Adversarial training can considerably robustify deep neural networks to resist adversarial attacks. However, some works suggested that adversarial training might comprise the privacy-preserving and generalization abilities. This paper establishes and quantifies the privacy-robustness trade-off and generalization-robustness trade-off in adversarial training from both theoretical and empirical aspects. We first define a notion, {\it robustified intensity} to measure the robustness of an adversarial training algorithm. This measure can be approximate empirically by an asymptotically consistent empirical estimator, {\it empirical robustified intensity}. Based on the robustified intensity, we prove that (1) adversarial training is $(\varepsilon, δ)$-differentially private, where the magnitude of the differential privacy has a positive correlation with the robustified intensity; and (2) the generalization error of adversarial training can be upper bounded by an $\mathcal O(\sqrt{\log N}/N)$ on-average bound and an $\mathcal O(1/\sqrt{N})$ high-probability bound, both of which have positive correlations with the robustified intensity. Additionally, our generalization bounds do not explicitly rely on the parameter size which would be prohibitively large in deep learning. Systematic experiments on standard datasets, CIFAR-10 and CIFAR-100, are in full agreement with our theories. The source code package is available at \url{https://github.com/fshp971/RPG}.
Adversarial examples that fool machine learning models, particularly deep neural networks, have been a topic of intense research interest, with attacks and defenses being developed in a tight back-and-forth. Most past defenses are best effort and have been shown to be vulnerable to sophisticated attacks. Recently a set of certified defenses have been introduced, which provide guarantees of robustness to norm-bounded attacks, but they either do not scale to large datasets or are limited in the types of models they can support. This paper presents the first certified defense that both scales to …
Université Paris-Dauphine, PSL Research University（巴黎第九大学，PSL研究大学）；Institut LIST, CEA（法国原子能与替代能源委员会LIST研究所）；Université Paris-Saclay（巴黎萨克雷大学）
This short note highlights some links between two lines of research within the emerging topic of trustworthy machine learning: differential privacy and robustness to adversarial examples. By abstracting the definitions of both notions, we show that they build upon the same theoretical ground and hence results obtained so far in one domain can be transferred to the other. More precisely, our analysis is based on two key elements: probabilistic mappings (also called randomized algorithms in the differential privacy community), and the Renyi divergence which subsumes a large family of divergences…
In this paper, we aim to understand the generalization properties of generative adversarial networks (GANs) from a new perspective of privacy protection. Theoretically, we prove that a differentially private learning algorithm used for training the GAN does not overfit to a certain degree, i.e., the generalization gap can be bounded. Moreover, some recent works, such as the Bayesian GAN, can be re-interpreted based on our theoretical insight from privacy protection. Quantitatively, to evaluate the information leakage of well-trained GAN models, we perform various membership attacks on these mo…
University of Electronic Science and Technology of China（电子科技大学）；Georgia State University（佐治亚州立大学）
Recently, the surge in popularity of Internet of Things (IoT), mobile devices, social media, etc. has opened up a large source for graph data. Graph embedding has been proved extremely useful to learn low-dimensional feature representations from graph structured data. These feature representations can be used for a variety of prediction tasks from node classification to link prediction. However, existing graph embedding methods do not consider users' privacy to prevent inference attacks. That is, adversaries can infer users' sensitive information by analyzing node representations learned from …
We study the transfer of adversarial robustness of deep neural networks between different perturbation types. While most work on adversarial examples has focused on $L_\infty$ and $L_2$-bounded perturbations, these do not capture all types of perturbations available to an adversary. The present work evaluates 32 attacks of 5 different types against models adversarially trained on a 100-class subset of ImageNet. Our empirical results suggest that evaluating on a wide range of perturbation sizes is necessary to understand whether adversarial robustness transfers between perturbation types. We fu…
Beijing Jiaotong University（北京交通大学）；Peng Cheng Laboratory（鹏城实验室）；Beijing University of Technology（北京工业大学）；Beijing Artificial Intelligence Institute（北京人工智能研究院）
While widely adopted in practical applications, face recognition has been critically discussed regarding the malicious use of face images and the potential privacy problems, e.g., deceiving payment system and causing personal sabotage. Online photo sharing services unintentionally act as the main repository for malicious crawler and face recognition applications. This work aims to develop a privacy-preserving solution, called Adversarial Privacy-preserving Filter (APF), to protect the online shared face images from being maliciously used.We propose an end-cloud collaborated adversarial attack …
With increasing usage of deep learning algorithms in many application, new research questions related to privacy and adversarial attacks are emerging. However, the deep learning algorithm improvement needs more and more data to be shared within research community. Methodologies like federated learning, differential privacy, additive secret sharing provides a way to train machine learning models on edge without moving the data from the edge. However, it is very computationally intensive and prone to adversarial attacks. Therefore, this work introduces a privacy preserving FedCollabNN framework …
Adversarial training was introduced as a way to improve the robustness of deep learning models to adversarial attacks. This training method improves robustness against adversarial attacks, but increases the models vulnerability to privacy attacks. In this work we demonstrate how model inversion attacks, extracting training data directly from the model, previously thought to be intractable become feasible when attacking a robustly trained model. The input space for a traditionally trained model is dominated by adversarial examples - data points that strongly activate a certain class but lack se…
Historically, machine learning methods have not been designed with security in mind. In turn, this has given rise to adversarial examples, carefully perturbed input samples aimed to mislead detection at test time, which have been applied to attack spam and malware classification, and more recently to attack image classification. Consequently, an abundance of research has been devoted to designing machine learning methods that are robust to adversarial examples. Unfortunately, there are desiderata besides robustness that a secure and safe machine learning model must satisfy, such as fairness an…
Adversarial training is one of the most effective approaches defending against adversarial examples for deep learning models. Unlike other defense strategies, adversarial training aims to promote the robustness of models intrinsically. During the last few years, adversarial training has been studied and discussed from various aspects. A variety of improvements and developments of adversarial training are proposed, which were, however, neglected in existing surveys. For the first time in this survey, we systematically review the recent progress on adversarial training for adversarial robustness…
George Mason University（乔治梅森大学）；Clarkson University（克拉克森大学）；Northeastern University（东北大学）
One popular hypothesis of neural network generalization is that the flat local minima of loss surface in parameter space leads to good generalization. However, we demonstrate that loss surface in parameter space has no obvious relationship with generalization, especially under adversarial settings. Through visualizing decision surfaces in both parameter space and input space, we instead show that the geometry property of decision surface in input space correlates well with the adversarial robustness. We then propose an adversarial robustness indicator, which can evaluate a neural network's int…
In Federated Learning (FL), models are as fragile as centrally trained models against adversarial examples. However, the adversarial robustness of federated learning remains largely unexplored. This paper casts light on the challenge of adversarial robustness of federated learning. To facilitate a better understanding of the adversarial vulnerability of the existing FL methods, we conduct comprehensive robustness evaluations on various attacks and adversarial training methods. Moreover, we reveal the negative impacts induced by directly adopting adversarial training in FL, which seriously hurt…
Privacy-preserving Universal Adversarial Defense for Black-box Models
School of Cyber Science and Engineering, Wuhan University（武汉大学网络科学与工程学院）；City University of Hong Kong (CityU)（香港城市大学）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
University of Florida（佛罗里达大学）；Washington University in St. Louis（圣路易斯华盛顿大学）
We present a framework to learn privacy-preserving encodings of images that inhibit inference of chosen private attributes, while allowing recovery of other desirable information. Rather than simply inhibiting a given fixed pre-trained estimator, our goal is that an estimator be unable to learn to accurately predict the private attributes even with knowledge of the encoding function. We use a natural adversarial optimization-based formulation for this---training the encoding function against a classifier for the private attribute, with both modeled as deep neural networks. The key contribution…
Heilongjiang University（黑龙江大学）；Southern University of Science and Technology（南方科技大学）
Generative Adversarial Network (GAN) and its variants serve as a perfect representation of the data generation model, providing researchers with a large amount of high-quality generated data. They illustrate a promising direction for research with limited data availability. When GAN learns the semantic-rich data distribution from a dataset, the density of the generated distribution tends to concentrate on the training data. Due to the gradient parameters of the deep neural network contain the data distribution of the training samples, they can easily remember the training samples. When GAN is …
It has been shown that deep neural networks (DNNs) may be vulnerable to adversarial attacks, raising the concern on their robustness particularly for safety-critical applications. Recognizing the local nature and limitations of existing adversarial attacks, we present a new type of global adversarial attacks for assessing global DNN robustness. More specifically, we propose a novel concept of global adversarial example pairs in which each pair of two examples are close to each other but have different class labels predicted by the DNN. We further propose two families of global attack methods a…
Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. We prove that a trade-off in robustness to different types of $\ell_p$-bounded and spatial perturbations must exist in a natural and simple statistical setting. We corro…
Information Technology University (ITU)-Punjab（旁遮普信息技术大学）；University of Southern Queensland（南昆士兰大学）
Deep learning has undoubtedly offered tremendous improvements in the performance of state-of-the-art speech emotion recognition (SER) systems. However, recent research on adversarial examples poses enormous challenges on the robustness of SER systems by showing the susceptibility of deep neural networks to adversarial examples as they rely only on small and imperceptible perturbations. In this study, we evaluate how adversarial examples can be used to attack SER systems and propose the first black-box adversarial attack on SER systems. We also explore potential defenses including adversarial t…
Google（谷歌）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
In this paper we study leveraging confidence information induced by adversarial training to reinforce adversarial robustness of a given adversarially trained model. A natural measure of confidence is $\|F({\bf x})\|_\infty$ (i.e. how confident $F$ is about its prediction?). We start by analyzing an adversarial training formulation proposed by Madry et al.. We demonstrate that, under a variety of instantiations, an only somewhat good solution to their objective induces confidence to be a discriminator, which can distinguish between right and wrong model predictions in a neighborhood of a point …
IBM Research（IBM研究院）；Michigan State University（密歇根州立大学）
Adversarial robustness studies the worst-case performance of a machine learning model to ensure safety and reliability. With the proliferation of deep-learning-based technology, the potential risks associated with model development and deployment can be amplified and become dreadful vulnerabilities. This paper provides a comprehensive overview of research topics and foundational principles of research methods for adversarial robustness of deep learning models, including attacks, defenses, verification, and novel applications.
We augment adversarial training (AT) with worst case adversarial training (WCAT) which improves adversarial robustness by 11% over the current state-of-the-art result in the $\ell_2$ norm on CIFAR-10. We obtain verifiable average case and worst case robustness guarantees, based on the expected and maximum values of the norm of the gradient of the loss. We interpret adversarial training as Total Variation Regularization, which is a fundamental tool in mathematical image processing, and WCAT as Lipschitz regularization.
TrajSyn: Privacy-Preserving Dataset Distillation from Federated Model Trajectories for Server-Side Adversarial Training
Computer Science Department, Columbia University（哥伦比亚大学计算机科学系）；School of Computer Science and Engineering, Vellore Institute of Technology（维洛雷理工学院计算机科学与工程学院）；School of Information Technology, Deakin University（德肯大学信息科技学院）
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）
Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and generalization are conflicting goals. In an effort to clarify the relationship between robustness and generalization, we assume an underlying, low-dimensional data manifold and show that: 1. regular adversarial examples leave the manifold; 2. adversarial examples constrained to the manifold, i.e., on-manifold adversarial examples, exist; 3. on-manifold adversarial exampl…
Nanjing University of Science and Technology（南京理工大学）；Data61, CSIRO（澳大利亚联邦科学与工业研究组织 Data61）；University of Technology Sydney（悉尼科技大学）；Jinan University（暨南大学）；Princeton University（普林斯顿大学）
Generative adversarial network (GAN) has attracted increasing attention recently owing to its impressive ability to generate realistic samples with high privacy protection. Without directly interactive with training examples, the generative model can be fully used to estimate the underlying distribution of an original dataset while the discriminative model can examine the quality of the generated samples by comparing the label values with the training examples. However, when GANs are applied on sensitive or private training examples, such as medical or financial records, it is still probable t…
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 …
A privacy-preserving adversarial network (PPAN) was recently proposed as an information-theoretical framework to address the issue of privacy in data sharing. The main idea of this model was using mutual information as the privacy measure and adversarial training of two deep neural networks, one as the mechanism and another as the adversary. The performance of the PPAN model for the discrete synthetic data, MNIST handwritten digits, and continuous Gaussian data was evaluated compared to the analytically optimal trade-off. In this study, we evaluate the PPAN model for continuous non-Gaussian da…
The existence of adversarial examples has led to considerable uncertainty regarding the trust one can justifiably put in predictions produced by automated systems. This uncertainty has, in turn, lead to considerable research effort in understanding adversarial robustness. In this work, we take first steps towards separating robustness analysis from the choice of robustness threshold and norm. We propose robustness curves as a more general view of the robustness behavior of a model and investigate under which circumstances they can qualitatively depend on the chosen norm.
Deep neural networks are susceptible to adversarial inputs and various methods have been proposed to defend these models against adversarial attacks under different perturbation models. The robustness of models to adversarial attacks has been analyzed by first constructing adversarial inputs for the model, and then testing the model performance on the constructed adversarial inputs. Most of these attacks require the model to be white-box, need access to data labels, and finding adversarial inputs can be computationally expensive. We propose a simple scoring method for black-box models which in…
Indian Institute of Technology, Hyderabad（印度理工学院海得拉巴分校）；Microsoft（微软）；Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）
Adversarial robustness of deep learning models has gained much traction in the last few years. Various attacks and defenses are proposed to improve the adversarial robustness of modern-day deep learning architectures. While all these approaches help improve the robustness, one promising direction for improving adversarial robustness is unexplored, i.e., the complex topology of the neural network architecture. In this work, we address the following question: Can the complex topology of a neural network give adversarial robustness without any form of adversarial training?. We answer this empiric…
We study the model robustness against adversarial examples, referred to as small perturbed input data that may however fool many state-of-the-art deep learning models. Unlike previous research, we establish a novel theory addressing the robustness issue from the perspective of stability of the loss function in the small neighborhood of natural examples. We propose to exploit an energy function to describe the stability and prove that reducing such energy guarantees the robustness against adversarial examples. We also show that the traditional training methods including adversarial training wit…
We evaluate the robustness of Adversarial Logit Pairing, a recently proposed defense against adversarial examples. We find that a network trained with Adversarial Logit Pairing achieves 0.6% accuracy in the threat model in which the defense is considered. We provide a brief overview of the defense and the threat models/claims considered, as well as a discussion of the methodology and results of our attack, which may offer insights into the reasons underlying the vulnerability of ALP to adversarial attack.
SAFE: Secure and Accurate Federated Learning for Privacy-Preserving Brain-Computer Interfaces
Key Laboratory of the Ministry of Education for Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（教育部图像处理与智能控制重点实验室，人工智能与自动化学院，华中科技大学）；Zhongguancun Academy（中关村学院）
Deep neural networks are vulnerable against adversarial examples. In this paper, we propose to train and test the networks with randomly subsampled images with high drop rates. We show that this approach significantly improves robustness against adversarial examples in all cases of bounded L0, L2 and L_inf perturbations, while reducing the standard accuracy by a small value. We argue that subsampling pixels can be thought to provide a set of robust features for the input image and, thus, improves robustness without performing adversarial training.
Neural Networks have been shown to be sensitive to common perturbations such as blur, Gaussian noise, rotations, etc. They are also vulnerable to some artificial malicious corruptions called adversarial examples. The adversarial examples study has recently become very popular and it sometimes even reduces the term "adversarial robustness" to the term "robustness". Yet, we do not know to what extent the adversarial robustness is related to the global robustness. Similarly, we do not know if a robustness to various common perturbations such as translations or contrast losses for instance, could …
Adversarial training has proven to be effective in hardening networks against adversarial examples. However, the gained robustness is limited by network capacity and number of training samples. Consequently, to build more robust models, it is common practice to train on widened networks with more parameters. To boost robustness, we propose a conditional normalization module to adapt networks when conditioned on input samples. Our adaptive networks, once adversarially trained, can outperform their non-adaptive counterparts on both clean validation accuracy and robustness. Our method is objectiv…
Adversarial training is one effective approach for training robust deep neural networks against adversarial attacks. While being able to bring reliable robustness, adversarial training (AT) methods in general favor high capacity models, i.e., the larger the model the better the robustness. This tends to limit their effectiveness on small models, which are more preferable in scenarios where storage or computing resources are very limited (e.g., mobile devices). In this paper, we leverage the concept of knowledge distillation to improve the robustness of small models by distilling from adversari…
Network pruning has been known to produce compact models without much accuracy degradation. However, how the pruning process affects a network's robustness and the working mechanism behind remain unresolved. In this work, we theoretically prove that the sparsity of network weights is closely associated with model robustness. Through experiments on a variety of adversarial pruning methods, we find that weights sparsity will not hurt but improve robustness, where both weights inheritance from the lottery ticket and adversarial training improve model robustness in network pruning. Based on these …
Flow-based generative models leverage invertible generator functions to fit a distribution to the training data using maximum likelihood. Despite their use in several application domains, robustness of these models to adversarial attacks has hardly been explored. In this paper, we study adversarial robustness of flow-based generative models both theoretically (for some simple models) and empirically (for more complex ones). First, we consider a linear flow-based generative model and compute optimal sample-specific and universal adversarial perturbations that maximally decrease the likelihood s…
PAT: Privacy-Preserving Adversarial Transfer for Accurate, Robust and Privacy-Preserving EEG Decoding
Hubei Key Laboratory of Brain-inspired Intelligent Systems, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院脑启发智能系统湖北省重点实验室）；Shenzhen Huazhong University of Science and Technology Research Institute（深圳华中科技大学研究院）；Zhongguancun Academy（中关村学院）
Neural networks lack adversarial robustness, i.e., they are vulnerable to adversarial examples that through small perturbations to inputs cause incorrect predictions. Further, trust is undermined when models give miscalibrated predictions, i.e., the predicted probability is not a good indicator of how much we should trust our model. In this paper, we study the connection between adversarial robustness and calibration and find that the inputs for which the model is sensitive to small perturbations (are easily attacked) are more likely to have poorly calibrated predictions. Based on this insight…
Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against adversarial attacks. Beside exploiting adversarial training framework, we show that by enforcing a Deep Neural Network (DNN) to be linear in transformed input and feature space improves robustness significantly. We also demonstrate that by augmenting the objective function with Local Lipschitz regularizer boost robustness of the model further. Our method out…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Texas, Austin（得克萨斯大学奥斯汀分校）；IBM research AI（IBM研究院人工智能部门）
Adversarial training has become one of the most effective methods for improving robustness of neural networks. However, it often suffers from poor generalization on both clean and perturbed data. In this paper, we propose a new algorithm, named Customized Adversarial Training (CAT), which adaptively customizes the perturbation level and the corresponding label for each training sample in adversarial training. We show that the proposed algorithm achieves better clean and robust accuracy than previous adversarial training methods through extensive experiments.
University of Oxford（牛津大学）；Oxford-Man Institute（牛津-曼学院）
It is desirable, and often a necessity, for machine learning models to be robust against adversarial attacks. This is particularly true for Bayesian models, as they are well-suited for safety-critical applications, in which adversarial attacks can have catastrophic outcomes. In this work, we take a deeper look at the adversarial robustness of Bayesian Neural Networks (BNNs). In particular, we consider whether the adversarial robustness of a BNN can be increased by model choices, particularly the Lipschitz continuity induced by the prior. Conducting in-depth analysis on the case of i.i.d., zero…
Convolutional neural networks (CNNs) are known for their good performance and generalization in vision-related tasks and have become state-of-the-art in both application and research-based domains. However, just like other neural network models, they suffer from a susceptibility to noise and adversarial attacks. An adversarial defence aims at reducing a neural network's susceptibility to adversarial attacks through learning or architectural modifications. We propose the weight map layer (WM) as a generic architectural addition to CNNs and show that it can increase their robustness to noise and…
Intuit Tech Futures（财捷科技未来部门）；Bar Ilan University（巴伊兰大学）；Intuit（财捷公司）
Latent factor models for recommender systems represent users and items as low dimensional vectors. Privacy risks of such systems have previously been studied mostly in the context of recovery of personal information in the form of usage records from the training data. However, the user representations themselves may be used together with external data to recover private user information such as gender and age. In this paper we show that user vectors calculated by a common recommender system can be exploited in this way. We propose the privacy-adversarial framework to eliminate such leakage of …
Michigan State University（密歇根州立大学）；International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术研究所）
In this paper, we design and evaluate a convolutional autoencoder that perturbs an input face image to impart privacy to a subject. Specifically, the proposed autoencoder transforms an input face image such that the transformed image can be successfully used for face recognition but not for gender classification. In order to train this autoencoder, we propose a novel training scheme, referred to as semi-adversarial training in this work. The training is facilitated by attaching a semi-adversarial module consisting of a pseudo gender classifier and a pseudo face matcher to the autoencoder. The …
University of Sydney（悉尼大学）；Huawei Technologies（华为技术有限公司）；Peking University（北京大学）
With the tremendous advances in the architecture and scale of convolutional neural networks (CNNs) over the past few decades, they can easily reach or even exceed the performance of humans in certain tasks. However, a recently discovered shortcoming of CNNs is that they are vulnerable to adversarial attacks. Although the adversarial robustness of CNNs can be improved by adversarial training, there is a trade-off between standard accuracy and adversarial robustness. From the neural architecture perspective, this paper aims to improve the adversarial robustness of the backbone CNNs that have a s…
Rafael - Advanced Defense Systems Ltd.（拉斐尔先进防御系统有限公司）
In this paper, we introduce a novel neural network training framework that increases model's adversarial robustness to adversarial attacks while maintaining high clean accuracy by combining contrastive learning (CL) with adversarial training (AT). We propose to improve model robustness to adversarial attacks by learning feature representations that are consistent under both data augmentations and adversarial perturbations. We leverage contrastive learning to improve adversarial robustness by considering an adversarial example as another positive example, and aim to maximize the similarity betw…
Tsinghua University（清华大学）；IBM Research（IBM研究院）；University of California, Los Angeles（加州大学洛杉矶分校）；SenseTime Research（商汤科技研究院）；Northeastern University（东北大学）
It is well known that deep neural networks (DNNs) are vulnerable to adversarial attacks, which are implemented by adding crafted perturbations onto benign examples. Min-max robust optimization based adversarial training can provide a notion of security against adversarial attacks. However, adversarial robustness requires a significantly larger capacity of the network than that for the natural training with only benign examples. This paper proposes a framework of concurrent adversarial training and weight pruning that enables model compression while still preserving the adversarial robustness a…
Neural networks have led to major improvements in image classification but suffer from being non-robust to adversarial changes, unreliable uncertainty estimates on out-distribution samples and their inscrutable black-box decisions. In this work we propose RATIO, a training procedure for Robustness via Adversarial Training on In- and Out-distribution, which leads to robust models with reliable and robust confidence estimates on the out-distribution. RATIO has similar generative properties to adversarial training so that visual counterfactuals produce class specific features. While adversarial t…
UvA-Bosch Delta Lab（阿姆斯特丹大学-博世德尔塔实验室）；University of Amsterdam（阿姆斯特丹大学）；Bosch Center for AI（博世人工智能中心）
In this paper we aim to explore the general robustness of neural network classifiers by utilizing adversarial as well as natural perturbations. Different from previous works which mainly focus on studying the robustness of neural networks against adversarial perturbations, we also evaluate their robustness on natural perturbations before and after robustification. After standardizing the comparison between adversarial and natural perturbations, we demonstrate that although adversarial training improves the performance of the networks against adversarial perturbations, it leads to drop in the p…
