While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are often followed by new attacks to defeat them. In this paper, we propose attack-agnostic robustness certificates for a multi-label classification problem using a deep ReLU network. Although computing the exact distance of a given input sample to the classification decision boundary requires solving a non-convex optimization, we characterize two lower bounds for such distances, namely the simplex certificate and the decision boundary certificate. These robustness certificates leverage the piece-wise linear structure of ReLU networks and use the fact that in a polyhedron around a given sample, the prediction function is linear. In particular, the proposed simplex certificate has a closed-form, is differentiable and is an order of magnitude faster to compute than the existing methods even for deep networks. In addition to theoretical bounds, we provide numerical results for our certificates over MNIST and compare them with some existing upper bounds.
The adversarial attacks and defenses have received significant attention from the machine learning community in the last couple of years @cite_9 @cite_18 @cite_53 @cite_49 @cite_11 @cite_17 @cite_56 @cite_28 @cite_21 @cite_37 @cite_52 @cite_26 @cite_47 @cite_13 @cite_24 @cite_12 . A wide range of defenses have been proposed to harden neural networks against adversarial attacks. However, a pattern has emerged in which the majority of adversarial defenses are broken by new attacks. For example, @cite_55 , @cite_49 , @cite_11 , @cite_18 broke several of these proposed defenses.
@cite_18 @cite_37 @cite_26 @cite_28 @cite_9 @cite_53 @cite_21 @cite_17 @cite_52 @cite_56 @cite_24 @cite_55 @cite_49 @cite_47 @cite_13 @cite_12 @cite_11
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Neural networks provide state-of-the-art results for most machine learning tasks. Unfortunately, neural networks are vulnerable to adversarial examples: given an input x and any target classification t, it is possible to find a new input x' that is similar to x but classified as t. This makes it difficult to apply neural networks in security-critical areas. Defensive distillation is a recently proposed approach that can take an arbitrary neural network, and increase its robustness, reducing the success rate of current attacks' ability to find adversarial examples from 95 to 0.5 .In this paper, we demonstrate that defensive distillation does not significantly increase the robustness of neural networks by introducing three new attack algorithms that are successful on both distilled and undistilled neural networks with 100 probability. Our attacks are tailored to three distance metrics used previously in the literature, and when compared to previous adversarial example generation algorithms, our attacks are often much more effective (and never worse). Furthermore, we propose using high-confidence adversarial examples in a simple transferability test we show can also be used to break defensive distillation. We hope our attacks will be used as a benchmark in future defense attempts to create neural networks that resist adversarial examples. Adversarial examples that fool machine learning models, particularly deep neural networks, have been a topic of intense research interest, with attacks and defenses being developed in a tight back-and-forth. Most past defenses are best effort and have been shown to be vulnerable to sophisticated attacks. Recently a set of certified defenses have been introduced, which provide guarantees of robustness to norm-bounded attacks, but they either do not scale to large datasets or are limited in the types of models they can support. This paper presents the first certified defense that both scales to large networks and datasets (such as Google's Inception network for ImageNet) and applies broadly to arbitrary model types. Our defense, called PixelDP, is based on a novel connection between robustness against adversarial examples and differential privacy, a cryptographically-inspired formalism, that provides a rigorous, generic, and flexible foundation for defense. Machine learning (ML) models, e.g., deep neural networks (DNNs), are vulnerable to adversarial examples: malicious inputs modified to yield erroneous model outputs, while appearing unmodified to human observers. Potential attacks include having malicious content like malware identified as legitimate or controlling vehicle behavior. Yet, all existing adversarial example attacks require knowledge of either the model internals or its training data. We introduce the first practical demonstration of an attacker controlling a remotely hosted DNN with no such knowledge. Indeed, the only capability of our black-box adversary is to observe labels given by the DNN to chosen inputs. Our attack strategy consists in training a local model to substitute for the target DNN, using inputs synthetically generated by an adversary and labeled by the target DNN. We use the local substitute to craft adversarial examples, and find that they are misclassified by the targeted DNN. To perform a real-world and properly-blinded evaluation, we attack a DNN hosted by MetaMind, an online deep learning API. We find that their DNN misclassifies 84.24 of the adversarial examples crafted with our substitute. We demonstrate the general applicability of our strategy to many ML techniques by conducting the same attack against models hosted by Amazon and Google, using logistic regression substitutes. They yield adversarial examples misclassified by Amazon and Google at rates of 96.19 and 88.94 . We also find that this black-box attack strategy is capable of evading defense strategies previously found to make adversarial example crafting harder. Machine learning (ML) models, e.g., deep neural networks (DNNs), are vulnerable to adversarial examples: malicious inputs modified to yield erroneous model outputs, while appearing unmodified to human observers. Potential attacks include having malicious content like malware identified as legitimate or controlling vehicle behavior. Yet, all existing adversarial example attacks require knowledge of either the model internals or its training data. We introduce the first practical demonstration of an attacker controlling a remotely hosted DNN with no such knowledge. Indeed, the only capability of our black-box adversary is to observe labels given by the DNN to chosen inputs. Our attack strategy consists in training a local model to substitute for the target DNN, using inputs synthetically generated by an adversary and labeled by the target DNN. We use the local substitute to craft adversarial examples, and find that they are misclassified by the targeted DNN. To perform a real-world and properly-blinded evaluation, we attack a DNN hosted by MetaMind, an online deep learning API. We find that their DNN misclassifies 84.24 of the adversarial examples crafted with our substitute. We demonstrate the general applicability of our strategy to many ML techniques by conducting the same attack against models hosted by Amazon and Google, using logistic regression substitutes. They yield adversarial examples misclassified by Amazon and Google at rates of 96.19 and 88.94 . We also find that this black-box attack strategy is capable of evading defense strategies previously found to make adversarial example crafting harder. 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). Neural networks provide state-of-the-art results for most machine learning tasks. Unfortunately, neural networks are vulnerable to adversarial examples: given an input @math and any target classification @math , it is possible to find a new input @math that is similar to @math but classified as @math . This makes it difficult to apply neural networks in security-critical areas. Defensive distillation is a recently proposed approach that can take an arbitrary neural network, and increase its robustness, reducing the success rate of current attacks' ability to find adversarial examples from @math to @math . In this paper, we demonstrate that defensive distillation does not significantly increase the robustness of neural networks by introducing three new attack algorithms that are successful on both distilled and undistilled neural networks with @math probability. Our attacks are tailored to three distance metrics used previously in the literature, and when compared to previous adversarial example generation algorithms, our attacks are often much more effective (and never worse). Furthermore, we propose using high-confidence adversarial examples in a simple transferability test we show can also be used to break defensive distillation. We hope our attacks will be used as a benchmark in future defense attempts to create neural networks that resist adversarial examples. Deep neural networks are vulnerable to adversarial examples, even in the black-box setting, where the attacker is restricted solely to query access. Existing black-box approaches to generating adversarial examples typically require a significant number of queries, either for training a substitute network or performing gradient estimation. We introduce GenAttack, a gradient-free optimization technique that uses genetic algorithms for synthesizing adversarial examples in the black-box setting. Our experiments on different datasets (MNIST, CIFAR-10, and ImageNet) show that GenAttack can successfully generate visually imperceptible adversarial examples against state-of-the-art image recognition models with orders of magnitude fewer queries than previous approaches. Against MNIST and CIFAR-10 models, GenAttack required roughly 2,126 and 2,568 times fewer queries respectively, than ZOO, the prior state-of-the-art black-box attack. In order to scale up the attack to large-scale high-dimensional ImageNet models, we perform a series of optimizations that further improve the query efficiency of our attack leading to 237 times fewer queries against the Inception-v3 model than ZOO. Furthermore, we show that GenAttack can successfully attack some state-of-the-art ImageNet defenses, including ensemble adversarial training and non-differentiable or randomized input transformations. Our results suggest that evolutionary algorithms open up a promising area of research into effective black-box attacks. Recent research has revealed that the output of Deep Neural Networks (DNN) can be easily altered by adding relatively small perturbations to the input vector. In this paper, we analyze an attack in an extremely limited scenario where only one pixel can be modified. For that we propose a novel method for generating one-pixel adversarial perturbations based on differential evolution(DE). It requires less adversarial information(a black-box attack) and can fool more types of networks due to the inherent features of DE. The results show that 68.36 of the natural images in CIFAR-10 test dataset and 41.22 of the ImageNet (ILSVRC 2012) validation images can be perturbed to at least one target class by modifying just one pixel with 73.22 and 5.52 confidence on average. Thus, the proposed attack explores a different take on adversarial machine learning in an extreme limited scenario, showing that current DNNs are also vulnerable to such low dimension attacks. Besides, we also illustrate an important application of DE (or broadly speaking, evolutionary computation) in the domain of adversarial machine learning: creating tools that can effectively generate low-cost adversarial attacks against neural networks for evaluating robustness. Recent work has demonstrated that neural networks are vulnerable to adversarial examples, i.e., inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much of the prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against any adversary. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest the notion of security against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models. Advances in deep learning have led to the broad adoption of Deep Neural Networks (DNNs) to a range of important machine learning problems, e.g., guiding autonomous vehicles, speech recognition, malware detection. Yet, machine learning models, including DNNs, were shown to be vulnerable to adversarial samples-subtly (and often humanly indistinguishably) modified malicious inputs crafted to compromise the integrity of their outputs. Adversarial examples thus enable adversaries to manipulate system behaviors. Potential attacks include attempts to control the behavior of vehicles, have spam content identified as legitimate content, or have malware identified as legitimate software. Adversarial examples are known to transfer from one model to another, even if the second model has a different architecture or was trained on a different set. We introduce the first practical demonstration that this cross-model transfer phenomenon enables attackers to control a remotely hosted DNN with no access to the model, its parameters, or its training data. In our demonstration, we only assume that the adversary can observe outputs from the target DNN given inputs chosen by the adversary. We introduce the attack strategy of fitting a substitute model to the input-output pairs in this manner, then crafting adversarial examples based on this auxiliary model. We evaluate the approach on existing DNN datasets and real-world settings. In one experiment, we force a DNN supported by MetaMind (one of the online APIs for DNN classifiers) to mis-classify inputs at a rate of 84.24 . We conclude with experiments exploring why adversarial samples transfer between DNNs, and a discussion on the applicability of our attack when targeting machine learning algorithms distinct from DNNs. Ongoing research has proposed several methods to defend neural networks against adversarial examples, many of which researchers have shown to be ineffective. We ask whether a strong defense can be created by combining multiple (possibly weak) defenses. To answer this question, we study three defenses that follow this approach. Two of these are recently proposed defenses that intentionally combine components designed to work well together. A third defense combines three independent defenses. For all the components of these defenses and the combined defenses themselves, we show that an adaptive adversary can create adversarial examples successfully with low distortion. Thus, our work implies that ensemble of weak defenses is not sufficient to provide strong defense against adversarial examples. 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. Neural networks are known to be vulnerable to adversarial examples: inputs that are close to natural inputs but classified incorrectly. In order to better understand the space of adversarial examples, we survey ten recent proposals that are designed for detection and compare their efficacy. We show that all can be defeated by constructing new loss functions. We conclude that adversarial examples are significantly harder to detect than previously appreciated, and the properties believed to be intrinsic to adversarial examples are in fact not. Finally, we propose several simple guidelines for evaluating future proposed defenses. Neural networks are known to be vulnerable to adversarial examples: inputs that are close to natural inputs but classified incorrectly. In order to better understand the space of adversarial examples, we survey ten recent proposals that are designed for detection and compare their efficacy. We show that all can be defeated by constructing new loss functions. We conclude that adversarial examples are significantly harder to detect than previously appreciated, and the properties believed to be intrinsic to adversarial examples are in fact not. Finally, we propose several simple guidelines for evaluating future proposed defenses. Deep neural networks are vulnerable to adversarial examples, which poses security concerns on these algorithms due to the potentially severe consequences. Adversarial attacks serve as an important surrogate to evaluate the robustness of deep learning models before they are deployed. However, most of existing adversarial attacks can only fool a black-box model with a low success rate. To address this issue, we propose a broad class of momentum-based iterative algorithms to boost adversarial attacks. By integrating the momentum term into the iterative process for attacks, our methods can stabilize update directions and escape from poor local maxima during the iterations, resulting in more transferable adversarial examples. To further improve the success rates for black-box attacks, we apply momentum iterative algorithms to an ensemble of models, and show that the adversarially trained models with a strong defense ability are also vulnerable to our black-box attacks. We hope that the proposed methods will serve as a benchmark for evaluating the robustness of various deep models and defense methods. With this method, we won the first places in NIPS 2017 Non-targeted Adversarial Attack and Targeted Adversarial Attack competitions. Due to deep cascades of nonlinear units, deep neural networks (DNNs) can automatically learn non-local generalization priors from data and have achieved high performance in various applications. However, such properties have also opened a door for adversaries to generate the so-called adversarial examples to fool DNNs. Specifically, adversaries can inject small perturbations to the input data and therefore decrease the performance of deep neural networks significantly. Even worse, these adversarial examples have the transferability to attack a black-box model based on finite queries without knowledge of the target model. Therefore, we aim to empirically compare different defensive strategies against various adversary models and analyze the cross-model efficiency for these robust learners. We conclude that the adversarial retraining framework also has the transferability, which can defend adversarial examples without requiring prior knowledge of the adversary models. We compare the general adversarial retraining framework with the state-of-the-art robust deep neural networks, such as distillation, autoencoder stacked with classifier (AEC), and our improved version, IAEC, to evaluate their robustness as well as the vulnerability in terms of the distortion required to mislead the learner. Our experimental results show that the adversarial retraining framework can defend most of the adversarial examples notably and consistently without adding additional vulnerabilities or performance penalty to the original model. Deep neural networks are vulnerable to adversarial examples, which poses security concerns on these algorithms due to the potentially severe consequences. Adversarial attacks serve as an important surrogate to evaluate the robustness of deep learning models before they are deployed. However, most of the existing adversarial attacks can only fool a black-box model with a low success rate because of the coupling of the attack ability and the transferability. To address this issue, we propose a broad class of momentum-based iterative algorithms to boost adversarial attacks. By integrating the momentum term into the iterative process for attacks, our methods can stabilize update directions and escape from poor local maxima during the iterations, resulting in more transferable adversarial examples. To further improve the success rates for black-box attacks, we apply momentum iterative algorithms to an ensemble of models, and show that the adversarially trained models with a strong defense ability are also vulnerable to our black-box attacks. We hope that the proposed methods will serve as a benchmark for evaluating the robustness of various deep models and defense methods. We won the first places in NIPS 2017 Non-targeted Adversarial Attack and Targeted Adversarial Attack competitions.