Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. Most existing approaches for crafting adversarial examples necessitate some knowledge (architecture, parameters, etc) of the network at hand. In this paper, we focus on image classifiers and propose a feature-guided black-box approach to test the safety of deep neural networks that requires no such knowledge. Our algorithm employs object detection techniques such as SIFT (Scale Invariant Feature Transform) to extract features from an image. These features are converted into a mutable saliency distribution, where high probability is assigned to pixels that affect the composition of the image with respect to the human visual system. We formulate the crafting of adversarial examples as a two-player turn-based stochastic game, where the first player's objective is to minimise the distance to an adversarial example by manipulating the features, and the second player can be cooperative, adversarial, or random. We show that, theoretically, the two-player game can converge to the optimal strategy, and that the optimal strategy represents a globally minimal adversarial image. For Lipschitz networks, we also identify conditions that provide safety guarantees that no adversarial examples exist. Using Monte Carlo tree search we gradually explore the game state space to search for adversarial examples. Our experiments show that, despite the black-box setting, manipulations guided by a perception-based saliency distribution are competitive with state-of-the-art methods that rely on white-box saliency matrices or sophisticated optimization procedures. Finally, we show how our method can be used to evaluate robustness of neural networks in safety-critical applications such as traffic sign recognition in self-driving cars.

Understanding the spatial arrangement and nature of real-world objects is of paramount importance to many complex engineering tasks, including autonomous navigation. Deep learning has revolutionized state-of-the-art performance for tasks in 3D environments; however, relatively little is known about the robustness of these approaches in an adversarial setting. The lack of comprehensive analysis makes it difficult to justify deployment of 3D deep learning models in real-world, safety-critical applications. In this work, we develop an algorithm for analysis of pointwise robustness of neural networks that operate on 3D data. We show that current approaches presented for understanding the resilience of state-of-the-art models vastly overestimate their robustness. We then use our algorithm to evaluate an array of state-of-the-art models in order to demonstrate their vulnerability to occlusion attacks. We show that, in the worst case, these networks can be reduced to 0% classification accuracy after the occlusion of at most 6.5% of the occupied input space.

Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. In this paper, we study two variants of pointwise robustness, the maximum safe radius problem, which for a given input sample computes the minimum distance to an adversarial example, and the feature robustness problem, which aims to quantify the robustness of individual features to adversarial perturbations. We demonstrate that, under the assumption of Lipschitz continuity, both problems can be approximated using finite optimisation by discretising the input space, and the approximation has provable guarantees, i.e., the error is bounded. We then show that the resulting optimisation problems can be reduced to the solution of two-player turn-based games, where the first player selects features and the second perturbs the image within the feature. While the second player aims to minimise the distance to an adversarial example, depending on the optimisation objective the first player can be cooperative or competitive. We employ an anytime approach to solve the games, in the sense of approximating the value of a game by monotonically improving its upper and lower bounds. The Monte Carlo tree search algorithm is applied to compute upper bounds for both games, and the Admissible A* and the Alpha-Beta Pruning algorithms are, respectively, used to compute lower bounds for the maximum safety radius and feature robustness games. When working on the upper bound of the maximum safe radius problem, our tool demonstrates competitive performance against existing adversarial example crafting algorithms. Furthermore, we show how our framework can be deployed to evaluate pointwise robustness of neural networks in safety-critical applications such as traffic sign recognition in self-driving cars. Figure 1: An adversarial example for a neural network trained on the GTSRB dataset. After a slight perturbation of Euclidean distance 0.88, the image classification changes from "go right or straight" to "go left or straight".

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We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.

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