ﻻ يوجد ملخص باللغة العربية
Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a textit{semi-random} noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifiers decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.
The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of clas
We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $ell_p$ ball for $p in [1, infty]$ and Gaussian noise with an arbitrary covariance matrix. We characterize this
This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of statistical l
A convolutional neural network strongly robust to adversarial perturbations at reasonable computational and performance cost has not yet been demonstrated. The primate visual ventral stream seems to be robust to small perturbations in visual stimuli
Deep neural networks (DNNs) show promise in breast cancer screening, but their robustness to input perturbations must be better understood before they can be clinically implemented. There exists extensive literature on this subject in the context of