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Register a new userGradient-Free Adversarial Attacks for Bayesian Neural Networks
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Matthew Wicker
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable adversarial robustness properties. However, when approximate Bayesian inference methods are employed, the adversarial robustness of BNNs is still not well understood. In this work, we employ gradient-free optimization methods in order to find adversarial examples for BNNs. In particular, we consider genetic algorithms, surrogate models, as well as zeroth order optimization methods and adapt them to the goal of finding adversarial examples for BNNs. In an empirical evaluation on the MNIST and Fashion MNIST datasets, we show that for various approximate Bayesian inference methods the usage of gradient-free algorithms can greatly improve the rate of finding adversarial examples compared to state-of-the-art gradient-based methods.
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Deep neural networks (DNNs) are playing key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in DNNs, which are almost imperceptibly different from original samples, but can greatly change the network output. Existing white-box attack algorithms can generate powerful adversarial examples. Nevertheless, most of the algorithms concentrate on how to iteratively make the best use of gradients to improve adversarial performance. In contrast, in this paper, we focus on the properties of the widely-used ReLU activation function, and discover that there exist two phenomena (i.e., wrong blocking and over transmission) misleading the calculation of gradients in ReLU during the backpropagation. Both issues enlarge the difference between the predicted changes of the loss function from gradient and corresponding actual changes, and mislead the gradients which results in larger perturbations. Therefore, we propose a universal adversarial example generation method, called ADV-ReLU, to enhance the performance of gradient based white-box attack algorithms. During the backpropagation of the network, our approach calculates the gradient of the loss function versus network input, maps the values to scores, and selects a part of them to update the misleading gradients. Comprehensive experimental results on emph{ImageNet} demonstrate that our ADV-ReLU can be easily integrated into many state-of-the-art gradient-based white-box attack algorithms, as well as transferred to black-box attack attackers, to further decrease perturbations in the ${ell _2}$-norm.
Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.
Deep neural networks (DNN) are known to be vulnerable to adversarial attacks. Numerous efforts either try to patch weaknesses in trained models, or try to make it difficult or costly to compute adversarial examples that exploit them. In our work, we explore a new honeypot approach to protect DNN models. We intentionally inject trapdoors, honeypot weaknesses in the classification manifold that attract attackers searching for adversarial examples. Attackers optimization algorithms gravitate towards trapdoors, leading them to produce attacks similar to trapdoors in the feature space. Our defense then identifies attacks by comparing neuron activation signatures of inputs to those of trapdoors. In this paper, we introduce trapdoors and describe an implementation of a trapdoor-enabled defense. First, we analytically prove that trapdoors shape the computation of adversarial attacks so that attack inputs will have feature representations very similar to those of trapdoors. Second, we experimentally show that trapdoor-protected models can detect, with high accuracy, adversarial examples generated by state-of-the-art attacks (PGD, optimization-based CW, Elastic Net, BPDA), with negligible impact on normal classification. These results generalize across classification domains, including image, facial, and traffic-sign recognition. We also present significant results measuring trapdoors robustness against customized adaptive attacks (countermeasures).
Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks. The term undercomplete refers to the fact that their proof only holds when the number of neurons is a vanishing fraction of the ambient dimension. We extend their result to the overcomplete case, where the number of neurons is larger than the dimension (yet also subexponential in the dimension). In fact we prove that a single step of gradient descent suffices. We also show this result for any subexponential width random neural network with smooth activation function.
Decision-based attacks (DBA), wherein attackers perturb inputs to spoof learning algorithms by observing solely the output labels, are a type of severe adversarial attacks against Deep Neural Networks (DNNs) requiring minimal knowledge of attackers. State-of-the-art DBA attacks relying on zeroth-order gradient estimation require an excessive number of queries. Recently, Bayesian optimization (BO) has shown promising in reducing the number of queries in score-based attacks (SBA), in which attackers need to observe real-valued probability scores as outputs. However, extending BO to the setting of DBA is nontrivial because in DBA only output labels instead of real-valued scores, as needed by BO, are available to attackers. In this paper, we close this gap by proposing an efficient DBA attack, namely BO-DBA. Different from existing approaches, BO-DBA generates adversarial examples by searching so-called emph{directions of perturbations}. It then formulates the problem as a BO problem that minimizes the real-valued distortion of perturbations. With the optimized perturbation generation process, BO-DBA converges much faster than the state-of-the-art DBA techniques. Experimental results on pre-trained ImageNet classifiers show that BO-DBA converges within 200 queries while the state-of-the-art DBA techniques need over 15,000 queries to achieve the same level of perturbation distortion. BO-DBA also shows similar attack success rates even as compared to BO-based SBA attacks but with less distortion.
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