Adversarial robustness of machine learning models has attracted considerable attention over recent years. Adversarial attacks undermine the reliability of and trust in machine learning models, but the construction of more robust models hinges on a rigorous understanding of adversarial robustness as a property of a given model. Point-wise measures for specific threat models are currently the most popular tool for comparing the robustness of classifiers and are used in most recent publications on adversarial robustness. In this work, we use recently proposed robustness curves to show that point-wise measures fail to capture important global properties that are essential to reliably compare the robustness of different classifiers. We introduce new ways in which robustness curves can be used to systematically uncover these properties and provide concrete recommendations for researchers and practitioners when assessing and comparing the robustness of trained models. Furthermore, we characterize scale as a way to distinguish small and large perturbations, and relate it to inherent properties of data sets, demonstrating that robustness thresholds must be chosen accordingly. We release code to reproduce all experiments presented in this paper, which includes a Python module to calculate robustness curves for arbitrary data sets and classifiers, supporting a number of frameworks, including TensorFlow, PyTorch and JAX.
Microsoft Research Cambridge（微软研究院剑桥分院）；University of Cambridge（剑桥大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Eberhard Karls University of Tübingen（图宾根大学）
There is a rising interest in studying the robustness of deep neural network classifiers against adversaries, with both advanced attack and defence techniques being actively developed. However, most recent work focuses on discriminative classifiers, which only model the conditional distribution of the labels given the inputs. In this paper, we propose and investigate the deep Bayes classifier, which improves classical naive Bayes with conditional deep generative models. We further develop detection methods for adversarial examples, which reject inputs with low likelihood under the generative m…
An adversarial attack paradigm explores various scenarios for the vulnerability of deep learning models: minor changes of the input can force a model failure. Most of the state of the art frameworks focus on adversarial attacks for images and other structured model inputs, but not for categorical sequences models. Successful attacks on classifiers of categorical sequences are challenging because the model input is tokens from finite sets, so a classifier score is non-differentiable with respect to inputs, and gradient-based attacks are not applicable. Common approaches deal with this problem w…
We provide a methodology, resilient feature engineering, for creating adversarially resilient classifiers. According to existing work, adversarial attacks identify weakly correlated or non-predictive features learned by the classifier during training and design the adversarial noise to utilize these features. Therefore, highly predictive features should be used first during classification in order to determine the set of possible output labels. Our methodology focuses the problem of designing resilient classifiers into a problem of designing resilient feature extractors for these highly predic…
This paper proposes a classification framework with a rejection option to mitigate the performance deterioration caused by adversarial examples. While recent machine learning algorithms achieve high prediction performance, they are empirically vulnerable to adversarial examples, which are slightly perturbed data samples that are wrongly classified. In real-world applications, adversarial attacks using such adversarial examples could cause serious problems. To this end, various methods are proposed to obtain a classifier that is robust against adversarial examples. Adversarial training is one 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…
Recent adversarial defense approaches have failed. Untargeted gradient-based attacks cause classifiers to choose any wrong class. Our novel white-box defense tricks untargeted attacks into becoming attacks targeted at designated target classes. From these target classes, we can derive the real classes. Our Target Training defense tricks the minimization at the core of untargeted, gradient-based adversarial attacks: minimize the sum of (1) perturbation and (2) classifier adversarial loss. Target Training changes the classifier minimally, and trains it with additional duplicated points (at 0 dis…
In this paper, we propose Code-Bridged Classifier (CBC), a framework for making a Convolutional Neural Network (CNNs) robust against adversarial attacks without increasing or even by decreasing the overall models' computational complexity. More specifically, we propose a stacked encoder-convolutional model, in which the input image is first encoded by the encoder module of a denoising auto-encoder, and then the resulting latent representation (without being decoded) is fed to a reduced complexity CNN for image classification. We illustrate that this network not only is more robust to adversari…
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…
Georgia Institute of Technology（佐治亚理工学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Adversarial training is a principled approach for training robust neural networks. Despite of tremendous successes in practice, its theoretical properties still remain largely unexplored. In this paper, we provide new theoretical insights of gradient descent based adversarial training by studying its computational properties, specifically on its inductive bias. We take the binary classification task on linearly separable data as an illustrative example, where the loss asymptotically attains its infimum as the parameter diverges to infinity along certain directions. Specifically, we show that w…
Motivated by safety-critical classification problems, we investigate adversarial attacks against cost-sensitive classifiers. We use current state-of-the-art adversarially-resistant neural network classifiers [1] as the underlying models. Cost-sensitive predictions are then achieved via a final processing step in the feed-forward evaluation of the network. We evaluate the effectiveness of cost-sensitive classifiers against a variety of attacks and we introduce a new cost-sensitive attack which performs better than targeted attacks in some cases. We also explored the measures a defender can take…
We introduce a novel approach for training adversarial models by replacing the discriminator score with a bi-modal Gaussian distribution over the real/fake indicator variables. In order to do this, we train the Gaussian classifier to match the target bi-modal distribution implicitly through meta-adversarial training. We hypothesize that this approach ensures a non-zero gradient to the generator, even in the limit of a perfect classifier. We test our method against standard benchmark image datasets as well as show the classifier output distribution is smooth and has overlap between the real and…
MIT Computer Science and Artificial Intelligence Lab（麻省理工学院计算机科学与人工智能实验室）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization. Specifically, an $\ell_2$ bounded adversary cannot alter the ensemble prediction generated by an additive isotropic Gaussian noise, where the radius for the adversary depends on both the variance of the distribution as well as the ensemble margin at the point of interest. We build on and considerably expand this work across broad classes of distributions. In particular, we offer adversarial robustness guarantees and associated algorithms for the discrete case where the advers…
We explore adversarial robustness in the setting in which it is acceptable for a classifier to abstain---that is, output no class---on adversarial examples. Adversarial examples are small perturbations of normal inputs to a classifier that cause the classifier to give incorrect output; they present security and safety challenges for machine learning systems. In many safety-critical applications, it is less costly for a classifier to abstain on adversarial examples than to give incorrect output for them. We first introduce a novel objective function for adversarial robustness with an abstain op…
Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant changes. For example, we can significantly change a face but well-trained neural networks still recognize the adversarial and the original example as the same person. Statistically, the existing adversarial attack increases Type II error and the proposed one aims at Type I error, which are hence named as Type II and Type I adversarial attack, respectively. T…
State-of-art deep neural networks (DNN) are vulnerable to attacks by adversarial examples: a carefully designed small perturbation to the input, that is imperceptible to human, can mislead DNN. To understand the root cause of adversarial examples, we quantify the probability of adversarial example existence for linear classifiers. Previous mathematical definition of adversarial examples only involves the overall perturbation amount, and we propose a more practical relevant definition of strong adversarial examples that separately limits the perturbation along the signal direction also. We show…
New Jersey Institute of Technology（新泽西理工学院）；Qatar Computing Research Institute（卡塔尔计算研究所）
Machine learning models, especially neural network (NN) classifiers, are widely used in many applications including natural language processing, computer vision and cybersecurity. They provide high accuracy under the assumption of attack-free scenarios. However, this assumption has been defied by the introduction of adversarial examples -- carefully perturbed samples of input that are usually misclassified. Many researchers have tried to develop a defense against adversarial examples; however, we are still far from achieving that goal. In this paper, we design a Generative Adversarial Net (GAN…
University of Maryland（马里兰大学）；Intelligent Automation, a BlueHalo Company（Intelligent Automation（BlueHalo 旗下公司））；Virginia Tech（弗吉尼亚理工大学）
This paper presents channel-aware adversarial attacks against deep learning-based wireless signal classifiers. There is a transmitter that transmits signals with different modulation types. A deep neural network is used at each receiver to classify its over-the-air received signals to modulation types. In the meantime, an adversary transmits an adversarial perturbation (subject to a power budget) to fool receivers into making errors in classifying signals that are received as superpositions of transmitted signals and adversarial perturbations. First, these evasion attacks are shown to fail whe…
EPFL（洛桑联邦理工学院）；University College London（伦敦大学学院）；University of California, Berkeley（加州大学伯克利分校）
Machine-learning models for security-critical applications such as bot, malware, or spam detection, operate in constrained discrete domains. These applications would benefit from having provable guarantees against adversarial examples. The existing literature on provable adversarial robustness of models, however, exclusively focuses on robustness to gradient-based attacks in domains such as images. These attacks model the adversarial cost, e.g., amount of distortion applied to an image, as a $p$-norm. We argue that this approach is not well-suited to model adversarial costs in constrained doma…
Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random perturbations. Towards explaining this gap, we highlight the hypothesis that $\textit{robust classification may require more complex classifiers (i.e. more capacity) than standard classification.}$ In this note, we show that this hypothesis is indeed possible, by giving several theoretical examples of classification tasks and sets of "simple" classifiers for …
We theoretically analyse the limits of robustness to test-time adversarial and noisy examples in classification. Our work focuses on deriving bounds which uniformly apply to all classifiers (i.e all measurable functions from features to labels) for a given problem. Our contributions are two-fold. (1) We use optimal transport theory to derive variational formulae for the Bayes-optimal error a classifier can make on a given classification problem, subject to adversarial attacks. The optimal adversarial attack is then an optimal transport plan for a certain binary cost-function induced by the spe…
School of Electrical and Electronic Engineering（电气与电子工程学院）；Nanyang Technological University（南洋理工大学）
Ideally, what confuses neural network should be confusing to humans. However, recent experiments have shown that small, imperceptible perturbations can change the network prediction. To address this gap in perception, we propose a novel approach for learning robust classifier. Our main idea is: adversarial examples for the robust classifier should be indistinguishable from the regular data of the adversarial target. We formulate a problem of learning robust classifier in the framework of Generative Adversarial Networks (GAN), where the adversarial attack on classifier acts as a generator, and …
Adversarial examples in machine learning for images are widely publicized and explored. Illustrations of misclassifications caused by slightly perturbed inputs are abundant and commonly known (e.g., a picture of panda imperceptibly perturbed to fool the classifier into incorrectly labeling it as a gibbon). Similar attacks on deep learning (DL) for radio frequency (RF) signals and their mitigation strategies are scarcely addressed in the published work. Yet, RF adversarial examples (AdExs) with minimal waveform perturbations can cause drastic, targeted misclassification results, particularly ag…
Classifiers fail to classify correctly input images that have been purposefully and imperceptibly perturbed to cause misclassification. This susceptability has been shown to be consistent across classifiers, regardless of their type, architecture or parameters. Common defenses against adversarial attacks modify the classifer boundary by training on additional adversarial examples created in various ways. In this paper, we introduce AutoGAN, which counters adversarial attacks by enhancing the lower-dimensional manifold defined by the training data and by projecting perturbed data points onto it…
University of Virginia（弗吉尼亚大学）；HRL Laboratories, LLC.（HRL实验室有限责任公司）
The vulnerabilities of deep neural networks against adversarial examples have become a significant concern for deploying these models in sensitive domains. Devising a definitive defense against such attacks is proven to be challenging, and the methods relying on detecting adversarial samples are only valid when the attacker is oblivious to the detection mechanism. In this paper we propose a principled adversarial example detection method that can withstand norm-constrained white-box attacks. Inspired by one-versus-the-rest classification, in a K class classification problem, we train K binary …
Pennsylvania State University（宾夕法尼亚州立大学）；The University of Hong Kong（香港大学）；University of California, Los Angeles（加州大学洛杉矶分校）
"Benign overfitting", where classifiers memorize noisy training data yet still achieve a good generalization performance, has drawn great attention in the machine learning community. To explain this surprising phenomenon, a series of works have provided theoretical justification in over-parameterized linear regression, classification, and kernel methods. However, it is not clear if benign overfitting still occurs in the presence of adversarial examples, i.e., examples with tiny and intentional perturbations to fool the classifiers. In this paper, we show that benign overfitting indeed occurs i…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
In this paper, the bias classifier is introduced, that is, the bias part of a DNN with Relu as the activation function is used as a classifier. The work is motivated by the fact that the bias part is a piecewise constant function with zero gradient and hence cannot be directly attacked by gradient-based methods to generate adversaries, such as FGSM. The existence of the bias classifier is proved and an effective training method for the bias classifier is given. It is proved that by adding a proper random first-degree part to the bias classifier, an information-theoretically safe classifier aga…
Monash University（莫纳什大学）；Defence Science and Technology Group, Department of Defence（国防部国防科学与技术集团）
Deep neural network image classifiers are reported to be susceptible to adversarial evasion attacks, which use carefully crafted images created to mislead a classifier. Recently, various kinds of adversarial attack methods have been proposed, most of which focus on adding small perturbations to input images. Despite the success of existing approaches, the way to generate realistic adversarial images with small perturbations remains a challenging problem. In this paper, we aim to address this problem by proposing a novel adversarial method, which generates adversarial examples by imposing not o…
In malware behavioral analysis, the list of accessed and created files very often indicates whether the examined file is malicious or benign. However, malware authors are trying to avoid detection by generating random filenames and/or modifying used filenames with new versions of the malware. These changes represent real-world adversarial examples. The goal of this work is to generate realistic adversarial examples and improve the classifier's robustness against these attacks. Our approach learns latent representations of input strings in an unsupervised fashion and uses gradient-based adversa…
University of Siena（锡耶纳大学）；University of Florence（佛罗伦萨大学）；University of Cagliari（卡利亚里大学）
Adversarial attacks on machine learning-based classifiers, along with defense mechanisms, have been widely studied in the context of single-label classification problems. In this paper, we shift the attention to multi-label classification, where the availability of domain knowledge on the relationships among the considered classes may offer a natural way to spot incoherent predictions, i.e., predictions associated to adversarial examples lying outside of the training data distribution. We explore this intuition in a framework in which first-order logic knowledge is converted into constraints a…
State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based adversarial attacks to generate adversarially perturbed images. We pose the question whether another type of optimization could give neural network classifiers an edge. Here, we introduce a novel approach that uses minimax optimization to foil gradient-based adversarial attacks. Our minimax classifier is the discriminator of a generative adversarial network (GAN) tha…
Recently, some works found an interesting phenomenon that adversarially robust classifiers can generate good images comparable to generative models. We investigate this phenomenon from an energy perspective and provide a novel explanation. We reformulate adversarial example generation, adversarial training, and image generation in terms of an energy function. We find that adversarial training contributes to obtaining an energy function that is flat and has low energy around the real data, which is the key for generative capability. Based on our new understanding, we further propose a better ad…
University of Maryland, College Park（马里兰大学帕克分校）；University of Maryland Institute for Advanced Computer Studies（马里兰大学高级计算机研究所）
In recent years, deep neural network approaches have been widely adopted for machine learning tasks, including classification. However, they were shown to be vulnerable to adversarial perturbations: carefully crafted small perturbations can cause misclassification of legitimate images. We propose Defense-GAN, a new framework leveraging the expressive capability of generative models to defend deep neural networks against such attacks. Defense-GAN is trained to model the distribution of unperturbed images. At inference time, it finds a close output to a given image which does not contain the adv…
University of Florida（佛罗里达大学）；National Cheng Kung University（国立成功大学）；University of Central Florida（中佛罗里达大学）
Machine learning researchers have long noticed the phenomenon that the model training process will be more effective and efficient when the training samples are densely sampled around the underlying decision boundary. While this observation has already been widely applied in a range of machine learning security techniques, it lacks theoretical analyses of the correctness of the observation. To address this challenge, we first add particular perturbation to original training examples using adversarial attack methods so that the generated examples could lie approximately on the decision boundary…
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…
Being an emerging class of in-memory computing architecture, brain-inspired hyperdimensional computing (HDC) mimics brain cognition and leverages random hypervectors (i.e., vectors with a dimensionality of thousands or even more) to represent features and to perform classification tasks. The unique hypervector representation enables HDC classifiers to exhibit high energy efficiency, low inference latency and strong robustness against hardware-induced bit errors. Consequently, they have been increasingly recognized as an appealing alternative to or even replacement of traditional deep neural ne…
Recently, generating adversarial examples has become an important means of measuring robustness of a deep learning model. Adversarial examples help us identify the susceptibilities of the model and further counter those vulnerabilities by applying adversarial training techniques. In natural language domain, small perturbations in the form of misspellings or paraphrases can drastically change the semantics of the text. We propose a reinforcement learning based approach towards generating adversarial examples in black-box settings. We demonstrate that our method is able to fool well-trained mode…
In this paper, we investigate the potential effect of the adversarially training on the robustness of six advanced deep neural networks against a variety of targeted and non-targeted adversarial attacks. We firstly show that, the ResNet-56 model trained on the 2D representation of the discrete wavelet transform appended with the tonnetz chromagram outperforms other models in terms of recognition accuracy. Then we demonstrate the positive impact of adversarially training on this model as well as other deep architectures against six types of attack algorithms (white and black-box) with the cost …
Deep neural networks have been shown to exhibit an intriguing vulnerability to adversarial input images corrupted with imperceptible perturbations. However, the majority of adversarial attacks assume global, fine-grained control over the image pixel space. In this paper, we consider a different setting: what happens if the adversary could only alter specific attributes of the input image? These would generate inputs that might be perceptibly different, but still natural-looking and enough to fool a classifier. We propose a novel approach to generate such `semantic' adversarial examples by opti…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Deep neural networks represent the state of the art in machine learning in a growing number of fields, including vision, speech and natural language processing. However, recent work raises important questions about the robustness of such architectures, by showing that it is possible to induce classification errors through tiny, almost imperceptible, perturbations. Vulnerability to such "adversarial attacks", or "adversarial examples", has been conjectured to be due to the excessive linearity of deep networks. In this paper, we study this phenomenon in the setting of a linear classifier, and sh…
Guardian of the Ensembles: Introducing Pairwise Adversarially Robust Loss for Resisting Adversarial Attacks in DNN Ensembles
Centre for Computational and Data Sciences, IIT Kharagpur（印度理工学院克勒格布尔分校计算与数据科学中心）；Computer Science and Engineering Department, IIT Kharagpur（印度理工学院克勒格布尔分校计算机科学与工程系）；Center for Cyber Security, New York University Abu Dhabi（纽约大学阿布扎比分校网络安全中心）；Department of Artificial Intelligence, IIT Kharagpur（印度理工学院克勒格布尔分校人工智能系）；Computer Science and Engineering Department, IIT Patna（印度理工学院巴特那分校计算机科学与工程系）
Deep-learning based classification algorithms have been shown to be susceptible to adversarial attacks: minor changes to the input of classifiers can dramatically change their outputs, while being imperceptible to humans. In this paper, we present a simple hypothesis about a feature compression property of artificial intelligence (AI) classifiers and present theoretical arguments to show that this hypothesis successfully accounts for the observed fragility of AI classifiers to small adversarial perturbations. Drawing on ideas from information and coding theory, we propose a general class of de…
Recently, it has been shown that, in spite of the significant performance of deep neural networks in different fields, those are vulnerable to adversarial examples. In this paper, we propose a gradient-based adversarial attack against transformer-based text classifiers. The adversarial perturbation in our method is imposed to be block-sparse so that the resultant adversarial example differs from the original sentence in only a few words. Due to the discrete nature of textual data, we perform gradient projection to find the minimizer of our proposed optimization problem. Experimental results de…
In this work, we investigate the phenomenon that robust image classifiers have human-recognizable features -- often referred to as interpretability -- as revealed through the input gradients of their score functions and their subsequent adversarial perturbations. In particular, we demonstrate that state-of-the-art methods for adversarial training incorporate two terms -- one that orients the decision boundary via minimizing the expected loss, and another that induces smoothness of the classifier's decision surface by penalizing the local Lipschitz constant. Through this demonstration, we provi…
As the name suggests, image spam is spam email that has been embedded in an image. Image spam was developed in an effort to evade text-based filters. Modern deep learning-based classifiers perform well in detecting typical image spam that is seen in the wild. In this chapter, we evaluate numerous adversarial techniques for the purpose of attacking deep learning-based image spam classifiers. Of the techniques tested, we find that universal perturbation performs best. Using universal adversarial perturbations, we propose and analyze a new transformation-based adversarial attack that enables us t…
Technion – Israel Institute of Technology（技术学院 – 以色列理工学院）；Bar-Ilan University（巴伊兰大学）；Ben-Gurion University of the Negev（贝加尔大学）；Institute of Science and Technology（科学与技术研究所）
Adversarial attack has cast a shadow on the massive success of deep neural networks. Despite being almost visually identical to the clean data, the adversarial images can fool deep neural networks into wrong predictions with very high confidence. In this paper, however, we show that we can build a simple binary classifier separating the adversarial apart from the clean data with accuracy over 99%. We also empirically show that the binary classifier is robust to a second-round adversarial attack. In other words, it is difficult to disguise adversarial samples to bypass the binary classifier. Fu…
University of Maryland（马里兰大学）；Intelligent Automation, Inc.（智能自动化公司）；Virginia Tech（弗吉尼亚理工大学）
We consider a wireless communication system, where a transmitter sends signals to a receiver with different modulation types while the receiver classifies the modulation types of the received signals using its deep learning-based classifier. Concurrently, an adversary transmits adversarial perturbations using its multiple antennas to fool the classifier into misclassifying the received signals. From the adversarial machine learning perspective, we show how to utilize multiple antennas at the adversary to improve the adversarial (evasion) attack performance. Two main points are considered while…
Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could outperform classical computers in solving certain notable machine learning tasks. Yet, quantum learning systems may also suffer from the vulnerability problem: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we study the universality …
Neural network classifiers are vulnerable to misclassification of adversarial samples, for which the current best defense trains classifiers with adversarial samples. However, adversarial samples are not optimal for steering attack convergence, based on the minimization at the core of adversarial attacks. The minimization perturbation term can be minimized towards $0$ by replacing adversarial samples in training with duplicated original samples, labeled differently only for training. Using only original samples, Target Training eliminates the need to generate adversarial samples for training a…
