Algorithmic trading systems are often completely automated, and deep learning is increasingly receiving attention in this domain. Nonetheless, little is known about the robustness properties of these models. We study valuation models for algorithmic trading from the perspective of adversarial machine learning. We introduce new attacks specific to this domain with size constraints that minimize attack costs. We further discuss how these attacks can be used as an analysis tool to study and evaluate the robustness properties of financial models. Finally, we investigate the feasibility of realistic adversarial attacks in which an adversarial trader fools automated trading systems into making inaccurate predictions.
Instituto Superior de Economia e Gestão（里斯本大学经济与管理高等学院）；Universidade de Lisboa（里斯本大学）；University of New Haven（纽黑文大学）；Royal Bank of Canada（加拿大皇家银行）
Deep Reinforcement Learning (DRL) has become an appealing solution to algorithmic trading such as high frequency trading of stocks and cyptocurrencies. However, DRL have been shown to be susceptible to adversarial attacks. It follows that algorithmic trading DRL agents may also be compromised by such adversarial techniques, leading to policy manipulation. In this paper, we develop a threat model for deep trading policies, and propose two attack techniques for manipulating the performance of such policies at test-time. Furthermore, we demonstrate the effectiveness of the proposed attacks agains…
While deep learning has led to remarkable results on a number of challenging problems, researchers have discovered a vulnerability of neural networks in adversarial settings, where small but carefully chosen perturbations to the input can make the models produce extremely inaccurate outputs. This makes these models particularly unsuitable for safety-critical application domains (e.g. self-driving cars) where robustness is extremely important. Recent work has shown that augmenting training with adversarially generated data provides some degree of robustness against test-time attacks. In this pa…
We study a security threat to adversarial multi-armed bandits, in which an attacker perturbs the loss or reward signal to control the behavior of the victim bandit player. We show that the attacker is able to mislead any no-regret adversarial bandit algorithm into selecting a suboptimal target arm in every but sublinear (T-o(T)) number of rounds, while incurring only sublinear (o(T)) cumulative attack cost. This result implies critical security concern in real-world bandit-based systems, e.g., in online recommendation, an attacker might be able to hijack the recommender system and promote a de…
Production machine learning systems are consistently under attack by adversarial actors. Various deep learning models must be capable of accurately detecting fake or adversarial input while maintaining speed. In this work, we propose one piece of the production protection system: detecting an incoming adversarial attack and its characteristics. Detecting types of adversarial attacks has two primary effects: the underlying model can be trained in a structured manner to be robust from those attacks and the attacks can be potentially filtered out in real-time before causing any downstream damage.…
Eindhoven University of Technology（埃因霍温理工大学）；National University of Singapore（新加坡国立大学）
Deep neural networks are vulnerable to adversarial examples that are crafted by imposing imperceptible changes to the inputs. However, these adversarial examples are most successful in white-box settings where the model and its parameters are available. Finding adversarial examples that are transferable to other models or developed in a black-box setting is significantly more difficult. In this paper, we propose the Direction-Aggregated adversarial attacks that deliver transferable adversarial examples. Our method utilizes aggregated direction during the attack process for avoiding the generat…
Despite significant improvements in natural language understanding models with the advent of models like BERT and XLNet, these neural-network based classifiers are vulnerable to blackbox adversarial attacks, where the attacker is only allowed to query the target model outputs. We add two more realistic restrictions on the attack methods, namely limiting the number of queries allowed (query budget) and crafting attacks that easily transfer across different pre-trained models (transferability), which render previous attack models impractical and ineffective. Here, we propose a target model agnos…
The vulnerability of deep neural networks to adversarial examples has motivated an increasing number of defense strategies for promoting model robustness. However, the progress is usually hampered by insufficient robustness evaluations. As the de facto standard to evaluate adversarial robustness, adversarial attacks typically solve an optimization problem of crafting adversarial examples with an iterative process. In this work, we propose a Model-Agnostic Meta-Attack (MAMA) approach to discover stronger attack algorithms automatically. Our method learns the optimizer in adversarial attacks par…
Southern University of Science and Technology（南方科技大学）
Deep neural networks have achieved impressive performance in various areas, but they are shown to be vulnerable to adversarial attacks. Previous works on adversarial attacks mainly focused on the single-task setting. However, in real applications, it is often desirable to attack several models for different tasks simultaneously. To this end, we propose Multi-Task adversarial Attack (MTA), a unified framework that can craft adversarial examples for multiple tasks efficiently by leveraging shared knowledge among tasks, which helps enable large-scale applications of adversarial attacks on real-wo…
With the fast development of machine learning technologies, deep learning models have been deployed in almost every aspect of everyday life. However, the privacy and security of these models are threatened by adversarial attacks. Among which black-box attack is closer to reality, where limited knowledge can be acquired from the model. In this paper, we provided basic background knowledge about adversarial attack and analyzed four black-box attack algorithms: Bandits, NES, Square Attack and ZOsignSGD comprehensively. We also explored the newly proposed Square Attack method with respect to squar…
IEMN-DOAE, UMR CNRS 8520 Polytechnic University Hauts-De-France（法国上法兰西理工大学 IEMN-DOAE, UMR CNRS 8520）；George Mason University（乔治梅森大学）；University of California Riverside（加州大学河滨分校）
Advances in deep learning have enabled a wide range of promising applications. However, these systems are vulnerable to Adversarial Machine Learning (AML) attacks; adversarially crafted perturbations to their inputs could cause them to misclassify. Several state-of-the-art adversarial attacks have demonstrated that they can reliably fool classifiers making these attacks a significant threat. Adversarial attack generation algorithms focus primarily on creating successful examples while controlling the noise magnitude and distribution to make detection more difficult. The underlying assumption o…
Tencent（腾讯）；Zhejiang University（浙江大学）；JD Explore Academy（京东探索研究院）；University of Munich（慕尼黑大学）
It is well known that adversarial attacks can fool deep neural networks with imperceptible perturbations. Although adversarial training significantly improves model robustness, failure cases of defense still broadly exist. In this work, we find that the adversarial attacks can also be vulnerable to small perturbations. Namely, on adversarially-trained models, perturbing adversarial examples with a small random noise may invalidate their misled predictions. After carefully examining state-of-the-art attacks of various kinds, we find that all these attacks have this deficiency to different exten…
Torchattacks is a PyTorch library that contains adversarial attacks to generate adversarial examples and to verify the robustness of deep learning models. The code can be found at https://github.com/Harry24k/adversarial-attacks-pytorch.
Guangzhou University（广州大学）；Cyberspace Institute of Advanced Technology（网络空间先进技术研究院）
Recent work shows that deep neural networks are vulnerable to adversarial examples. Much work studies adversarial example generation, while very little work focuses on more critical adversarial defense. Existing adversarial detection methods usually make assumptions about the adversarial example and attack method (e.g., the word frequency of the adversarial example, the perturbation level of the attack method). However, this limits the applicability of the detection method. To this end, we propose TREATED, a universal adversarial detection method that can defend against attacks of various pert…
Beijing University of Posts and Telecommunications（北京邮电大学）
Deep neural networks (DNNs) are sensitive and susceptible to tiny perturbation by adversarial attacks which causes erroneous predictions. Various methods, including adversarial defense and uncertainty inference (UI), have been developed in recent years to overcome the adversarial attacks. In this paper, we propose a multi-head uncertainty inference (MH-UI) framework for detecting adversarial attack examples. We adopt a multi-head architecture with multiple prediction heads (i.e., classifiers) to obtain predictions from different depths in the DNNs and introduce shallow information for the UI. …
Machine Learning (ML) models are known to be vulnerable to adversarial inputs and researchers have demonstrated that even production systems, such as self-driving cars and ML-as-a-service offerings, are susceptible. These systems represent a target for bad actors. Their disruption can cause real physical and economic harm. When attacks on production ML systems occur, the ability to attribute the attack to the responsible threat group is a critical step in formulating a response and holding the attackers accountable. We pose the following question: can adversarially perturbed inputs be attribut…
Most state-of-the-art machine learning (ML) classification systems are vulnerable to adversarial perturbations. As a consequence, adversarial robustness poses a significant challenge for the deployment of ML-based systems in safety- and security-critical environments like autonomous driving, disease detection or unmanned aerial vehicles. In the past years we have seen an impressive amount of publications presenting more and more new adversarial attacks. However, the attack research seems to be rather unstructured and new attacks often appear to be random selections from the unlimited set of po…
Technical University of Munich（慕尼黑工业大学）；University of Maryland, College Park（马里兰大学帕克分校）
Adversarial Training is proved to be an efficient method to defend against adversarial examples, being one of the few defenses that withstand strong attacks. However, traditional defense mechanisms assume a uniform attack over the examples according to the underlying data distribution, which is apparently unrealistic as the attacker could choose to focus on more vulnerable examples. We present a weighted minimax risk optimization that defends against non-uniform attacks, achieving robustness against adversarial examples under perturbed test data distributions. Our modified risk considers impor…
MagNet and "Efficient Defenses..." were recently proposed as a defense to adversarial examples. We find that we can construct adversarial examples that defeat these defenses with only a slight increase in distortion.
University of Science and Technology of China（中国科学技术大学）
Deep Neural Networks (DNNs) have recently led to significant improvements in many fields. However, DNNs are vulnerable to adversarial examples which are samples with imperceptible perturbations while dramatically misleading the DNNs. Adversarial attacks can be used to evaluate the robustness of deep learning models before they are deployed. Unfortunately, most of existing adversarial attacks can only fool a black-box model with a low success rate. To improve the success rates for black-box adversarial attacks, we proposed an iterated adversarial attack against an ensemble of image classifiers.…
With the excellent accuracy and feasibility, the Neural Networks have been widely applied into the novel intelligent applications and systems. However, with the appearance of the Adversarial Attack, the NN based system performance becomes extremely vulnerable:the image classification results can be arbitrarily misled by the adversarial examples, which are crafted images with human unperceivable pixel-level perturbation. As this raised a significant system security issue, we implemented a series of investigations on the adversarial attack in this work: We first identify an image's pixel vulnera…
Adversarial attacks have been extensively investigated for machine learning systems including deep learning in the digital domain. However, the adversarial attacks on optical neural networks (ONN) have been seldom considered previously. In this work, we first construct an accurate image classifier with an ONN using a mesh of interconnected Mach-Zehnder interferometers (MZI). Then a corresponding adversarial attack scheme is proposed for the first time. The attacked images are visually very similar to the original ones but the ONN system becomes malfunctioned and generates wrong classification …
This paper extensively evaluates the vulnerability of capsule networks to different adversarial attacks. Recent work suggests that these architectures are more robust towards adversarial attacks than other neural networks. However, our experiments show that capsule networks can be fooled as easily as convolutional neural networks.
Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspective that adversarial attacks are likely caused by numerical instability in learned functions. We introduce a stability inducing, regularization based defense against adversarial attacks in the regression setting. Our new and easy to implement defense is shown to outperform prio…
Deep neural networks are vulnerable to adversarial attacks. White-box adversarial attacks can fool neural networks with small adversarial perturbations, especially for large size images. However, keeping successful adversarial perturbations imperceptible is especially challenging for transfer-based black-box adversarial attacks. Often such adversarial examples can be easily spotted due to their unpleasantly poor visual qualities, which compromises the threat of adversarial attacks in practice. In this study, to improve the image quality of black-box adversarial examples perceptually, we propos…
Huazhong University of Science and Technology（华中科技大学）；Cornell University（康奈尔大学）
The black-box adversarial attack has attracted impressive attention for its practical use in the field of deep learning security. Meanwhile, it is very challenging as there is no access to the network architecture or internal weights of the target model. Based on the hypothesis that if an example remains adversarial for multiple models, then it is more likely to transfer the attack capability to other models, the ensemble-based adversarial attack methods are efficient and widely used for black-box attacks. However, ways of ensemble attack are rather less investigated, and existing ensemble att…
Under adversarial attacks, time series regression and classification are vulnerable. Adversarial defense, on the other hand, can make the models more resilient. It is important to evaluate how vulnerable different time series models are to attacks and how well they recover using defense. The sensitivity to various attacks and the robustness using the defense of several time series models are investigated in this study. Experiments are run on seven-time series models with three adversarial attacks and one adversarial defense. According to the findings, all models, particularly GRU and RNN, appe…
Monash University（莫纳什大学）；Defence Science and Technology Group, Department of Defence（国防部国防科学技术集团）
Deep neural network image classifiers are reported to be susceptible to adversarial evasion attacks, which use carefully crafted images created to mislead a classifier. Many adversarial attacks belong to the category of dense attacks, which generate adversarial examples by perturbing all the pixels of a natural image. To generate sparse perturbations, sparse attacks have been recently developed, which are usually independent attacks derived by modifying a dense attack's algorithm with sparsity regularisations, resulting in reduced attack efficiency. In this paper, we aim to tackle this task fr…
Recent studies have shown that adversarial examples hand-crafted on one white-box model can be used to attack other black-box models. Such cross-model transferability makes it feasible to perform black-box attacks, which has raised security concerns for real-world DNNs applications. Nevertheless, existing works mostly focus on investigating the adversarial transferability across different deep models that share the same modality of input data. The cross-modal transferability of adversarial perturbation has never been explored. This paper investigates the transferability of adversarial perturba…
Air Traffic Control and Navigation College, Air Force Engineering University（空军工程大学空管领航学院）；Information and Navigation College, Air Force Engineering University（空军工程大学信息与导航学院）；Henan University of Technology（河南工业大学）
Vulnerability of various machine learning methods to adversarial examples has been recently explored in the literature. Power systems which use these vulnerable methods face a huge threat against adversarial examples. To this end, we first propose a signal-specific method and a universal signal-agnostic method to attack power systems using generated adversarial examples. Black-box attacks based on transferable characteristics and the above two methods are also proposed and evaluated. We then adopt adversarial training to defend systems against adversarial attacks. Experimental analyses demonst…
Machine learning models have made many decision support systems to be faster, more accurate, and more efficient. However, applications of machine learning in network security face a more disproportionate threat of active adversarial attacks compared to other domains. This is because machine learning applications in network security such as malware detection, intrusion detection, and spam filtering are by themselves adversarial in nature. In what could be considered an arm's race between attackers and defenders, adversaries constantly probe machine learning systems with inputs that are explicit…
Condition-based maintenance (CBM) strategies exploit machine learning models to assess the health status of systems based on the collected data from the physical environment, while machine learning models are vulnerable to adversarial attacks. A malicious adversary can manipulate the collected data to deceive the machine learning model and affect the CBM system's performance. Adversarial machine learning techniques introduced in the computer vision domain can be used to make stealthy attacks on CBM systems by adding perturbation to data to confuse trained models. The stealthy nature causes dif…
Machine learning (ML) algorithms are increasingly being integrated into embedded and IoT systems that surround us, and they are vulnerable to adversarial attacks. The deployment of these ML algorithms on resource-limited embedded platforms also requires the use of model compression techniques. The impact of such model compression techniques on adversarial robustness in ML is an important and emerging area of research. This article provides an overview of the landscape of adversarial attacks and ML model compression techniques relevant to embedded systems. We then describe efforts that seek to …
Adversarial attacks modify images with perturbations that change the prediction of classifiers. These modified images, known as adversarial examples, expose the vulnerabilities of deep neural network classifiers. In this paper, we investigate the predictability of the mapping between the classes predicted for original images and for their corresponding adversarial examples. This predictability relates to the possibility of retrieving the original predictions and hence reversing the induced misclassification. We refer to this property as the reversibility of an adversarial attack, and quantify …
Tsinghua University（清华大学）；HeartVoice Medical Technology（心之声医疗科技）；University of Science and Technology of China（中国科学技术大学）；HeartRhythm Medical（心律医疗）；Tianjin Institute of Cardiology（天津心脏病学研究所）；Second Hospital of Tianjin Medical University（天津医科大学第二医院）；Peking University（北京大学）
In clinics, doctors rely on electrocardiograms (ECGs) to assess severe cardiac disorders. Owing to the development of technology and the increase in health awareness, ECG signals are currently obtained by using medical and commercial devices. Deep neural networks (DNNs) can be used to analyze these signals because of their high accuracy rate. However, researchers have found that adversarial attacks can significantly reduce the accuracy of DNNs. Studies have been conducted to defend ECG-based DNNs against traditional adversarial attacks, such as projected gradient descent (PGD), and smooth adve…
Information Technology University, Punjab, Pakistan（巴基斯坦旁遮普信息技术大学）；Hamad Bin Khalifa University, Qatar（卡塔尔哈马德·本·哈利法大学）
Recently, many deep neural networks (DNN) based modulation classification schemes have been proposed in the literature. We have evaluated the robustness of two famous such modulation classifiers (based on the techniques of convolutional neural networks and long short term memory) against adversarial machine learning attacks in black-box settings. We have used Carlini \& Wagner (C-W) attack for performing the adversarial attack. To the best of our knowledge, the robustness of these modulation classifiers has not been evaluated through C-W attack before. Our results clearly indicate that state-o…
Adversarial attacks are inputs that are similar to original inputs but altered on purpose. Speech-to-text neural networks that are widely used today are prone to misclassify adversarial attacks. In this study, first, we investigate the presence of targeted adversarial attacks by altering wave forms from Common Voice data set. We craft adversarial wave forms via Connectionist Temporal Classification Loss Function, and attack DeepSpeech, a speech-to-text neural network implemented by Mozilla. We achieve 100% adversarial success rate (zero successful classification by DeepSpeech) on all 25 advers…
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Universiteit van Amsterdam（阿姆斯特丹大学）
In this work, we explore adversarial attacks on the Variational Autoencoders (VAE). We show how to modify data point to obtain a prescribed latent code (supervised attack) or just get a drastically different code (unsupervised attack). We examine the influence of model modifications ($β$-VAE, NVAE) on the robustness of VAEs and suggest metrics to quantify it.
Shenzhen Research Institute of Big Data（深圳大数据研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；JD Explore Academy（京东探索研究院）；Tencent AI Lab（腾讯人工智能实验室）
Deep neural networks (DNNs) have been shown to be vulnerable to adversarial examples, which can produce erroneous predictions by injecting imperceptible perturbations. In this work, we study the transferability of adversarial examples, which is significant due to its threat to real-world applications where model architecture or parameters are usually unknown. Many existing works reveal that the adversarial examples are likely to overfit the surrogate model that they are generated from, limiting its transfer attack performance against different target models. To mitigate the overfitting of the …
Adversarial attacks for image classification are small perturbations to images that are designed to cause misclassification by a model. Adversarial attacks formally correspond to an optimization problem: find a minimum norm image perturbation, constrained to cause misclassification. A number of effective attacks have been developed. However, to date, no gradient-based attacks have used best practices from the optimization literature to solve this constrained minimization problem. We design a new untargeted attack, based on these best practices, using the established logarithmic barrier method.…
We introduce a feature scattering-based adversarial training approach for improving model robustness against adversarial attacks. Conventional adversarial training approaches leverage a supervised scheme (either targeted or non-targeted) in generating attacks for training, which typically suffer from issues such as label leaking as noted in recent works. Differently, the proposed approach generates adversarial images for training through feature scattering in the latent space, which is unsupervised in nature and avoids label leaking. More importantly, this new approach generates perturbed imag…
As adversarial attacks pose a serious threat to the security of AI system in practice, such attacks have been extensively studied in the context of computer vision applications. However, few attentions have been paid to the adversarial research on automatic path finding. In this paper, we show dominant adversarial examples are effective when targeting A3C path finding, and design a Common Dominant Adversarial Examples Generation Method (CDG) to generate dominant adversarial examples against any given map. In addition, we propose Gradient Band-based Adversarial Training, which trained with a si…
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…
Johns Hopkins University（约翰斯·霍普金斯大学）；University of Maryland, College Park（马里兰大学帕克分校）
The adversarial attack literature contains a myriad of algorithms for crafting perturbations which yield pathological behavior in neural networks. In many cases, multiple algorithms target the same tasks and even enforce the same constraints. In this work, we show that different attack algorithms produce adversarial examples which are distinct not only in their effectiveness but also in how they qualitatively affect their victims. We begin by demonstrating that one can determine the attack algorithm that crafted an adversarial example. Then, we leverage recent advances in parameter-space salie…
We present a method for adversarial attack detection based on the inspection of a sparse set of neurons. We follow the hypothesis that adversarial attacks introduce imperceptible perturbations in the input and that these perturbations change the state of neurons relevant for the concepts modelled by the attacked model. Therefore, monitoring the status of these neurons would enable the detection of adversarial attacks. Focusing on the image classification task, our method identifies neurons that are relevant for the classes predicted by the model. A deeper qualitative inspection of these sparse…
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；NVIDIA（英伟达）；California Institute of Technology（加州理工学院）；Stanford University（斯坦福大学）
Trajectory prediction is essential for autonomous vehicles (AVs) to plan correct and safe driving behaviors. While many prior works aim to achieve higher prediction accuracy, few study the adversarial robustness of their methods. To bridge this gap, we propose to study the adversarial robustness of data-driven trajectory prediction systems. We devise an optimization-based adversarial attack framework that leverages a carefully-designed differentiable dynamic model to generate realistic adversarial trajectories. Empirically, we benchmark the adversarial robustness of state-of-the-art prediction…
University of Florida（佛罗里达大学）；Tongdun Technology（同盾科技）
Recent studies have shown that state-of-the-art deep learning models are vulnerable to the inputs with small perturbations (adversarial examples). We observe two critical obstacles in adversarial examples: (i) Strong adversarial attacks (e.g., C&W attack) require manually tuning hyper-parameters and take a long time to construct an adversarial example, making it impractical to attack real-time systems; (ii) Most of the studies focus on non-sequential tasks, such as image classification, yet only a few consider sequential tasks. In this work, we speed up adversarial attacks, especially on seque…
Most deep learning models are easily vulnerable to adversarial attacks. Various adversarial attacks are designed to evaluate the robustness of models and develop defense model. Currently, adversarial attacks are brought up to attack their own target model with their own evaluation metrics. And most of the black-box adversarial attack algorithms cannot achieve the expected success rate compared with white-box attacks. In this paper, comprehensive evaluation metrics are brought up for different adversarial attack methods. A novel perturbation optimized black-box adversarial attack based on genet…
The forecast of electrical loads is essential for the planning and operation of the power system. Recently, advances in deep learning have enabled more accurate forecasts. However, deep neural networks are prone to adversarial attacks. Although most of the literature focuses on integrity-based attacks, this paper proposes availability-based adversarial attacks, which can be more easily implemented by attackers. For each forecast instance, the availability attack position is optimally solved by mixed-integer reformulation of the artificial neural network. To tackle this attack, an adversarial t…
Deep learning technologies have become the backbone for the development of computer vision. With further explorations, deep neural networks have been found vulnerable to well-designed adversarial attacks. Most of the vision devices are equipped with image signal processing (ISP) pipeline to implement RAW-to-RGB transformations and embedded into data preprocessing module for efficient image processing. Actually, ISP pipeline can introduce adversarial behaviors to post-capture images while data preprocessing may destroy attack patterns. However, none of the existing adversarial attacks takes int…
We propose the first general-purpose gradient-based attack against transformer models. Instead of searching for a single adversarial example, we search for a distribution of adversarial examples parameterized by a continuous-valued matrix, hence enabling gradient-based optimization. We empirically demonstrate that our white-box attack attains state-of-the-art attack performance on a variety of natural language tasks. Furthermore, we show that a powerful black-box transfer attack, enabled by sampling from the adversarial distribution, matches or exceeds existing methods, while only requiring ha…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；University of Tübingen（图宾根大学）
Adversarial training yields robust models against a specific threat model, e.g., $L_\infty$ adversarial examples. Typically robustness does not generalize to previously unseen threat models, e.g., other $L_p$ norms, or larger perturbations. Our confidence-calibrated adversarial training (CCAT) tackles this problem by biasing the model towards low confidence predictions on adversarial examples. By allowing to reject examples with low confidence, robustness generalizes beyond the threat model employed during training. CCAT, trained only on $L_\infty$ adversarial examples, increases robustness ag…
