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.
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed recently in the literature, but existing guarantees are loose. We prove a tight robustness guarantee in $\ell_2$ norm for smoothing with Gaussian noise. We use randomized smoothing to obtain an ImageNet classifier with e.g. a certified top-1 accuracy of 49% under adversarial perturbations with $\ell_2$ norm less than 0.5 (=127/255). No certified defense has been…
Duke University（杜克大学）；University at Buffalo, SUNY（纽约州立大学布法罗分校）
The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning algorithm. Although a significant body of work on developing defensive models has been considered, most such models are heuristic and are often vulnerable to adaptive attacks. Defensive methods that provide theoretical robustness guarantees have been studied intensively, yet most fail to obtain non-trivial robustness when a large-scale model and data are prese…
Adversarial training is one of the most popular ways to learn robust models but is usually attack-dependent and time costly. In this paper, we propose the MACER algorithm, which learns robust models without using adversarial training but performs better than all existing provable l2-defenses. Recent work shows that randomized smoothing can be used to provide a certified l2 radius to smoothed classifiers, and our algorithm trains provably robust smoothed classifiers via MAximizing the CErtified Radius (MACER). The attack-free characteristic makes MACER faster to train and easier to optimize. In…
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
Machine learning algorithms are known to be susceptible to data poisoning attacks, where an adversary manipulates the training data to degrade performance of the resulting classifier. In this work, we present a unifying view of randomized smoothing over arbitrary functions, and we leverage this novel characterization to propose a new strategy for building classifiers that are pointwise-certifiably robust to general data poisoning attacks. As a specific instantiation, we utilize our framework to build linear classifiers that are robust to a strong variant of label flipping, where each test exam…
FairDP: Certified Fairness with Differential Privacy
New Jersey Institute of Technology（新泽西理工学院）；University of Virginia（弗吉尼亚大学）；Qatar Computing Research Institute (QCRI)（卡塔尔计算研究所）；University of Florida（佛罗里达大学）；University of Pennsylvania（宾夕法尼亚大学）
Adversarial training instances can severely distort a model's behavior. This work investigates certified regression defenses, which provide guaranteed limits on how much a regressor's prediction may change under a poisoning attack. Our key insight is that certified regression reduces to voting-based certified classification when using median as a model's primary decision function. Coupling our reduction with existing certified classifiers, we propose six new regressors provably-robust to poisoning attacks. To the extent of our knowledge, this is the first work that certifies the robustness of …
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
A recent technique of randomized smoothing has shown that the worst-case (adversarial) $\ell_2$-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged prediction over Gaussian noise. In this paradigm, one should rethink the notion of adversarial robustness in terms of generalization ability of a classifier under noisy observations. We found that the trade-off between accuracy and certified robustness of smoothed classifiers can be greatly controlled by simply regularizing the prediction consistency over noise. This…
University of Sydney（悉尼大学）；University of Science and Technology of China（中国科学技术大学）；Microsoft Research Asia（微软亚洲研究院）
Adversarial training can considerably robustify deep neural networks to resist adversarial attacks. However, some works suggested that adversarial training might comprise the privacy-preserving and generalization abilities. This paper establishes and quantifies the privacy-robustness trade-off and generalization-robustness trade-off in adversarial training from both theoretical and empirical aspects. We first define a notion, {\it robustified intensity} to measure the robustness of an adversarial training algorithm. This measure can be approximate empirically by an asymptotically consistent em…
Google Research（谷歌研究院）；Department of Computer Science, Rutgers University（罗格斯大学计算机科学系）；Department of Computer Science, Northwestern University（西北大学计算机科学系）
Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time. In this work we highlight the benefits of natural low rank representations that often exist for real data such as images, for training neural networks with certified robustness guarantees. Our first contribution is for certified robustness to perturbations measured in $\ell_2$ norm. We exploit low rank data representations to provide improved guarantees over state-of-the-art randomized smoothing-based approaches on standard benchmark datasets such as CIFAR-10 and C…
Université Paris-Dauphine, PSL Research University（巴黎第九大学，PSL研究大学）；Institut LIST, CEA（法国原子能与替代能源委员会LIST研究所）；Université Paris-Saclay（巴黎萨克雷大学）
This short note highlights some links between two lines of research within the emerging topic of trustworthy machine learning: differential privacy and robustness to adversarial examples. By abstracting the definitions of both notions, we show that they build upon the same theoretical ground and hence results obtained so far in one domain can be transferred to the other. More precisely, our analysis is based on two key elements: probabilistic mappings (also called randomized algorithms in the differential privacy community), and the Renyi divergence which subsumes a large family of divergences…
Adversarial Training (AT) is crucial for obtaining deep neural networks that are robust to adversarial attacks, yet recent works found that it could also make models more vulnerable to privacy attacks. In this work, we further reveal this unsettling property of AT by designing a novel privacy attack that is practically applicable to the privacy-sensitive Federated Learning (FL) systems. Using our method, the attacker can exploit AT models in the FL system to accurately reconstruct users' private training images even when the training batch size is large. Code is available at https://github.com…
Adversarial training was introduced as a way to improve the robustness of deep learning models to adversarial attacks. This training method improves robustness against adversarial attacks, but increases the models vulnerability to privacy attacks. In this work we demonstrate how model inversion attacks, extracting training data directly from the model, previously thought to be intractable become feasible when attacking a robustly trained model. The input space for a traditionally trained model is dominated by adversarial examples - data points that strongly activate a certain class but lack se…
Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning
Department of Electrical and Computer Engineering（电气与计算机工程系）；Georgia Institute of Technology（佐治亚理工学院）；Department of Mathematics（数学系）；Massachusetts Institute of Technology（麻省理工学院）
A streaming algorithm is said to be adversarially robust if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an adaptive adversary. We establish a connection between adversarial robustness of streaming algorithms and the notion of differential privacy. This connection allows us to design new adversarially robust streaming algorithms that outperform the current state-of-the-art constructions for many interesting regimes of parameters.
University of Maryland, College Park（马里兰大学帕克分校）；Cornell University（康奈尔大学）
Adversarial patch attacks are among one of the most practical threat models against real-world computer vision systems. This paper studies certified and empirical defenses against patch attacks. We begin with a set of experiments showing that most existing defenses, which work by pre-processing input images to mitigate adversarial patches, are easily broken by simple white-box adversaries. Motivated by this finding, we propose the first certified defense against patch attacks, and propose faster methods for its training. Furthermore, we experiment with different patch shapes for testing, obtai…
It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more relevant. In this work, we aim to derive certified robustness for top-$k$ predictions. In particular, our certified robustness is based on randomized smoothing, which turns any classifier to a new classifier via adding noise to an input example. We adopt randomized smoothing because…
To deflect adversarial attacks, a range of "certified" classifiers have been proposed. In addition to labeling an image, certified classifiers produce (when possible) a certificate guaranteeing that the input image is not an $\ell_p$-bounded adversarial example. We present a new attack that exploits not only the labelling function of a classifier, but also the certificate generator. The proposed method applies large perturbations that place images far from a class boundary while maintaining the imperceptibility property of adversarial examples. The proposed "Shadow Attack" causes certifiably r…
University of Tsukuba（筑波大学）；NEC Corporation（日本电气股份有限公司）
How can we make machine learning provably robust against adversarial examples in a scalable way? Since certified defense methods, which ensure $ε$-robust, consume huge resources, they can only achieve small degree of robustness in practice. Lipschitz margin training (LMT) is a scalable certified defense, but it can also only achieve small robustness due to over-regularization. How can we make certified defense more efficiently? We present LC-LMT, a light weight Lipschitz margin training which solves the above problem. Our method has the following properties; (a) efficient: it can achieve $ε$-r…
Machine learning models are vulnerable to adversarial attacks. One approach to addressing this vulnerability is certification, which focuses on models that are guaranteed to be robust for a given perturbation size. A drawback of recent certified models is that they are stochastic: they require multiple computationally expensive model evaluations with random noise added to a given input. In our work, we present a deterministic certification approach which results in a certifiably robust model. This approach is based on an equivalence between training with a particular regularized loss, and the …
State-of-the-art NLP models can often be fooled by human-unaware transformations such as synonymous word substitution. For security reasons, it is of critical importance to develop models with certified robustness that can provably guarantee that the prediction is can not be altered by any possible synonymous word substitution. In this work, we propose a certified robust method based on a new randomized smoothing technique, which constructs a stochastic ensemble by applying random word substitutions on the input sentences, and leverage the statistical properties of the ensemble to provably cer…
Shanghai Jiao Tong University（上海交通大学）；Hong Kong University of Science and Technology（香港科技大学）
The robustness of deep neural networks (DNNs) against adversarial example attacks has raised wide attention. For smoothed classifiers, we propose the worst-case adversarial loss over input distributions as a robustness certificate. Compared with previous certificates, our certificate better describes the empirical performance of the smoothed classifiers. By exploiting duality and the smoothness property, we provide an easy-to-compute upper bound as a surrogate for the certificate. We adopt a noisy adversarial learning procedure to minimize the surrogate loss to improve model robustness. We sho…
In the last couple of years, several adversarial attack methods based on different threat models have been proposed for the image classification problem. Most existing defenses consider additive threat models in which sample perturbations have bounded L_p norms. These defenses, however, can be vulnerable against adversarial attacks under non-additive threat models. An example of an attack method based on a non-additive threat model is the Wasserstein adversarial attack proposed by Wong et al. (2019), where the distance between an image and its adversarial example is determined by the Wasserste…
Graph classification has practical applications in diverse fields. Recent studies show that graph-based machine learning models are especially vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. By adding or deleting a small number of edges in the graph, adversaries could greatly change the graph label predicted by a graph classification model. In this work, we propose to build a smoothed graph classification model with certified robustness guarantee. We have proven that the resulting graph classification model would output the same prediction for a graph under $…
A Certified Unlearning Approach without Access to Source Data
Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA（加州大学河滨分校电子与计算机工程系）；Brookhaven National Laboratory, Upton, NY, USA（布鲁克海文国家实验室）
Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race between defenders who attempt to train robust networks and attackers who try to construct adversarial examples. One promise of ending the arms race is developing certified defenses, ones which are provably robust against all attackers in some family. These certified defenses are based on convex relaxations which construct an upper bound on the worst case loss over…
Thanks to recent advances in deep neural networks (DNNs), face recognition systems have become highly accurate in classifying a large number of face images. However, recent studies have found that DNNs could be vulnerable to adversarial examples, raising concerns about the robustness of such systems. Adversarial examples that are not restricted to small perturbations could be more serious since conventional certified defenses might be ineffective against them. To shed light on the vulnerability to such adversarial examples, we propose a flexible and efficient method for generating unrestricted…
Fudan University（复旦大学）；University College London（伦敦大学学院）
Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in the feature space that separates similar and dissimilar pairs of instances to guarantee their generalization ability. In this paper, we advocate imposing an adversarial margin in the input space so as to improve the generalization and robustness of metric learning algorithms. We first show that, the adversarial margin, defined as the distance between traini…
Bosch Center for Artificial Intelligence, Robert Bosch GmbH（罗伯特·博世有限公司博世人工智能中心）
Adversarial patches pose a realistic threat model for physical world attacks on autonomous systems via their perception component. Autonomous systems in safety-critical domains such as automated driving should thus contain a fail-safe fallback component that combines certifiable robustness against patches with efficient inference while maintaining high performance on clean inputs. We propose BagCert, a novel combination of model architecture and certification procedure that allows efficient certification. We derive a loss that enables end-to-end optimization of certified robustness against pat…
Training neural networks to be certifiably robust is critical to ensure their safety against adversarial attacks. However, it is currently very difficult to train a neural network that is both accurate and certifiably robust. In this work we take a step towards addressing this challenge. We prove that for every continuous function $f$, there exists a network $n$ such that: (i) $n$ approximates $f$ arbitrarily close, and (ii) simple interval bound propagation of a region $B$ through $n$ yields a result that is arbitrarily close to the optimal output of $f$ on $B$. Our result can be seen as a Un…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab, IBM Research（MIT-IBM沃森人工智能实验室，IBM研究院）
Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We develop a new regularizer that is both more efficient than existing certified defenses, requiring only one additional forward propagation through a network, and can be used to train networks with similar certified accuracy. Through experiments on MNIST and CIFAR-10 we demonstrate improvements in training speed and comparable certified accuracy compared to state-…
Center for Data Science, Peking University（北京大学数据科学中心）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；National School of Development, Peking University（北京大学国家发展研究院）；Beijing International Center for Mathematical Research（北京国际数学研究中心）；Institute for Artificial Inteligence, Peking University（北京大学人工智能研究所）
Randomized smoothing has achieved state-of-the-art certified robustness against $l_2$-norm adversarial attacks. However, it is not wholly resolved on how to find the optimal base classifier for randomized smoothing. In this work, we employ a Smoothed WEighted ENsembling (SWEEN) scheme to improve the performance of randomized smoothed classifiers. We show the ensembling generality that SWEEN can help achieve optimal certified robustness. Furthermore, theoretical analysis proves that the optimal SWEEN model can be obtained from training under mild assumptions. We also develop an adaptive predict…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz constant may indeed enable adversarially robust neural networks. However, the methods currently employed for computing it suffer from theoretical and practical limitations. We argue that addressing this shortcoming is a promising direction for future research into certified adversarial defenses.
Arizona State University（亚利桑那州立大学）；Stanford University（斯坦福大学）
We present a data-driven framework called generative adversarial privacy (GAP). Inspired by recent advancements in generative adversarial networks (GANs), GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrained minimax game between a privatizer and an adversary. We show that for appropriately chosen adversarial loss functions, GAP provides privacy guarantees against strong information-theoretic adversaries. We also evaluate GAP's performance on the GENKI face database.
Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in practice. In this work, we strike a better balance by considering a model that involves learning a representation while at the same time giving a precise generalization bound and a robustness certificate. We focus on the hypothesis class obtained by combining a sparsity-promoting encoder coupled with a linear classifier, and show an interesting interplay betw…
A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification output will provably remain unchanged. Exactly computing the robustness certificates for neural networks is difficult since it requires solving a non-convex optimization. In this paper, we provide computationally-efficient robustness certificates for neural networks with differentiable activation functions in two steps. First, we show that if the eigenvalues of…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Boston University（波士顿大学）
We propose a data-driven framework for optimizing privacy-preserving data release mechanisms to attain the information-theoretically optimal tradeoff between minimizing distortion of useful data and concealing specific sensitive information. Our approach employs adversarially-trained neural networks to implement randomized mechanisms and to perform a variational approximation of mutual information privacy. We validate our Privacy-Preserving Adversarial Networks (PPAN) framework via proof-of-concept experiments on discrete and continuous synthetic data, as well as the MNIST handwritten digits d…
