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Register a new userRobustness of classifiers: from adversarial to random noise
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Added by
Seyed-Mohsen Moosavi-Dezfooli
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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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.
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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 classifiers to adversarial perturbations, and show fundamental upper bounds on the robustness of classifiers. Specifically, we establish a general upper bound on the robustness of classifiers to adversarial perturbations, and then illustrate the obtained upper bound on the families of linear and quadratic classifiers. In both cases, our upper bound depends on a distinguishability measure that captures the notion of difficulty of the classification task. Our results for both classes imply that in tasks involving small distinguishability, no classifier in the considered set will be robust to adversarial perturbations, even if a good accuracy is achieved. Our theoretical framework moreover suggests that the phenomenon of adversarial instability is due to the low flexibility of classifiers, compared to the difficulty of the classification task (captured by the distinguishability). Moreover, we show the existence of a clear distinction between the robustness of a classifier to random noise and its robustness to adversarial perturbations. Specifically, the former is shown to be larger than the latter by a factor that is proportional to sqrt{d} (with d being the signal dimension) for linear classifiers. This result gives a theoretical explanation for the discrepancy between the two robustness properties in high dimensional problems, which was empirically observed in the context of neural networks. To the best of our knowledge, our results provide the first theoretical work that addresses the phenomenon of adversarial instability recently observed for deep networks. Our analysis is complemented by experimental results on controlled and real-world data.
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 robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.
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 learning theory and information theory. To this aim, we introduce a new notion of robustness for randomized classifiers, enforcing local Lipschitzness using probability metrics. Equipped with this definition, we make two new contributions. The first one consists in devising a new upper bound on the adversarial generalization gap of randomized classifiers. More precisely, we devise bounds on the generalization gap and the adversarial gap (emph{i.e.} the gap between the risk and the worst-case risk under attack) of randomized classifiers. The second contribution presents a yet simple but efficient noise injection method to design robust randomized classifiers. We show that our results are applicable to a wide range of machine learning models under mild hypotheses. We further corroborate our findings with experimental results using deep neural networks on standard image datasets, namely CIFAR-10 and CIFAR-100. All robust models we trained models can simultaneously achieve state-of-the-art accuracy (over $0.82$ clean accuracy on CIFAR-10) and enjoy emph{guaranteed} robust accuracy bounds ($0.45$ against $ell_2$ adversaries with magnitude $0.5$ on CIFAR-10).
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 but the underlying mechanisms that give rise to this robust perception are not understood. In this work, we investigate the role of two biologically plausible mechanisms in adversarial robustness. We demonstrate that the non-uniform sampling performed by the primate retina and the presence of multiple receptive fields with a range of receptive field sizes at each eccentricity improve the robustness of neural networks to small adversarial perturbations. We verify that these two mechanisms do not suffer from gradient obfuscation and study their contribution to adversarial robustness through ablation studies.
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 natural images that can potentially be built upon. However, it cannot be assumed that conclusions about robustness will transfer from natural images to mammogram images, due to significant differences between the two image modalities. In order to determine whether conclusions will transfer, we measure the sensitivity of a radiologist-level screening mammogram image classifier to four commonly studied input perturbations that natural image classifiers are sensitive to. We find that mammogram image classifiers are also sensitive to these perturbations, which suggests that we can build on the existing literature. We also perform a detailed analysis on the effects of low-pass filtering, and find that it degrades the visibility of clinically meaningful features called microcalcifications. Since low-pass filtering removes semantically meaningful information that is predictive of breast cancer, we argue that it is undesirable for mammogram image classifiers to be invariant to it. This is in contrast to natural images, where we do not want DNNs to be sensitive to low-pass filtering due to its tendency to remove information that is human-incomprehensible.
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