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This paper presents novel methods for estimating certified radii in randomized smoothing, a technique crucial for certifying the robustness of neural networks against adversarial perturbations. Our proposed techniques significantly improve…

Machine Learning · Computer Science 2025-03-13 Zixuan Liang

Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems. It uses the probabilities of predicting the top two most-likely classes around an input point under a…

Machine Learning · Computer Science 2020-10-26 Aounon Kumar , Alexander Levine , Soheil Feizi , Tom Goldstein

One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a…

Machine Learning · Computer Science 2021-04-14 Xingjian Zhen , Rudrasis Chakraborty , Vikas Singh

Randomized smoothing (RS) has been shown to be a fast, scalable technique for certifying the robustness of deep neural network classifiers. However, methods based on RS require augmenting data with large amounts of noise, which leads to…

Machine Learning · Computer Science 2022-05-13 Ameya Joshi , Minh Pham , Minsu Cho , Leonid Boytsov , Filipe Condessa , J. Zico Kolter , Chinmay Hegde

Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…

Machine Learning · Computer Science 2024-04-29 Emmanouil Seferis , Stefanos Kollias , Chih-Hong Cheng

Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the norm used for…

Machine Learning · Computer Science 2022-07-06 Motasem Alfarra , Adel Bibi , Philip H. S. Torr , Bernard Ghanem

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 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

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 is a recently proposed defense against adversarial attacks that has achieved SOTA provable robustness against $\ell_2$ perturbations. A number of publications have extended the guarantees to other metrics, such as…

Machine Learning · Computer Science 2020-10-15 Jeet Mohapatra , Ching-Yun Ko , Tsui-Wei Weng , Pin-Yu Chen , Sijia Liu , Luca Daniel

As deep learning models continue to advance and are increasingly utilized in real-world systems, the issue of robustness remains a major challenge. Existing certified training methods produce models that achieve high provable robustness…

Machine Learning · Computer Science 2023-07-26 Zhakshylyk Nurlanov , Frank R. Schmidt , Florian Bernard

In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…

Machine Learning · Statistics 2018-05-21 Wenjie Huang

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…

Machine Learning · Computer Science 2024-03-19 Blaise Delattre , Alexandre Araujo , Quentin Barthélemy , Alexandre Allauzen

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 is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…

Machine Learning · Computer Science 2023-04-26 Václav Voráček , Matthias Hein

Randomized smoothing is the primary certified robustness method for accessing the robustness of deep learning models to adversarial perturbations in the l2-norm, by adding isotropic Gaussian noise to the input image and returning the…

Machine Learning · Computer Science 2024-04-09 Chengyan Fu , Wenjie Wang

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

Randomized smoothing-based certification is an effective approach for obtaining robustness certificates of deep neural networks (DNNs) against adversarial attacks. This method constructs a smoothed DNN model and certifies its robustness…

Machine Learning · Computer Science 2024-04-12 Shubham Ugare , Tarun Suresh , Debangshu Banerjee , Gagandeep Singh , Sasa Misailovic

Randomized Smoothing (RS) is a prominent technique for certifying the robustness of neural networks against adversarial perturbations. With RS, achieving high accuracy at small radii requires a small noise variance, while achieving high…

Machine Learning · Computer Science 2026-03-10 Chenhao Sun , Yuhao Mao , Martin Vechev

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

Machine Learning · Computer Science 2017-07-04 Jonas Moritz Kohler , Aurelien Lucchi
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