase , Ye Wang , Toshiaki Koike-Akino , Jing Liu , Kieran Parsons

Randomized smoothing (RS) is a well known certified defense against adversarial attacks, which creates a smoothed classifier by predicting the most likely class under random noise perturbations of inputs during inference. While initial work…

Machine Learning · Computer Science 2023-04-21 Soumalya Nandi , Sravanti Addepalli , Harsh Rangwani , R. Venkatesh Babu

Randomized smoothing is the current state-of-the-art method for producing provably robust classifiers. While randomized smoothing typically yields robust $\ell_2$-ball certificates, recent research has generalized provable robustness to…

Machine Learning · Computer Science 2023-09-26 Samuel Pfrommer , Brendon G. Anderson , Somayeh Sojoudi

Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not…

Machine Learning · Computer Science 2020-06-09 Jamie Hayes

It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to…

Machine Learning · Computer Science 2019-12-23 Jinyuan Jia , Xiaoyu Cao , Binghui Wang , Neil Zhenqiang Gong

Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that…

Machine Learning · Computer Science 2022-06-06 Raphael Ettedgui , Alexandre Araujo , Rafael Pinot , Yann Chevaleyre , Jamal Atif

Randomized smoothing is a technique for providing provable robustness guarantees against adversarial attacks while making minimal assumptions about a classifier. This method relies on taking a majority vote of any base classifier over…

Machine Learning · Computer Science 2023-05-09 Ambar Pal , Jeremias Sulam

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…

Machine Learning · Computer Science 2022-12-21 Jongheon Jeong , Seojin Kim , Jinwoo Shin

Randomized smoothing is a general technique for computing sample-dependent robustness guarantees against adversarial attacks for deep classifiers. Prior works on randomized smoothing against L_1 adversarial attacks use additive smoothing…

Machine Learning · Computer Science 2021-06-14 Alexander Levine , Soheil Feizi

A reliable application of deep neural network classifiers requires robustness certificates against adversarial perturbations. Gaussian smoothing is a widely analyzed approach to certifying robustness against norm-bounded perturbations,…

Machine Learning · Computer Science 2024-09-23 Hossein Goli , Farzan Farnia

Randomized smoothing has emerged as a potent certifiable defense against adversarial attacks by employing smoothing noises from specific distributions to ensure the robustness of a smoothed classifier. However, the utilization of Monte…

Machine Learning · Computer Science 2025-04-01 Devansh Bhardwaj , Kshitiz Kaushik , Sarthak Gupta

Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for…

Machine Learning · Computer Science 2020-10-21 Dinghuai Zhang , Mao Ye , Chengyue Gong , Zhanxing Zhu , Qiang Liu

As ML models are increasingly deployed in critical applications, robustness against adversarial perturbations is crucial. While numerous defenses have been proposed to counter such attacks, they typically assume that all adversarial…

Machine Learning · Computer Science 2025-06-11 Yuan Xin , Dingfan Chen , Michael Backes , Xiao Zhang

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded…

Machine Learning · Statistics 2020-02-19 Huijie Feng , Chunpeng Wu , Guoyang Chen , Weifeng Zhang , Yang Ning

Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably…

Machine Learning · Computer Science 2024-11-12 Yan Scholten , Jan Schuchardt , Aleksandar Bojchevski , Stephan Günnemann

Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the…

Machine Learning · Computer Science 2021-11-18 Jongheon Jeong , Sejun Park , Minkyu Kim , Heung-Chang Lee , Doguk Kim , Jinwoo Shin

A recent technique of randomized smoothing has shown that the worst-case (adversarial) $\ell_2$-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged…

Machine Learning · Computer Science 2021-01-11 Jongheon Jeong , Jinwoo Shin

The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…

Machine Learning · Computer Science 2022-01-13 Aounon Kumar , Tom Goldstein
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