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Register a new userResidual Error: a New Performance Measure for Adversarial Robustness
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Added by
Hossein Aboutalebi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous predictions in the presence of adversarially perturbed data makes deep neural networks difficult to adopt for certain real-world, mission-critical applications. While much of the research focus has revolved around adversarial example creation and adversarial hardening, the area of performance measures for assessing adversarial robustness is not well explored. Motivated by this, this study presents the concept of residual error, a new performance measure for not only assessing the adversarial robustness of a deep neural network at the individual sample level, but also can be used to differentiate between adversarial and non-adversarial examples to facilitate for adversarial example detection. Furthermore, we introduce a hybrid model for approximating the residual error in a tractable manner. Experimental results using the case of image classification demonstrates the effectiveness and efficacy of the proposed residual error metric for assessing several well-known deep neural network architectures. These results thus illustrate that the proposed measure could be a useful tool for not only assessing the robustness of deep neural networks used in mission-critical scenarios, but also in the design of adversarially robust models.
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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.
Recent work has uncovered the interesting (and somewhat surprising) finding that training models to be invariant to adversarial perturbations requires substantially larger datasets than those required for standard classification. This result is a key hurdle in the deployment of robust machine learning models in many real world applications where labeled data is expensive. Our main insight is that unlabeled data can be a competitive alternative to labeled data for training adversarially robust models. Theoretically, we show that in a simple statistical setting, the sample complexity for learning an adversarially robust model from unlabeled data matches the fully supervised case up to constant factors. On standard datasets like CIFAR-10, a simple Unsupervised Adversarial Training (UAT) approach using unlabeled data improves robust accuracy by 21.7% over using 4K supervised examples alone, and captures over 95% of the improvement from the same number of labeled examples. Finally, we report an improvement of 4% over the previous state-of-the-art on CIFAR-10 against the strongest known attack by using additional unlabeled data from the uncurated 80 Million Tiny Images dataset. This demonstrates that our finding extends as well to the more realistic case where unlabeled data is also uncurated, therefore opening a new avenue for improving adversarial training.
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.
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.
Extensive Unsupervised Domain Adaptation (UDA) studies have shown great success in practice by learning transferable representations across a labeled source domain and an unlabeled target domain with deep models. However, previous works focus on improving the generalization ability of UDA models on clean examples without considering the adversarial robustness, which is crucial in real-world applications. Conventional adversarial training methods are not suitable for the adversarial robustness on the unlabeled target domain of UDA since they train models with adversarial examples generated by the supervised loss function. In this work, we leverage intermediate representations learned by multiple robust ImageNet models to improve the robustness of UDA models. Our method works by aligning the features of the UDA model with the robust features learned by ImageNet pre-trained models along with domain adaptation training. It utilizes both labeled and unlabeled domains and instills robustness without any adversarial intervention or label requirement during domain adaptation training. Experimental results show that our method significantly improves adversarial robustness compared to the baseline while keeping clean accuracy on various UDA benchmarks.
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