We propose gradient adversarial training, an auxiliary deep learning framework applicable to different machine learning problems. In gradient adversarial training, we leverage a prior belief that in many contexts, simultaneous gradient updates should be statistically indistinguishable from each other. We enforce this consistency using an auxiliary network that classifies the origin of the gradient tensor, and the main network serves as an adversary to the auxiliary network in addition to performing standard task-based training. We demonstrate gradient adversarial training for three different scenarios: (1) as a defense to adversarial examples we classify gradient tensors and tune them to be agnostic to the class of their corresponding example, (2) for knowledge distillation, we do binary classification of gradient tensors derived from the student or teacher network and tune the student gradient tensor to mimic the teacher's gradient tensor; and (3) for multi-task learning we classify the gradient tensors derived from different task loss functions and tune them to be statistically indistinguishable. For each of the three scenarios we show the potential of gradient adversarial training procedure. Specifically, gradient adversarial training increases the robustness of a network to adversarial attacks, is able to better distill the knowledge from a teacher network to a student network compared to soft targets, and boosts multi-task learning by aligning the gradient tensors derived from the task specific loss functions. Overall, our experiments demonstrate that gradient tensors contain latent information about whatever tasks are being trained, and can support diverse machine learning problems when intelligently guided through adversarialization using a auxiliary network.
In this work we revisit gradient regularization for adversarial robustness with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gradient information. These bounds strongly motivate input gradient regularization. Second, we implement a scaleable version of input gradient regularization which avoids double backpropagation: adversarially robust ImageNet models are trained in 33 hours on four consumer grade GPUs. Finally, we show experimentally and through theoretical certification that input gradient regularization is competitive with adversarial …
Adversarial examples are input examples that are specifically crafted to deceive machine learning classifiers. State-of-the-art adversarial example detection methods characterize an input example as adversarial either by quantifying the magnitude of feature variations under multiple perturbations or by measuring its distance from estimated benign example distribution. Instead of using such metrics, the proposed method is based on the observation that the directions of adversarial gradients when crafting (new) adversarial examples play a key role in characterizing the adversarial space. Compare…
The effects of adversarial training on semantic segmentation networks has not been thoroughly explored. While previous work has shown that adversarially-trained image classifiers can be used to perform image synthesis, we have yet to understand how best to leverage an adversarially-trained segmentation network to do the same. Using a simple optimizer, we demonstrate that adversarially-trained semantic segmentation networks can be used to perform image inpainting and generation. Our experiments demonstrate that adversarially-trained segmentation networks are more robust and indeed exhibit perce…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Satrec Initiative（Satrec Initiative公司）；SI Analytics
Adversarial training is a training scheme designed to counter adversarial attacks by augmenting the training dataset with adversarial examples. Surprisingly, several studies have observed that loss gradients from adversarially trained DNNs are visually more interpretable than those from standard DNNs. Although this phenomenon is interesting, there are only few works that have offered an explanation. In this paper, we attempted to bridge this gap between adversarial robustness and gradient interpretability. To this end, we identified that loss gradients from adversarially trained DNNs align bet…
Optical Data Processing Division, Signal and Image Processing Group, SAC, ISRO（印度空间研究组织航天应用中心光学数据处理部、信号与图像处理组）
Generative Adversarial Networks (GAN) have shown promising results on a wide variety of complex tasks. Recent experiments show adversarial training provides useful gradients to the generator that helps attain better performance. In this paper, we intend to theoretically analyze whether supervised learning with adversarial features can outperform sole supervision, or not. First, we show that supervised learning without adversarial features suffer from vanishing gradient issue in near optimal region. Second, we analyze how adversarial learning augmented with supervised signal mitigates this vani…
University of Science and Technology of China（中国科学技术大学）
Improving the resistance of deep neural networks against adversarial attacks is important for deploying models to realistic applications. However, most defense methods are designed to defend against intensity perturbations and ignore location perturbations, which should be equally important for deep model security. In this paper, we focus on adversarial deformations, a typical class of location perturbations, and propose a flow gradient regularization to improve the resistance of models. Theoretically, we prove that, compared with input gradient regularization, regularizing flow gradients is a…
Adversarial attacks have been extensively studied in recent years since they can identify the vulnerability of deep learning models before deployed. In this paper, we consider the black-box adversarial setting, where the adversary needs to craft adversarial examples without access to the gradients of a target model. Previous methods attempted to approximate the true gradient either by using the transfer gradient of a surrogate white-box model or based on the feedback of model queries. However, the existing methods inevitably suffer from low attack success rates or poor query efficiency since i…
We propose to utilize gradients for detecting adversarial and out-of-distribution samples. We introduce confounding labels -- labels that differ from normal labels seen during training -- in gradient generation to probe the effective expressivity of neural networks. Gradients depict the amount of change required for a model to properly represent given inputs, providing insight into the representational power of the model established by network architectural properties as well as training data. By introducing a label of different design, we remove the dependency on ground truth labels for gradi…
Waterloo AI Institute, University of Waterloo（滑铁卢人工智能研究所，滑铁卢大学）
The incredible effectiveness of adversarial attacks on fooling deep neural networks poses a tremendous hurdle in the widespread adoption of deep learning in safety and security-critical domains. While adversarial defense mechanisms have been proposed since the discovery of the adversarial vulnerability issue of deep neural networks, there is a long path to fully understand and address this issue. In this study, we hypothesize that part of the reason for the incredible effectiveness of adversarial attacks is their ability to implicitly tap into and exploit the gradient flow of a deep neural net…
Australian National University（澳大利亚国立大学）；Amazon Science（亚马逊科学）；DATA61, CSIRO（联邦科学与工业研究组织数据61）
Neural network quantization has become increasingly popular due to efficient memory consumption and faster computation resulting from bitwise operations on the quantized networks. Even though they exhibit excellent generalization capabilities, their robustness properties are not well-understood. In this work, we systematically study the robustness of quantized networks against gradient based adversarial attacks and demonstrate that these quantized models suffer from gradient vanishing issues and show a fake sense of robustness. By attributing gradient vanishing to poor forward-backward signal …
The vulnerability of deep neural networks to adversarial examples has drawn tremendous attention from the community. Three approaches, optimizing standard objective functions, exploiting attention maps, and smoothing decision surfaces, are commonly used to craft adversarial examples. By tightly integrating the three approaches, we propose a new and simple algorithm named Transferable Attack based on Integrated Gradients (TAIG) in this paper, which can find highly transferable adversarial examples for black-box attacks. Unlike previous methods using multiple computational terms or combining wit…
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…
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…
Adversarial attacks optimize against models to defeat defenses. Existing defenses are static, and stay the same once trained, even while attacks change. We argue that models should fight back, and optimize their defenses against attacks at test time. We propose dynamic defenses, to adapt the model and input during testing, by defensive entropy minimization (dent). Dent alters testing, but not training, for compatibility with existing models and train-time defenses. Dent improves the robustness of adversarially-trained defenses and nominally-trained models against white-box, black-box, and adap…
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…
Shanghai Jiao Tong University（上海交通大学）；OPPO Research Institute（OPPO研究院）；Tsinghua University（清华大学）
As designers of artificial intelligence try to outwit hackers, both sides continue to hone in on AI's inherent vulnerabilities. Designed and trained from certain statistical distributions of data, AI's deep neural networks (DNNs) remain vulnerable to deceptive inputs that violate a DNN's statistical, predictive assumptions. Before being fed into a neural network, however, most existing adversarial examples cannot maintain malicious functionality when applied to an affine transformation. For practical purposes, maintaining that malicious functionality serves as an important measure of the robus…
We consider the black-box adversarial setting, where the adversary has to generate adversarial perturbations without access to the target models to compute gradients. Previous methods tried to approximate the gradient either by using a transfer gradient of a surrogate white-box model, or based on the query feedback. However, these methods often suffer from low attack success rates or poor query efficiency since it is non-trivial to estimate the gradient in a high-dimensional space with limited information. To address these problems, we propose a prior-guided random gradient-free (P-RGF) method…
Hong Kong University of Science and Technology（香港科技大学）；University of California at Berkeley（加州大学伯克利分校）；University of Waterloo（滑铁卢大学）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
In this paper we introduce a provably stable architecture for Neural Ordinary Differential Equations (ODEs) which achieves non-trivial adversarial robustness under white-box adversarial attacks even when the network is trained naturally. For most existing defense methods withstanding strong white-box attacks, to improve robustness of neural networks, they need to be trained adversarially, hence have to strike a trade-off between natural accuracy and adversarial robustness. Inspired by dynamical system theory, we design a stabilized neural ODE network named SONet whose ODE blocks are skew-symme…
Huazhong University of Science and Technology（华中科技大学）；Peking University（北京大学）；Cornell University（康奈尔大学）
Deep learning models are vulnerable to adversarial examples crafted by applying human-imperceptible perturbations on benign inputs. However, under the black-box setting, most existing adversaries often have a poor transferability to attack other defense models. In this work, from the perspective of regarding the adversarial example generation as an optimization process, we propose two new methods to improve the transferability of adversarial examples, namely Nesterov Iterative Fast Gradient Sign Method (NI-FGSM) and Scale-Invariant attack Method (SIM). NI-FGSM aims to adapt Nesterov accelerate…
Ghent University（根特大学）；Ghent University Global Campus（根特大学全球校区）
After the discovery of adversarial examples and their adverse effects on deep learning models, many studies focused on finding more diverse methods to generate these carefully crafted samples. Although empirical results on the effectiveness of adversarial example generation methods against defense mechanisms are discussed in detail in the literature, an in-depth study of the theoretical properties and the perturbation effectiveness of these adversarial attacks has largely been lacking. In this paper, we investigate the objective functions of three popular methods for adversarial example genera…
Deep neural networks are susceptible to small-but-specific adversarial perturbations capable of deceiving the network. This vulnerability can lead to potentially harmful consequences in security-critical applications. To address this vulnerability, we propose a novel metric called \emph{Gradient Similarity} that allows us to capture the influence of training data on test inputs. We show that \emph{Gradient Similarity} behaves differently for normal and adversarial inputs, and enables us to detect a variety of adversarial attacks with a near perfect ROC-AUC of 95-100\%. Even white-box adversari…
Adversarial robust models have been shown to learn more robust and interpretable features than standard trained models. As shown in [\cite{tsipras2018robustness}], such robust models inherit useful interpretable properties where the gradient aligns perceptually well with images, and adding a large targeted adversarial perturbation leads to an image resembling the target class. We perform experiments to show that interpretable and perceptually aligned gradients are present even in models that do not show high robustness to adversarial attacks. Specifically, we perform adversarial training with …
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…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
Deep learning models suffer from a phenomenon called adversarial attacks: we can apply minor changes to the model input to fool a classifier for a particular example. The literature mostly considers adversarial attacks on models with images and other structured inputs. However, the adversarial attacks for categorical sequences can also be harmful. Successful attacks for inputs in the form of categorical sequences should address the following challenges: (1) non-differentiability of the target function, (2) constraints on transformations of initial sequences, and (3) diversity of possible probl…
Deep neural networks (DNNs) are playing key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in DNNs, which are almost imperceptibly different from original samples, but can greatly change the network output. Existing white-box attack algorithms can generate powerful adversarial examples. Nevertheless, most of the algorithms concentrate on how to iteratively make the best use of gradients to improve adversarial performance. In contrast, in this paper, …
Deep neural networks have been shown to be vulnerable to adversarial examples---maliciously crafted examples that can trigger the target model to misbehave by adding imperceptible perturbations. Existing attack methods for k-nearest neighbor~(kNN) based algorithms either require large perturbations or are not applicable for large k. To handle this problem, this paper proposes a new method called AdvKNN for evaluating the adversarial robustness of kNN-based models. Firstly, we propose a deep kNN block to approximate the output of kNN methods, which is differentiable thus can provide gradients f…
Princeton University（普林斯顿大学）；University of Oxford（牛津大学）
The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable adversarial robustness properties. However, when approximate Bayesian inference methods are employed, the adversarial robustness of BNNs is still not well understood. In this work, we employ gradient-free optimization methods in order to find adversarial examples for BNNs. In particular, we consider genetic algorithms, surrogate models, as well as zeroth order optimi…
The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in several machine learning algorithms was discovered: small perturbations added to the input data lead to consistent misclassification of data samples. Samples that easily mislead the model are called adversarial examples. Training a "maxout" network on adversarial examples has shown to decrease this vulnerability, but also increase classification performance. Thi…
Illinois Institute of Technology（伊利诺伊理工学院）；Rochester Institute of Technology（罗切斯特理工学院）
Deep learning models have been shown to be vulnerable to adversarial attacks. In particular, gradient-based attacks have demonstrated high success rates recently. The gradient measures how each image pixel affects the model output, which contains critical information for generating malicious perturbations. In this paper, we show that the gradients can also be exploited as a powerful weapon to defend against adversarial attacks. By using both gradient maps and adversarial images as inputs, we propose a Two-stream Restoration Network (TRN) to restore the adversarial images. To optimally restore …
Institute of Information Science（信息科学研究所）；Beijing Jiaotong University（北京交通大学）
Recent studies have shown that deep neural networks are vulnerable to adversarial examples, but most of the methods proposed to defense adversarial examples cannot solve this problem fundamentally. In this paper, we theoretically prove that there is an upper bound for neural networks with identity mappings to constrain the error caused by adversarial noises. However, in actual computations, this kind of neural network no longer holds any upper bound and is therefore susceptible to adversarial examples. Following similar procedures, we explain why adversarial examples can fool other deep neural…
While multi-step adversarial training is widely popular as an effective defense method against strong adversarial attacks, its computational cost is notoriously expensive, compared to standard training. Several single-step adversarial training methods have been proposed to mitigate the above-mentioned overhead cost; however, their performance is not sufficiently reliable depending on the optimization setting. To overcome such limitations, we deviate from the existing input-space-based adversarial training regime and propose a single-step latent adversarial training method (SLAT), which leverag…
Fudan University（复旦大学）；The University of Melbourne（墨尔本大学）
Evaluating the robustness of a defense model is a challenging task in adversarial robustness research. Obfuscated gradients have previously been found to exist in many defense methods and cause a false signal of robustness. In this paper, we identify a more subtle situation called Imbalanced Gradients that can also cause overestimated adversarial robustness. The phenomenon of imbalanced gradients occurs when the gradient of one term of the margin loss dominates and pushes the attack towards to a suboptimal direction. To exploit imbalanced gradients, we formulate a Margin Decomposition (MD) att…
Most adversarial attack defense methods rely on obfuscating gradients. These methods are successful in defending against gradient-based attacks; however, they are easily circumvented by attacks which either do not use the gradient or by attacks which approximate and use the corrected gradient. Defenses that do not obfuscate gradients such as adversarial training exist, but these approaches generally make assumptions about the attack such as its magnitude. We propose a classification model that does not obfuscate gradients and is robust by construction without assuming prior knowledge about the…
Adversarial training is an effective methodology for training deep neural networks that are robust against adversarial, norm-bounded perturbations. However, the computational cost of adversarial training grows prohibitively as the size of the model and number of input dimensions increase. Further, training against less expensive and therefore weaker adversaries produces models that are robust against weak attacks but break down under attacks that are stronger. This is often attributed to the phenomenon of gradient obfuscation; such models have a highly non-linear loss surface in the vicinity o…
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…
Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg（卢森堡大学安全、可靠性与信任跨学科中心）
Deep Neural Networks (DNNs) are vulnerable to adversarial examples, which causes serious threats to security-critical applications. This motivated much research on providing mechanisms to make models more robust against adversarial attacks. Unfortunately, most of these defenses, such as gradient masking, are easily overcome through different attack means. In this paper, we propose MUTEN, a low-cost method to improve the success rate of well-known attacks against gradient-masking models. Our idea is to apply the attacks on an ensemble model which is built by mutating the original model elements…
Adversarial examples, crafted by adding imperceptible perturbations to natural inputs, can easily fool deep neural networks (DNNs). One of the most successful methods for training adversarially robust DNNs is solving a nonconvex-nonconcave minimax problem with an adversarial training (AT) algorithm. However, among the many AT algorithms, only Dynamic AT (DAT) and You Only Propagate Once (YOPO) guarantee convergence to a stationary point. In this work, we generalize the stochastic primal-dual hybrid gradient algorithm to develop semi-implicit hybrid gradient methods (SI-HGs) for finding station…
Saarland University（萨尔兰大学）；University of Tübingen（蒂宾根大学）
Recently, Kannan et al. [2018] proposed several logit regularization methods to improve the adversarial robustness of classifiers. We show that the computationally fast methods they propose - Clean Logit Pairing (CLP) and Logit Squeezing (LSQ) - just make the gradient-based optimization problem of crafting adversarial examples harder without providing actual robustness. We find that Adversarial Logit Pairing (ALP) may indeed provide robustness against adversarial examples, especially when combined with adversarial training, and we examine it in a variety of settings. However, the increase in a…
Adversarial training is a technique for training robust machine learning models. To encourage robustness, it iteratively computes adversarial examples for the model, and then re-trains on these examples via some update rule. This work analyzes the performance of adversarial training on linearly separable data, and provides bounds on the number of iterations required for large margin. We show that when the update rule is given by an arbitrary empirical risk minimizer, adversarial training may require exponentially many iterations to obtain large margin. However, if gradient or stochastic gradie…
Algebraic Adversarial Attacks on Integrated Gradients
School of Electrical and Mechanical Engineering, The University of Adelaide（阿德莱德大学机电工程学院）；School of Computer and Mathematical Sciences, The University of Adelaide（阿德莱德大学计算机与数学科学学院）；Information Sciences Division, Defence Science & Technology Group（国防科技集团信息科学部）
Georg-August University of Göttingen（哥廷根乔治-奥古斯特大学）；University of Tübingen（图宾根大学）
A recent paper by Liu et al. combines the topics of adversarial training and Bayesian Neural Networks (BNN) and suggests that adversarially trained BNNs are more robust against adversarial attacks than their non-Bayesian counterparts. Here, I analyze the proposed defense and suggest that one needs to adjust the adversarial attack to incorporate the stochastic nature of a Bayesian network to perform an accurate evaluation of its robustness. Using this new type of attack I show that there appears to be no strong evidence for higher robustness of the adversarially trained BNNs.
University of Oregon（俄勒冈大学）；Nanyang Technological University（南洋理工大学）
Deep neural networks (DNNs) have had many successes, but they suffer from two major issues: (1) a vulnerability to adversarial examples and (2) a tendency to elude human interpretation. Interestingly, recent empirical and theoretical evidence suggests these two seemingly disparate issues are actually connected. In particular, robust models tend to provide more interpretable gradients than non-robust models. However, whether this relationship works in the opposite direction remains obscure. With this paper, we seek empirical answers to the following question: can models acquire adversarial robu…
Politecnico di Torino（都灵理工大学）；Technische Universität Wien (TU Wien)（维也纳工业大学（维也纳技术大学））；New York University Abu Dhabi（纽约大学阿布扎比分校）
Adversarial training is exploited to develop a robust Deep Neural Network (DNN) model against the malicious altered data. These attacks may have catastrophic effects on DNN models but are indistinguishable for a human being. For example, an external attack can modify an image adding noises invisible for a human eye, but a DNN model misclassified the image. A key objective for developing robust DNN models is to use a learning algorithm that is fast but can also give model that is robust against different types of adversarial attacks. Especially for adversarial training, enormously long training…
Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学保尔森工程与应用科学学院）
Deep neural networks have proven remarkably effective at solving many classification problems, but have been criticized recently for two major weaknesses: the reasons behind their predictions are uninterpretable, and the predictions themselves can often be fooled by small adversarial perturbations. These problems pose major obstacles for the adoption of neural networks in domains that require security or transparency. In this work, we evaluate the effectiveness of defenses that differentiably penalize the degree to which small changes in inputs can alter model predictions. Across multiple atta…
Deep neural networks have shown to be very vulnerable to adversarial examples crafted by adding human-imperceptible perturbations to benign inputs. After achieving impressive attack success rates in the white-box setting, more focus is shifted to black-box attacks. In either case, the common gradient-based approaches generally use the $sign$ function to generate perturbations at the end of the process. However, only a few works pay attention to the limitation of the $sign$ function. Deviation between the original gradient and the generated noises may lead to inaccurate gradient update estimati…
Modern neural networks are highly non-robust against adversarial manipulation. A significant amount of work has been invested in techniques to compute lower bounds on robustness through formal guarantees and to build provably robust models. However, it is still difficult to get guarantees for larger networks or robustness against larger perturbations. Thus attack strategies are needed to provide tight upper bounds on the actual robustness. We significantly improve the randomized gradient-free attack for ReLU networks [9], in particular by scaling it up to large networks. We show that our attac…
Making deep neural networks robust to small adversarial noises has recently been sought in many applications. Adversarial training through iterative projected gradient descent (PGD) has been established as one of the mainstream ideas to achieve this goal. However, PGD is computationally demanding and often prohibitive in case of large datasets and models. For this reason, single-step PGD, also known as FGSM, has recently gained interest in the field. Unfortunately, FGSM-training leads to a phenomenon called ``catastrophic overfitting," which is a sudden drop in the adversarial accuracy under t…
Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and deploying this method - expensive in terms of extra memory and computation costs; accuracy trade-off between clean and adversarial examples; and lack of diversity of adversarial perturbations. Classical adversarial training uses fixed, precomputed perturbations in adversarial examples (input space). In contrast, we introduce dynamic adversarial perturbations i…
University of Trieste（的里雅斯特大学）；University of Oxford（牛津大学）；SISSA（国际高等研究院）
Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we …
