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.