Many studies have been done to prove the vulnerability of neural networks to adversarial example. A trained and well-behaved model can be fooled by a visually imperceptible perturbation, i.e., an originally correctly classified image could be misclassified after a slight perturbation. In this paper, we propose a black-box strategy to attack such networks using an evolution algorithm. First, we formalize the generation of an adversarial example into the optimization problem of perturbations that represent the noise added to an original image at each pixel. To solve this optimization problem in a black-box way, we find that an evolution algorithm perfectly meets our requirement since it can work without any gradient information. Therefore, we test various evolution algorithms, including a simple genetic algorithm, a parameter-exploring policy gradient, an OpenAI evolution strategy, and a covariance matrix adaptive evolution strategy. Experimental results show that a covariance matrix adaptive evolution Strategy performs best in this optimization problem. Additionally, we also perform several experiments to explore the effect of different regularizations on improving the quality of an adversarial example.
Although DCNNs have been proven to be a powerful learning model, @cite_3 first found that a hardly perceptible perturbation would lead to misclassification of the trained Network. @cite_10 applied the FGS algorithm to generate an adversarial example and explained that the linear nature of DCNNs was responsible for its vulnerability:
@cite_10 @cite_3
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Previous theoretical work on deep learning and neural network optimization tend to focus on avoiding saddle points and local minima. However, the practical observation is that, at least in the case of the most successful Deep Convolutional Neural Networks (DCNNs), practitioners can always increase the network size to fit the training data (an extreme example would be [1]). The most successful DCNNs such as VGG and ResNets are best used with a degree of "overparametrization". In this work, we characterize with a mix of theory and experiments, the landscape of the empirical risk of overparametrized DCNNs. We first prove in the regression framework the existence of a large number of degenerate global minimizers with zero empirical error (modulo inconsistent equations). The argument that relies on the use of Bezout theorem is rigorous when the RELUs are replaced by a polynomial nonlinearity (which empirically works as well). As described in our Theory III [2] paper, the same minimizers are degenerate and thus very likely to be found by SGD that will furthermore select with higher probability the most robust zero-minimizer. We further experimentally explored and visualized the landscape of empirical risk of a DCNN on CIFAR-10 during the entire training process and especially the global minima. Finally, based on our theoretical and experimental results, we propose an intuitive model of the landscape of DCNN's empirical loss surface, which might not be as complicated as people commonly believe. In recent years, defending adversarial perturbations to natural examples in order to build robust machine learning models trained by deep neural networks (DNNs) has become an emerging research field in the conjunction of deep learning and security. In particular, MagNet consisting of an adversary detector and a data reformer is by far one of the strongest defenses in the black-box oblivious attack setting, where the attacker aims to craft transferable adversarial examples from an undefended DNN model to bypass an unknown defense module deployed on the same DNN model. Under this setting, MagNet can successfully defend a variety of attacks in DNNs, including the high-confidence adversarial examples generated by the Carlini and Wagner's attack based on the @math distortion metric. However, in this paper, under the same attack setting we show that adversarial examples crafted based on the @math distortion metric can easily bypass MagNet and mislead the target DNN image classifiers on MNIST and CIFAR-10. We also provide explanations on why the considered approach can yield adversarial examples with superior attack performance and conduct extensive experiments on variants of MagNet to verify its lack of robustness to @math distortion based attacks. Notably, our results substantially weaken the assumption of effective threat models on MagNet that require knowing the deployed defense technique when attacking DNNs (i.e., the gray-box attack setting). Recent work has shown deep neural networks (DNNs) to be highly susceptible to well-designed, small perturbations at the input layer, or so-called adversarial examples. Taking images as an example, such distortions are often imperceptible, but can result in 100 mis-classification for a state of the art DNN. We study the structure of adversarial examples and explore network topology, pre-processing and training strategies to improve the robustness of DNNs. We perform various experiments to assess the removability of adversarial examples by corrupting with additional noise and pre-processing with denoising autoencoders (DAEs). We find that DAEs can remove substantial amounts of the adversarial noise. How- ever, when stacking the DAE with the original DNN, the resulting network can again be attacked by new adversarial examples with even smaller distortion. As a solution, we propose Deep Contractive Network, a model with a new end-to-end training procedure that includes a smoothness penalty inspired by the contractive autoencoder (CAE). This increases the network robustness to adversarial examples, without a significant performance penalty. Recent development in the field of Deep Learning have exposed the underlying vulnerability of Deep Neural Network (DNN) against adversarial examples. In image classification, an adversarial example is a carefully modified image that is visually imperceptible to the original image but can cause DNN model to misclassify it. Training the network with Gaussian noise is an effective technique to perform model regularization, thus improving model robustness against input variation. Inspired by this classical method, we explore to utilize the regularization characteristic of noise injection to improve DNN's robustness against adversarial attack. In this work, we propose Parametric-Noise-Injection (PNI) which involves trainable Gaussian noise injection at each layer on either activation or weights through solving the min-max optimization problem, embedded with adversarial training. These parameters are trained explicitly to achieve improved robustness. To the best of our knowledge, this is the first work that uses trainable noise injection to improve network robustness against adversarial attacks, rather than manually configuring the injected noise level through cross-validation. The extensive results show that our proposed PNI technique effectively improves the robustness against a variety of powerful white-box and black-box attacks such as PGD, C & W, FGSM, transferable attack and ZOO attack. Last but not the least, PNI method improves both clean- and perturbed-data accuracy in comparison to the state-of-the-art defense methods, which outperforms current unbroken PGD defense by 1.1 and 6.8 on clean test data and perturbed test data respectively using Resnet-20 architecture.