First-order Adversarial Vulnerability of Neural Networks and Input Dimension
Facebook AI Research（Facebook人工智能研究院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Carl-Johann Simon-Gabriel, Yann Ollivier, Léon Bottou, Bernhard Schölkopf, David Lopez-Paz
备注：
Paper previously called: "Adversarial Vulnerability of Neural Networks Increases with Input Dimension". 9 pages main text and references, 11 pages appendix, 14 figures
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisingly, vulnerability does not depend on network topology: for many standard network architectures, we prove that at initialization, the $\ell_1$-norm of these gradients grows as the square root of the input dimension, leaving the networks increasingly vulnerable with growing image size. We empirically show that this dimension dependence persists after either usual or robust training, but gets attenuated with higher regularization.
Despite the remarkable performance of deep neural networks on various computer vision tasks, they are known to be susceptible to adversarial perturbations, which makes it challenging to deploy them in real-world safety-critical applications. In this paper, we conjecture that the leading cause of adversarial vulnerability is the distortion in the latent feature space, and provide methods to suppress them effectively. Explicitly, we define \emph{vulnerability} for each latent feature and then propose a new loss for adversarial learning, \emph{Vulnerability Suppression (VS)} loss, that aims to mi…
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.
Neural networks are vulnerable to adversarial attacks -- small visually imperceptible crafted noise which when added to the input drastically changes the output. The most effective method of defending against these adversarial attacks is to use the methodology of adversarial training. We analyze the adversarially trained robust models to study their vulnerability against adversarial attacks at the level of the latent layers. Our analysis reveals that contrary to the input layer which is robust to adversarial attack, the latent layer of these robust models are highly susceptible to adversarial …
Univ Lyon（里昂大学）；ENS de Lyon（里昂高等师范学院）；CNRS（法国国家科学研究中心）；UCBL（里昂第一大学）；DeepMind（深度思维）；University of Cambridge（剑桥大学）
Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the data is generated with a smooth generative model. We derive fundamental upper bounds on the robustness to perturbations of any classification function, and prove the existence of adversarial perturbations that transfer well across different classifiers with small risk. Our analy…
Korea Advanced Institute of Science Technology (KAIST)（韩国科学技术院）
Batch normalization (BN) has been widely used in modern deep neural networks (DNNs) due to improved convergence. BN is observed to increase the model accuracy while at the cost of adversarial robustness. There is an increasing interest in the ML community to understand the impact of BN on DNNs, especially related to the model robustness. This work attempts to understand the impact of BN on DNNs from a non-robust feature perspective. Straightforwardly, the improved accuracy can be attributed to the better utilization of useful features. It remains unclear whether BN mainly favors learning robus…
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.
University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；University College London（伦敦大学学院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Google Brain（谷歌大脑）
Batch normalization (batch norm) is often used in an attempt to stabilize and accelerate training in deep neural networks. In many cases it indeed decreases the number of parameter updates required to achieve low training error. However, it also reduces robustness to small adversarial input perturbations and noise by double-digit percentages, as we show on five standard datasets. Furthermore, substituting weight decay for batch norm is sufficient to nullify the relationship between adversarial vulnerability and the input dimension. Our work is consistent with a mean-field analysis that found t…
Deep neural networks are susceptible to adversarial manipulations in the input domain. The extent of vulnerability has been explored intensively in cases of $\ell_p$-bounded and $\ell_p$-minimal adversarial perturbations. However, the vulnerability of DNNs to adversarial perturbations with specific statistical properties or frequency-domain characteristics has not been sufficiently explored. In this paper, we study the smoothness of perturbations and propose SmoothFool, a general and computationally efficient framework for computing smooth adversarial perturbations. Through extensive experimen…
Adversarial attack perturbs an image with an imperceptible noise, leading to incorrect model prediction. Recently, a few works showed inherent bias associated with such attack (robustness bias), where certain subgroups in a dataset (e.g. based on class, gender, etc.) are less robust than others. This bias not only persists even after adversarial training, but often results in severe performance discrepancies across these subgroups. Existing works characterize the subgroup's robustness bias by only checking individual sample's proximity to the decision boundary. In this work, we argue that this…
University of Sheffield（谢菲尔德大学）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
Machine learning (ML) classification is increasingly used in safety-critical systems. Protecting ML classifiers from adversarial examples is crucial. We propose that the main threat is that of an attacker perturbing a confidently classified input to produce a confident misclassification. To protect against this we devise an adversarial bound (AB) for a Gaussian process classifier, that holds for the entire input domain, bounding the potential for any future adversarial method to cause such misclassification. This is a formal guarantee of robustness, not just an empirically derived result. We i…
Vector Institute（向量研究所）；University of Toronto（多伦多大学）；University of Bremen（不来梅大学）；Center for Industrial Mathematics（工业数学中心）；University of Tübingen（图宾根大学）
Despite their impressive performance, deep neural networks exhibit striking failures on out-of-distribution inputs. One core idea of adversarial example research is to reveal neural network errors under such distribution shifts. We decompose these errors into two complementary sources: sensitivity and invariance. We show deep networks are not only too sensitive to task-irrelevant changes of their input, as is well-known from epsilon-adversarial examples, but are also too invariant to a wide range of task-relevant changes, thus making vast regions in input space vulnerable to adversarial attack…
School of Physics, Sun Yat-sen University（中山大学物理学院）
Artificial neural networks can achieve impressive performances, and even outperform humans in some specific tasks. Nevertheless, unlike biological brains, the artificial neural networks suffer from tiny perturbations in sensory input, under various kinds of adversarial attacks. It is therefore necessary to study the origin of the adversarial vulnerability. Here, we establish a fundamental relationship between geometry of hidden representations (manifold perspective) and the generalization capability of the deep networks. For this purpose, we choose a deep neural network trained by local errors…
Batch Normalization (BatchNorm) is effective for improving the performance and accelerating the training of deep neural networks. However, it has also shown to be a cause of adversarial vulnerability, i.e., networks without it are more robust to adversarial attacks. In this paper, we investigate how BatchNorm causes this vulnerability and proposed new normalization that is robust to adversarial attacks. We first observe that adversarial images tend to shift the distribution of BatchNorm input, and this shift makes train-time estimated population statistics inaccurate. We hypothesize that these…
Waterloo AI Institute, University of Waterloo（滑铁卢大学滑铁卢人工智能研究所）；ADC Automotive Distance Control Systems GmbH, Continental（大陆集团ADC汽车距离控制系统有限公司）
Prior studies have unveiled the vulnerability of the deep neural networks in the context of adversarial machine learning, leading to great recent attention into this area. One interesting question that has yet to be fully explored is the bias-variance relationship of adversarial machine learning, which can potentially provide deeper insights into this behaviour. The notion of bias and variance is one of the main approaches to analyze and evaluate the generalization and reliability of a machine learning model. Although it has been extensively used in other machine learning models, it is not wel…
Recently, Convolutional Neural Networks (CNNs) demonstrate a considerable vulnerability to adversarial attacks, which can be easily misled by adversarial perturbations. With more aggressive methods proposed, adversarial attacks can be also applied to the physical world, causing practical issues to various CNN powered applications. To secure CNNs, adversarial attack detection is considered as the most critical approach. However, most existing works focus on superficial patterns and merely search a particular method to differentiate the adversarial inputs and natural inputs, ignoring the analysi…
The adversarial vulnerability of deep neural networks (DNNs) has been actively investigated in the past several years. This paper investigates the scale-variant property of cross-entropy loss, which is the most commonly used loss function in classification tasks, and its impact on the effective margin and adversarial robustness of deep neural networks. Since the loss function is not invariant to logit scaling, increasing the effective weight norm will make the loss approach zero and its gradient vanish while the effective margin is not adequately maximized. On typical DNNs, we demonstrate that…
Huazhong University of Science and Technology（华中科技大学）
Deep learning has been successfully used in numerous applications because of its outstanding performance and the ability to avoid manual feature engineering. One such application is electroencephalogram (EEG) based brain-computer interface (BCI), where multiple convolutional neural network (CNN) models have been proposed for EEG classification. However, it has been found that deep learning models can be easily fooled with adversarial examples, which are normal examples with small deliberate perturbations. This paper proposes an unsupervised fast gradient sign method (UFGSM) to attack three pop…
Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges. To better understand adversarial robustness, we consider the underlying problem of learning robust representations. We develop a notion of representation vulnerability that captures the maximum change of mutual information between the input and output distributions, under the worst-case input perturbation. Then, we prove a theorem that establishes a lower bound on the minimum adversarial risk that can be achieved for any downstream classifier based on its representation vulner…
East China Normal University（华东师范大学）；University of Virginia（弗吉尼亚大学）；Shanghai University（上海大学）；Westlake Institute for Brain-Like Science and Technology（西湖高等研究院脑与脑类科学研究所）
Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide a reasonable explanation for the vulnerability of deep learning models. By considering the data space as a non-linear space with the Fisher information metric induced from a neural network, we first propose an adversarial attack algorithm termed one-step spectral attack (OSSA). The method is described by a constrained quadratic form of the Fisher information…
Deep Neural Networks (DNNs) are often vulnerable to adversarial examples.Several proposed defenses deploy an ensemble of models with the hope that, although the individual models may be vulnerable, an adversary will not be able to find an adversarial example that succeeds against the ensemble. Depending on how the ensemble is used, an attacker may need to find a single adversarial example that succeeds against all, or a majority, of the models in the ensemble. The effectiveness of ensemble defenses against strong adversaries depends on the vulnerability spaces of models in the ensemble being d…
Duke University（杜克大学）；Radiance Technologies（辐射技术公司）
Recent research finds CNN models for image classification demonstrate overlapped adversarial vulnerabilities: adversarial attacks can mislead CNN models with small perturbations, which can effectively transfer between different models trained on the same dataset. Adversarial training, as a general robustness improvement technique, eliminates the vulnerability in a single model by forcing it to learn robust features. The process is hard, often requires models with large capacity, and suffers from significant loss on clean data accuracy. Alternatively, ensemble methods are proposed to induce sub…
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 …
Ghent University（根特大学）；Ghent University Global Campus（根特大学全球校区）
Deep learning models, which are increasingly being used in the field of medical image analysis, come with a major security risk, namely, their vulnerability to adversarial examples. Adversarial examples are carefully crafted samples that force machine learning models to make mistakes during testing time. These malicious samples have been shown to be highly effective in misguiding classification tasks. However, research on the influence of adversarial examples on segmentation is significantly lacking. Given that a large portion of medical imaging problems are effectively segmentation problems, …
Previous work on adversarially robust neural networks for image classification requires large training sets and computationally expensive training procedures. On the other hand, few-shot learning methods are highly vulnerable to adversarial examples. The goal of our work is to produce networks which both perform well at few-shot classification tasks and are simultaneously robust to adversarial examples. We develop an algorithm, called Adversarial Querying (AQ), for producing adversarially robust meta-learners, and we thoroughly investigate the causes for adversarial vulnerability. Moreover, ou…
Georgia Institute of Technology（佐治亚理工学院）；IBM Research（IBM研究院）；Preferred Network America（美国首选网络公司）；Columbia University（哥伦比亚大学）
Recent deep neural networks based techniques, especially those equipped with the ability of self-adaptation in the system level such as deep reinforcement learning (DRL), are shown to possess many advantages of optimizing robot learning systems (e.g., autonomous navigation and continuous robot arm control.) However, the learning-based systems and the associated models may be threatened by the risks of intentionally adaptive (e.g., noisy sensor confusion) and adversarial perturbations from real-world scenarios. In this paper, we introduce timing-based adversarial strategies against a DRL-based …
Michigan State University（密歇根州立大学）；Texas A&M University（得克萨斯农工大学）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）
Deep neural networks (DNNs) have achieved significant performance in various tasks. However, recent studies have shown that DNNs can be easily fooled by small perturbation on the input, called adversarial attacks. As the extensions of DNNs to graphs, Graph Neural Networks (GNNs) have been demonstrated to inherit this vulnerability. Adversary can mislead GNNs to give wrong predictions by modifying the graph structure such as manipulating a few edges. This vulnerability has arisen tremendous concerns for adapting GNNs in safety-critical applications and has attracted increasing research attentio…
While machine learning is going through an era of celebrated success, concerns have been raised about the vulnerability of its backbone: stochastic gradient descent (SGD). Recent approaches have been proposed to ensure the robustness of distributed SGD against adversarial (Byzantine) workers sending poisoned gradients during the training phase. Some of these approaches have been proven Byzantine-resilient: they ensure the convergence of SGD despite the presence of a minority of adversarial workers. We show in this paper that convergence is not enough. In high dimension $d \gg 1$, an adver\-sar…
School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学院）
The Renormalisation Group (RG) provides a framework in which it is possible to assess whether a deep-learning network is sensitive to small changes in the input data and hence prone to error, or susceptible to adversarial attack. Distinct classification outputs are associated with different RG fixed points and sensitivity to small changes in the input data is due to the presence of relevant operators at a fixed point. A numerical scheme, based on Monte Carlo RG ideas, is proposed for identifying the existence of relevant operators and the corresponding directions of greatest sensitivity in the…
