Deep CNNs are known to exhibit the following peculiarity: on the one hand they generalize extremely well to a test set, while on the other hand they are extremely sensitive to so-called adversarial perturbations. The extreme sensitivity of high performance CNNs to adversarial examples casts serious doubt that these networks are learning high level abstractions in the dataset. We are concerned with the following question: How can a deep CNN that does not learn any high level semantics of the dataset manage to generalize so well? The goal of this article is to measure the tendency of CNNs to learn surface statistical regularities of the dataset. To this end, we use Fourier filtering to construct datasets which share the exact same high level abstractions but exhibit qualitatively different surface statistical regularities. For the SVHN and CIFAR-10 datasets, we present two Fourier filtered variants: a low frequency variant and a randomly filtered variant. Each of the Fourier filtering schemes is tuned to preserve the recognizability of the objects. Our main finding is that CNNs exhibit a tendency to latch onto the Fourier image statistics of the training dataset, sometimes exhibiting up to a 28 generalization gap across the various test sets. Moreover, we observe that significantly increasing the depth of a network has a very marginal impact on closing the aforementioned generalization gap. Thus we provide quantitative evidence supporting the hypothesis that deep CNNs tend to learn surface statistical regularities in the dataset rather than higher-level abstract concepts.
As a response to these adversarial examples, there have been various attempts to increase the robustness of deep neural networks to adversarial perturbations. @cite_20 employed defensive-distillation. @cite_4 used so-called contractive networks. Moreover, @cite_4 posited that the core problem with adversarial examples emanates from the current training setup used in deep learning, rather than the network architecture. Along these lines, @cite_29 obtained promising results by modifying the training regime of SGD by forcing the convolutional layers to be approximate Parseval tight frames @cite_1 . This method led to state of the art performance on the CIFAR-10 100 as well as the SVHN dataset while also increasing the robustness of the network to adversarial examples. Similarly in @cite_17 the training loop is modified to improve robustness to adversarial examples. Specifically @cite_17 modifies SGD by rescaling the batch gradients and reports an increased robustness to adversarial examples for the MNIST and CIFAR-10 datasets, though the CIFAR-10 models suffer a non-trivial degradation in clean test accuracy.
@cite_4 @cite_29 @cite_1 @cite_20 @cite_17
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Recent work has developed methods for learning deep network classifiers that are robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this paper, in an effort to scale these approaches to substantially larger models, we extend previous work in three main directly. First, we present a technique for extending these training procedures to much more general networks, with skip connections (such as ResNets) and general nonlinearities; the approach is fully modular, and can be implemented automatically analogously to automatic differentiation. Second, in the specific case of l∞ adversarial perturbations and networks with ReLU nonlinearities, we adopt a nonlinear random projection for training, which scales in the number of hidden units (previous approached scaled quadratically). Third, we show how to further improve robust error through cascade models. On both MNIST and CIFAR data sets, we train classifiers that improve substantially on the state of the art in provable robust adversarial error bounds: from 5.8 to 3.1 on MNIST (with l∞ perturbations of ϵ=0.1), and from 80 to 36.4 on CIFAR (with l∞ perturbations of ϵ=2 255). It is well known that it is possible to construct "adversarial examples" for neural networks: inputs which are misclassified by the network yet indistinguishable from true data. We propose a simple modification to standard neural network architectures, thermometer encoding, which significantly increases the robustness of the network to adversarial examples. We demonstrate this robustness with experiments on the MNIST, CIFAR-10, CIFAR-100, and SVHN datasets, and show that models with thermometer-encoded inputs consistently have higher accuracy on adversarial examples, without decreasing generalization. State-of-the-art accuracy under the strongest known white-box attack was increased from 93.20 to 94.30 on MNIST and 50.00 to 79.16 on CIFAR-10. We explore the properties of these networks, providing evidence that thermometer encodings help neural networks to find more-non-linear decision boundaries. Deep neural networks are known to be vulnerable to adversarial examples, i.e., images that are maliciously perturbed to fool the model. Generating adversarial examples has been mostly limited to finding small perturbations that maximize the model prediction error. Such images, however, contain artificial perturbations that make them somewhat distinguishable from natural images. This property is used by several defense methods to counter adversarial examples by applying denoising filters or training the model to be robust to small perturbations. In this paper, we introduce a new class of adversarial examples, namely "Semantic Adversarial Examples," as images that are arbitrarily perturbed to fool the model, but in such a way that the modified image semantically represents the same object as the original image. We formulate the problem of generating such images as a constrained optimization problem and develop an adversarial transformation based on the shape bias property of human cognitive system. In our method, we generate adversarial images by first converting the RGB image into the HSV (Hue, Saturation and Value) color space and then randomly shifting the Hue and Saturation components, while keeping the Value component the same. Our experimental results on CIFAR10 dataset show that the accuracy of VGG16 network on adversarial color-shifted images is 5.7 . Deep neural networks are known to be vulnerable to adversarial examples, i.e., images that are maliciously perturbed to fool the model. Generating adversarial examples has been mostly limited to finding small perturbations that maximize the model prediction error. Such images, however, contain artificial perturbations that make them somewhat distinguishable from natural images. This property is used by several defense methods to counter adversarial examples by applying denoising filters or training the model to be robust to small perturbations. In this paper, we introduce a new class of adversarial examples, namely "Semantic Adversarial Examples," as images that are arbitrarily perturbed to fool the model, but in such a way that the modified image semantically represents the same object as the original image. We formulate the problem of generating such images as a constrained optimization problem and develop an adversarial transformation based on the shape bias property of human cognitive system. In our method, we generate adversarial images by first converting the RGB image into the HSV (Hue, Saturation and Value) color space and then randomly shifting the Hue and Saturation components, while keeping the Value component the same. Our experimental results on CIFAR10 dataset show that the accuracy of VGG16 network on adversarial color-shifted images is 5.7 .