State-of-the-art Deep Neural Networks can be easily fooled into providing incorrect high-confidence predictions for images with small amounts of adversarial noise. Does this expose a flaw with deep neural networks, or do we simply need a better way to estimate confidence? In this paper we consider the problem of accurately estimating predictive confidence. We formulate this problem as that of density modelling, and show how traditional methods such as softmax produce poor estimates. To address this issue, we propose a novel confidence measure based on density modelling approaches. We test these measures on images distorted by blur, JPEG compression, random noise and adversarial noise. Experiments show that our confidence measure consistently shows reduced confidence scores in the presence of such distortions - a property which softmax often lacks.
Modern neural network architectures are sensitive to adversarial examples @cite_11 . These are images produced by the addition of small perturbations to correctly classified samples. Generating adversarial examples to the classifier is one of the active areas of research in the Deep Learning Community. Goodfellow al @cite_12 presented a method to generate adversarial examples and also showed that retraining the network with these examples can be used for regularization. Nyugen al @cite_5 also strengthened the claim that networks can be fooled easily by generating . Moosavi al @cite_13 presented an effective and fast way of generating the perturbations required to misclassify any image. Moosavi al @cite_14 also show that there exists universal adversarial perturbations given a classifier, that can be applied to any image for misclassification . Researchers have also shown that results of face recognition algorithms can be tampered by wearing a specific design of eyeglass frames @cite_4 . Such examples present a challenge to the idea of using neural networks for commercial applications, since security could be easily compromised. These can be overcome (in principle) by using a good uncertainty estimate of predictions.
@cite_14 @cite_4 @cite_5 @cite_13 @cite_12 @cite_11
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Deep neural network-based classifiers are known to be vulnerable to adversarial examples that can fool them into misclassifying their input through the addition of small-magnitude perturbations. However, recent studies have demonstrated that such adversarial examples are not very effective in the physical world--they either completely fail to cause misclassification or only work in restricted cases where a relatively complex image is perturbed and printed on paper. In this paper we propose a new attack algorithm--Robust Physical Perturbations (RP2)-- that generates perturbations by taking images under different conditions into account. Our algorithm can create spatially-constrained perturbations that mimic vandalism or art to reduce the likelihood of detection by a casual observer. We show that adversarial examples generated by RP2 achieve high success rates under various conditions for real road sign recognition by using an evaluation methodology that captures physical world conditions. We physically realized and evaluated two attacks, one that causes a Stop sign to be misclassified as a Speed Limit sign in 100 of the testing conditions, and one that causes a Right Turn sign to be misclassified as either a Stop or Added Lane sign in 100 of the testing conditions. Neural networks have demonstrated considerable success in a wide variety of real-world problems. However, the presence of adversarial examples - slightly perturbed inputs that are misclassified with high confidence - limits our ability to guarantee performance for these networks in safety-critical applications. We demonstrate that, for networks that are piecewise affine (for example, deep networks with ReLU and maxpool units), proving no adversarial example exists - or finding the closest example if one does exist - can be naturally formulated as solving a mixed integer program. Solves for a fully-connected MNIST classifier with three hidden layers can be completed an order of magnitude faster than those of the best existing approach. To address the concern that adversarial examples are irrelevant because pixel-wise attacks are unlikely to happen in natural images, we search for adversaries over a natural class of perturbations written as convolutions with an adversarial blurring kernel. When searching over blurred images, we find that as opposed to pixelwise attacks, some misclassifications are impossible. Even more interestingly, a small fraction of input images are provably robust to blurs: every blurred version of the input is classified with the same, correct label. Recent studies show that the state-of-the-art deep neural networks (DNNs) are vulnerable to adversarial examples, resulting from small-magnitude perturbations added to the input. Given that that emerging physical systems are using DNNs in safety-critical situations, adversarial examples could mislead these systems and cause dangerous situations. Therefore, understanding adversarial examples in the physical world is an important step towards developing resilient learning algorithms. We propose a general attack algorithm, Robust Physical Perturbations (RP2), to generate robust visual adversarial perturbations under different physical conditions. Using the real-world case of road sign classification, we show that adversarial examples generated using RP2 achieve high targeted misclassification rates against standard-architecture road sign classifiers in the physical world under various environmental conditions, including viewpoints. Due to the current lack of a standardized testing method, we propose a two-stage evaluation methodology for robust physical adversarial examples consisting of lab and field tests. Using this methodology, we evaluate the efficacy of physical adversarial manipulations on real objects. With a perturbation in the form of only black and white stickers, we attack a real stop sign, causing targeted misclassification in 100 of the images obtained in lab settings, and in 84.8 of the captured video frames obtained on a moving vehicle (field test) for the target classifier. Recent studies show that the state-of-the-art deep neural networks (DNNs) are vulnerable to adversarial examples, resulting from small-magnitude perturbations added to the input. Given that that emerging physical systems are using DNNs in safety-critical situations, adversarial examples could mislead these systems and cause dangerous situations.Therefore, understanding adversarial examples in the physical world is an important step towards developing resilient learning algorithms. We propose a general attack algorithm,Robust Physical Perturbations (RP2), to generate robust visual adversarial perturbations under different physical conditions. Using the real-world case of road sign classification, we show that adversarial examples generated using RP2 achieve high targeted misclassification rates against standard-architecture road sign classifiers in the physical world under various environmental conditions, including viewpoints. Due to the current lack of a standardized testing method, we propose a two-stage evaluation methodology for robust physical adversarial examples consisting of lab and field tests. Using this methodology, we evaluate the efficacy of physical adversarial manipulations on real objects. Witha perturbation in the form of only black and white stickers,we attack a real stop sign, causing targeted misclassification in 100 of the images obtained in lab settings, and in 84.8 of the captured video frames obtained on a moving vehicle(field test) for the target classifier.