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Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defense mechanisms often fail, as new attacks constantly emerge, rendering existing defenses…

Machine Learning · Computer Science 2024-10-25 Anupriya Kumari , Devansh Bhardwaj , Sukrit Jindal

We consider the sound ranging, or source localization, problem - find the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points - in the proper metric spaces (any closed ball…

Functional Analysis · Mathematics 2021-03-16 Sergij V. Goncharov

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

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

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…

Numerical Analysis · Mathematics 2026-03-09 El-Mehdi El Arar , Massimiliano Fasi , Silviu-Ioan Filip , Mantas Mikaitis

The current state-of-the-art defense methods against adversarial examples typically focus on improving either empirical or certified robustness. Among them, adversarially trained (AT) models produce empirical state-of-the-art defense…

Machine Learning · Computer Science 2022-08-02 Jay Nandy , Sudipan Saha , Wynne Hsu , Mong Li Lee , Xiao Xiang Zhu

Adversarial data examples have drawn significant attention from the machine learning and security communities. A line of work on tackling adversarial examples is certified robustness via randomized smoothing that can provide a theoretical…

Machine Learning · Computer Science 2021-08-24 Haowen Lin , Jian Lou , Li Xiong , Cyrus Shahabi

We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…

Machine Learning · Computer Science 2025-04-29 Stanislav Semenov

We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…

Numerical Analysis · Mathematics 2016-04-08 Charles L. Epstein , Michael O'Neil

We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the $\ell_p$ ball of radius $\epsilon$ when $p>2$. Although random smoothing has been well understood for the $\ell_2$ case using…

Machine Learning · Computer Science 2020-03-06 Avrim Blum , Travis Dick , Naren Manoj , Hongyang Zhang

Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation…

Optimization and Control · Mathematics 2015-09-14 Shibdas Roy , Obaid Ur Rehman , Ian R. Petersen , Elanor H. Huntington

Sensitivity-based robustness certification has emerged as a practical approach for certifying neural network robustness, including in settings that require verifiable guarantees. A key advantage of these methods is that certification is…

Machine Learning · Computer Science 2026-03-26 Toby Murray

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

Numerical Analysis · Mathematics 2025-06-05 Dakang Cen , Wenlong Zhang , Junbin Zhong

We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…

Logic in Computer Science · Computer Science 2021-05-28 George Constantinides , Fredrik Dahlqvist , Zvonimir Rakamaric , Rocco Salvia

Smoothing is widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks…

Signal Processing · Electrical Eng. & Systems 2023-10-30 Keisuke Ozawa , Tomoya Itakura , Taisuke Ono

Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…

Probability · Mathematics 2009-03-10 Clément Dombry

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper…

Machine Learning · Computer Science 2025-04-10 Blaise Delattre , Paul Caillon , Quentin Barthélemy , Erwan Fagnou , Alexandre Allauzen

Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal…

Machine Learning · Computer Science 2026-05-14 Blaise Delattre , Hengyu Wu , Paul Caillon , Wei Yang Bryan Lim , Yang Cao

We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…

Optimization and Control · Mathematics 2025-12-19 El Mahdi Chayti , Taha El Bakkali El Kadi , Omar Saadi , Martin Jaggi

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