Recent advances in machine learning (ML) algorithms, especially deep neural networks (DNNs), have demonstrated remarkable success (sometimes exceeding human-level performance) on several tasks, including face and speech recognition. However, ML algorithms are vulnerable to \emph{adversarial attacks}, such test-time, training-time, and backdoor attacks. In test-time attacks an adversary crafts adversarial examples, which are specially crafted perturbations imperceptible to humans which, when added to an input example, force a machine learning model to misclassify the given input example. Adversarial examples are a concern when deploying ML algorithms in critical contexts, such as information security and autonomous driving. Researchers have responded with a plethora of defenses. One promising defense is \emph{randomized smoothing} in which a classifier's prediction is smoothed by adding random noise to the input example we wish to classify. In this paper, we theoretically and empirically explore randomized smoothing. We investigate the effect of randomized smoothing on the feasible hypotheses space, and show that for some noise levels the set of hypotheses which are feasible shrinks due to smoothing, giving one reason why the natural accuracy drops after smoothing. To perform our analysis, we introduce a model for randomized smoothing which abstracts away specifics, such as the exact distribution of the noise. We complement our theoretical results with extensive experiments.
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…
Randomized smoothing is a popular way of providing robustness guarantees against adversarial attacks: randomly-smoothed functions have a universal Lipschitz-like bound, allowing for robustness certificates to be easily computed. In this work, we show that there also exists a universal curvature-like bound for Gaussian random smoothing: given the exact value and gradient of a smoothed function, we compute a lower bound on the distance of a point to its closest adversarial example, called the Second-order Smoothing (SoS) robustness certificate. In addition to proving the correctness of this nove…
MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural networks or devising worst-case analytical robustness verification with guarantees, few methods could enjoy both scalability and robustness guarantees at the same time. As an alternative to these attempts, randomized smoothing adopts a different prediction rule that enables statistical robustness arguments which easily scale to large networks. However, in t…
In recent years, Deep Neural Networks (DNNs) have had a dramatic impact on a variety of problems that were long considered very difficult, e. g., image classification and automatic language translation to name just a few. The accuracy of modern DNNs in classification tasks is remarkable indeed. At the same time, attackers have devised powerful methods to construct specially-crafted malicious inputs (often referred to as adversarial examples) that can trick DNNs into mis-classifying them. What is worse is that despite the many defense mechanisms proposed to protect DNNs against adversarial atta…
The safety and robustness of learning-based decision-making systems are under threats from adversarial examples, as imperceptible perturbations can mislead neural networks to completely different outputs. In this paper, we present an adaptive view of the issue via evaluating various test-time smoothing defense against white-box untargeted adversarial examples. Through controlled experiments with pretrained ResNet-152 on ImageNet, we first illustrate the non-monotonic relation between adversarial attacks and smoothing defenses. Then at the dataset level, we observe large variance among samples …
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…
Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$; however, substantial effort was needed to derive such new guarantees. This begs the question: can we find a general theory for randomized smoothing? We propose a novel framework for devising and analyzing randomized smoothing schemes, and validate its effectiveness in practice. Our theoretical contributions are: (1) we show that for an appropriate notion of "opti…
MIT（麻省理工学院）；MIT-IBM Watson AI Lab, IBM Research（麻省理工学院-IBM Watson人工智能实验室，IBM研究）
Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved SOTA provable robustness against $\ell_2$ perturbations. A number of publications have extended the guarantees to other metrics, such as $\ell_1$ or $\ell_\infty$, by using different smoothing measures. Although the current framework has been shown to yield near-optimal $\ell_p$ radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers…
Mila（米拉）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Peking University（北京大学）
Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for $\ell_2$ perturbation. We propose a general framework of adversarial certification with non-Gaussian noise and for more general types of attacks, from a unified functional optimization perspective. Our new framework allows us to identify a key trade-off between accuracy and robustness via designing smoothing distributions, helping to design new families of n…
Patch adversarial attacks on images, in which the attacker can distort pixels within a region of bounded size, are an important threat model since they provide a quantitative model for physical adversarial attacks. In this paper, we introduce a certifiable defense against patch attacks that guarantees for a given image and patch attack size, no patch adversarial examples exist. Our method is related to the broad class of randomized smoothing robustness schemes which provide high-confidence probabilistic robustness certificates. By exploiting the fact that patch attacks are more constrained tha…
We present a method for provably defending any pretrained image classifier against $\ell_p$ adversarial attacks. This method, for instance, allows public vision API providers and users to seamlessly convert pretrained non-robust classification services into provably robust ones. By prepending a custom-trained denoiser to any off-the-shelf image classifier and using randomized smoothing, we effectively create a new classifier that is guaranteed to be $\ell_p$-robust to adversarial examples, without modifying the pretrained classifier. Our approach applies to both the white-box and the black-box…
PSL, Université Paris-Dauphine, Miles Team（PSL，巴黎 Dauphine 大学，Miles 团队）；Wavestone；Facebook AI Research（Facebook 人工智能研究）；CEA, Université Paris-Saclay（法国原子能委员会，巴黎萨克雷大学）
This paper tackles the problem of defending a neural network against adversarial attacks crafted with different norms (in particular $\ell_\infty$ and $\ell_2$ bounded adversarial examples). It has been observed that defense mechanisms designed to protect against one type of attacks often offer poor performance against the other. We show that $\ell_\infty$ defense mechanisms cannot offer good protection against $\ell_2$ attacks and vice-versa, and we provide both theoretical and empirical insights on this phenomenon. Then, we discuss various ways of combining existing defense mechanisms in ord…
Microsoft Corporation（微软公司）；Stanford University（斯坦福大学）
Adversarial perturbations dramatically decrease the accuracy of state-of-the-art image classifiers. In this paper, we propose and analyze a simple and computationally efficient defense strategy: inject random Gaussian noise, discretize each pixel, and then feed the result into any pre-trained classifier. Theoretically, we show that our randomized discretization strategy reduces the KL divergence between original and adversarial inputs, leading to a lower bound on the classification accuracy of any classifier against any (potentially whitebox) $\ell_\infty$-bounded adversarial attack. Empirical…
Randomized smoothing is a recent and celebrated solution to certify the robustness of any classifier. While it indeed provides a theoretical robustness against adversarial attacks, the dimensionality of current classifiers necessarily imposes Monte Carlo approaches for its application in practice. This paper questions the effectiveness of randomized smoothing as a defense, against state of the art black-box attacks. This is a novel perspective, as previous research works considered the certification as an unquestionable guarantee. We first formally highlight the mismatch between a theoretical …
University of Toronto（多伦多大学）；State University of New York at Buffalo（纽约州立大学布法罗分校）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
As a certified defensive technique, randomized smoothing has received considerable attention due to its scalability to large datasets and neural networks. However, several important questions remain unanswered, such as (i) whether the Gaussian mechanism is an appropriate option for certifying $\ell_2$-norm robustness, and (ii) whether there is an appropriate randomized (smoothing) mechanism to certify $\ell_\infty$-norm robustness. To shed light on these questions, we argue that the main difficulty is how to assess the appropriateness of each randomized mechanism. In this paper, we propose a g…
Randomized smoothing is a general technique for computing sample-dependent robustness guarantees against adversarial attacks for deep classifiers. Prior works on randomized smoothing against L_1 adversarial attacks use additive smoothing noise and provide probabilistic robustness guarantees. In this work, we propose a non-additive and deterministic smoothing method, Deterministic Smoothing with Splitting Noise (DSSN). To develop DSSN, we first develop SSN, a randomized method which involves generating each noisy smoothing sample by first randomly splitting the input space and then returning a …
School of Computation, Information & Technology, Technical Univ. of Munich（慕尼黑工业大学计算、信息与技术学院）；Fraunhofer Institute for Cognitive Systems IKS（弗劳恩霍夫认知系统研究所IKS）
Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on. However, it has remained unclear as to whether there are conditions under which no better attacks or defenses can be proposed. In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium. Under a locally linear decision boundary model for the underlying binary classifier, we prove that the Fast Gradient M…
Adversarial training is one of the strongest defenses against adversarial attacks, but it requires adversarial examples to be generated for every mini-batch during optimization. The expense of producing these examples during training often precludes adversarial training from use on complex image datasets. In this study, we explore the mechanisms by which adversarial training improves classifier robustness, and show that these mechanisms can be effectively mimicked using simple regularization methods, including label smoothing and logit squeezing. Remarkably, using these simple regularization m…
Despite the vulnerability of object detectors to adversarial attacks, very few defenses are known to date. While adversarial training can improve the empirical robustness of image classifiers, a direct extension to object detection is very expensive. This work is motivated by recent progress on certified classification by randomized smoothing. We start by presenting a reduction from object detection to a regression problem. Then, to enable certified regression, where standard mean smoothing fails, we propose median smoothing, which is of independent interest. We obtain the first model-agnostic…
National Technical University of Athens（希腊雅典国家技术大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CSX-AI（CSX-AI公司）；Carl von Ossietzky University of Oldenburg（奥尔登堡卡尔·冯·奥西特齐大学）；Chalmers University of Technology（查尔姆斯理工大学）
DNNs are known to be vulnerable to so-called adversarial attacks that manipulate inputs to cause incorrect results that can be beneficial to an attacker or damaging to the victim. Recent works have proposed approximate computation as a defense mechanism against machine learning attacks. We show that these approaches, while successful for a range of inputs, are insufficient to address stronger, high-confidence adversarial attacks. To address this, we propose DNNSHIELD, a hardware-accelerated defense that adapts the strength of the response to the confidence of the adversarial input. Our approac…
Recently, techniques have been developed to provably guarantee the robustness of a classifier to adversarial perturbations of bounded L_1 and L_2 magnitudes by using randomized smoothing: the robust classification is a consensus of base classifications on randomly noised samples where the noise is additive. In this paper, we extend this technique to the L_0 threat model. We propose an efficient and certifiably robust defense against sparse adversarial attacks by randomly ablating input features, rather than using additive noise. Experimentally, on MNIST, we can certify the classifications of o…
Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ adversarial training to improve the performance of randomized smoothing. We design an adapted attack for smoothed classifiers, and we show how this attack can be used in an adversarial training setting to boost the provable robustness of smoothed classifiers. We demonstrate through extensive experimentation that our method consistently outperforms all existing provabl…
It is becoming increasingly imperative to design robust ML defenses. However, recent work has found that many defenses that initially resist state-of-the-art attacks can be broken by an adaptive adversary. In this work we take steps to simplify the design of defenses and argue that white-box defenses should eschew randomness when possible. We begin by illustrating a new issue with the deployment of randomized defenses that reduces their security compared to their deterministic counterparts. We then provide evidence that making defenses deterministic simplifies robustness evaluation, without re…
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…
Université Paris-Dauphine, PSL Research University（巴黎多芬大学，PSL研究大学）；CNRS（法国国家科学研究中心）；Institut LIST, CEA（法国原子能与替代能源委员会列表研究所）；Université Paris-Saclay（巴黎萨克雷大学）
Is there a classifier that ensures optimal robustness against all adversarial attacks? This paper answers this question by adopting a game-theoretic point of view. We show that adversarial attacks and defenses form an infinite zero-sum game where classical results (e.g. Sion theorem) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by…
USC Ming Hsieh Department of Electrical and Computer Engineering（南加州大学明谢电子与计算机工程系）
A variety of recent works have looked into defenses for deep neural networks against adversarial attacks particularly within the image processing domain. Speech processing applications such as automatic speech recognition (ASR) are increasingly relying on deep learning models, and so are also prone to adversarial attacks. However, many of the defenses explored for ASR simply adapt the image-domain defenses, which may not provide optimal robustness. This paper explores speech specific defenses using the mel spectral domain, and introduces a novel defense method called 'mel domain noise flooding…
Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation over Transformation (EOT) attack. We investigate the effect of the adversarial attacks using proxy gradients on randomized neural networks and demonstrate that it highly relies on the directional distribution of the loss gradients of the randomized neural network. We show in particular that proxy gradients are less effective when the gradients are more scattere…
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not constrained by the size of the classifier's architecture. Here, we extend the work of Li et al. \cite{li2018second}, studying how the choice of divergence between smoothing measures affects the final robustness guarantee, and how the choice of smoothing measure itself can lead to guarantees in differing threat models. To this end, we develop a method to certify ro…
National Taiwan University（台湾大学）；The Chinese University of Hong Kong（香港中文大学）
Various forefront countermeasure methods for automatic speaker verification (ASV) with considerable performance in anti-spoofing are proposed in the ASVspoof 2019 challenge. However, previous work has shown that countermeasure models are vulnerable to adversarial examples indistinguishable from natural data. A good countermeasure model should not only be robust against spoofing audio, including synthetic, converted, and replayed audios; but counteract deliberately generated examples by malicious adversaries. In this work, we introduce a passive defense method, spatial smoothing, and a proactiv…
Fudan University（复旦大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Despite neural networks have achieved prominent performance on many natural language processing (NLP) tasks, they are vulnerable to adversarial examples. In this paper, we propose Dirichlet Neighborhood Ensemble (DNE), a randomized smoothing method for training a robust model to defense substitution-based attacks. During training, DNE forms virtual sentences by sampling embedding vectors for each word in an input sentence from a convex hull spanned by the word and its synonyms, and it augments them with the training data. In such a way, the model is robust to adversarial attacks while maintain…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured outputs like sets, images, language, etc. We model the output space as a metric space under a distance/similarity function, such as intersection-over-union, perceptual similarity, total variation distance, etc. Such models are used in many machine learning problems like image segmentation, object detection, generative models, image/audio-to-text systems, etc. B…
