Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent \emph{adversarial training} methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggest that a variety of other factors (size and quality of training data, model size, etc.) affect this tradeoff in somewhat surprising ways. In this paper we provide a precise and comprehensive understanding of the role of adversarial training in the context of linear regression with Gaussian features. In particular, we characterize the fundamental tradeoff between the accuracies achievable by any algorithm regardless of computational power or size of the training data. Furthermore, we precisely characterize the standard/robust accuracy and the corresponding tradeoff achieved by a contemporary mini-max adversarial training approach in a high-dimensional regime where the number of data points and the parameters of the model grow in proportion to each other. Our theory for adversarial training algorithms also facilitates the rigorous study of how a variety of factors (size and quality of training data, model overparametrization etc.) affect the tradeoff between these two competing accuracies.
University of Southern California（南加州大学）；Adobe Research（奥多比研究院）
Adversarial training is among the most effective techniques to improve the robustness of models against adversarial perturbations. However, the full effect of this approach on models is not well understood. For example, while adversarial training can reduce the adversarial risk (prediction error against an adversary), it sometimes increase standard risk (generalization error when there is no adversary). Even more, such behavior is impacted by various elements of the learning problem, including the size and quality of training data, specific forms of adversarial perturbations in the input, mode…
Over the past few years, several adversarial training methods have been proposed to improve the robustness of machine learning models against adversarial perturbations in the input. Despite remarkable progress in this regard, adversarial training is often observed to drop the standard test accuracy. This phenomenon has intrigued the research community to investigate the potential tradeoff between standard accuracy (a.k.a generalization) and robust accuracy (a.k.a robust generalization) as two performance measures. In this paper, we revisit this tradeoff for latent models and argue that this tr…
Facebook AI Research（Facebook人工智能研究院）；University of Maryland（马里兰大学）；Georgia Institute of Technology（佐治亚理工学院）
Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test set. We hypothesize that this poor generalization is a consequence of adversarial training with uniform perturbation radius around every training sample. Samples close to decision boundary can be morphed into a different class under a small perturbation budget, and enforcing large margins around these samples produce poor decision boundaries that generalize po…
While adversarial training can improve robust accuracy (against an adversary), it sometimes hurts standard accuracy (when there is no adversary). Previous work has studied this tradeoff between standard and robust accuracy, but only in the setting where no predictor performs well on both objectives in the infinite data limit. In this paper, we show that even when the optimal predictor with infinite data performs well on both objectives, a tradeoff can still manifest itself with finite data. Furthermore, since our construction is based on a convex learning problem, we rule out optimization conc…
University of Bergen（卑尔根大学）；Institute of Marine Research（海洋研究所）
Previous studies on robustness have argued that there is a tradeoff between accuracy and adversarial accuracy. The tradeoff can be inevitable even when we neglect generalization. We argue that the tradeoff is inherent to the commonly used definition of adversarial accuracy, which uses an adversary that can construct adversarial points constrained by $ε$-balls around data points. As $ε$ gets large, the adversary may use real data points from other classes as adversarial examples. We propose a Voronoi-epsilon adversary which is constrained both by Voronoi cells and by $ε$-balls. This adversary b…
Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class has low standard and robust error. In this work, we precisely characterize the effect of augmentation on the standard error in linear regression when the optimal linear predictor has zero standard and robust error. In particular, we show that the standard error could increase even …
Several existing works study either adversarial or natural distributional robustness of deep neural networks separately. In practice, however, models need to enjoy both types of robustness to ensure reliability. In this work, we bridge this gap and show that in fact, explicit tradeoffs exist between adversarial and natural distributional robustness. We first consider a simple linear regression setting on Gaussian data with disjoint sets of core and spurious features. In this setting, through theoretical and empirical analysis, we show that (i) adversarial training with $\ell_1$ and $\ell_2$ no…
Khoury College of Computer Sciences（胡里计算机学院）；Northeastern University（东北大学）
Motivated by the need for fair algorithmic decision making in the age of automation and artificially-intelligent technology, this technical report provides a theoretical insight into adversarial training for fairness in deep learning. We build upon previous work in adversarial fairness, show the persistent tradeoff between fair predictions and model performance, and explore further mechanisms that help in offsetting this tradeoff.
Massachusetts Institute of Technology（麻省理工学院）；Institute of Science and Technology Austria (IST Austria)（奥地利科学技术研究所（IST Austria））
Adversarial training (i.e., training on adversarially perturbed input data) is a well-studied method for making neural networks robust to potential adversarial attacks during inference. However, the improved robustness does not come for free but rather is accompanied by a decrease in overall model accuracy and performance. Recent work has shown that, in practical robot learning applications, the effects of adversarial training do not pose a fair trade-off but inflict a net loss when measured in holistic robot performance. This work revisits the robustness-accuracy trade-off in robot learning b…
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…
Purdue University（普渡大学）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）
Adversarially robust learning aims to design algorithms that are robust to small adversarial perturbations on input variables. Beyond the existing studies on the predictive performance to adversarial samples, our goal is to understand statistical properties of adversarially robust estimates and analyze adversarial risk in the setup of linear regression models. By discovering the statistical minimax rate of convergence of adversarially robust estimators, we emphasize the importance of incorporating model information, e.g., sparsity, in adversarially robust learning. Further, we reveal an explic…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Rochester（罗切斯特大学）；Texas A&M University（德州农工大学）；Kwai Inc（快手公司）
Adversarial training and its many variants substantially improve deep network robustness, yet at the cost of compromising standard accuracy. Moreover, the training process is heavy and hence it becomes impractical to thoroughly explore the trade-off between accuracy and robustness. This paper asks this new question: how to quickly calibrate a trained model in-situ, to examine the achievable trade-offs between its standard and robust accuracies, without (re-)training it many times? Our proposed framework, Once-for-all Adversarial Training (OAT), is built on an innovative model-conditional train…
Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random perturbations. Towards explaining this gap, we highlight the hypothesis that $\textit{robust classification may require more complex classifiers (i.e. more capacity) than standard classification.}$ In this note, we show that this hypothesis is indeed possible, by giving several theoretical examples of classification tasks and sets of "simple" classifiers for …
Improving the Robustness/Accuracy Tradeoff Against Adversarial Attacks Using Information Bottleneck Distillation Through Dual Teachers
Joint Graduate School of Mathematics for Innovation（联合创新数学研究生院）；Kyushu University（九州大学）；Faculty of Information Science and Electrical Engineering（信息科学与电气工程学院）；Université Savoie Mont Blanc（萨瓦大学）
Multivariate time series (MTS) regression tasks are common in many real-world data mining applications including finance, cybersecurity, energy, healthcare, prognostics, and many others. Due to the tremendous success of deep learning (DL) algorithms in various domains including image recognition and computer vision, researchers started adopting these techniques for solving MTS data mining problems, many of which are targeted for safety-critical and cost-critical applications. Unfortunately, DL algorithms are known for their susceptibility to adversarial examples which also makes the DL regress…
NTT Secure Platform Laboratories（NTT安全平台实验室）；NTT Software Innovation Center（NTT软件创新中心）；NTT Communication Science Laboratories（NTT通信科学实验室）
Adversarial training is actively studied for learning robust models against adversarial examples. A recent study finds that adversarially trained models degenerate generalization performance on adversarial examples when their weight loss landscape, which is loss changes with respect to weights, is sharp. Unfortunately, it has been experimentally shown that adversarial training sharpens the weight loss landscape, but this phenomenon has not been theoretically clarified. Therefore, we theoretically analyze this phenomenon in this paper. As a first step, this paper proves that adversarial trainin…
Adversarial training tends to result in models that are less accurate on natural (unperturbed) examples compared to standard models. This can be attributed to either an algorithmic shortcoming or a fundamental property of the training data distribution, which admits different solutions for optimal standard and adversarial classifiers. In this work, we focus on the latter case under a binary Gaussian mixture classification problem. Unlike earlier work, we aim to derive the natural accuracy gap between the optimal Bayes and adversarial classifiers, and study the effect of different distributiona…
University of Michigan（密歇根大学）；University of California, Davis（加利福尼亚大学戴维斯分校）
In this paper, we investigate the adversarial robustness of multivariate $M$-Estimators. In the considered model, after observing the whole dataset, an adversary can modify all data points with the goal of maximizing inference errors. We use adversarial influence function (AIF) to measure the asymptotic rate at which the adversary can change the inference result. We first characterize the adversary's optimal modification strategy and its corresponding AIF. From the defender's perspective, we would like to design an estimator that has a small AIF. For the case of joint location and scale estima…
This paper analyzes $\ell_1$ regularized linear regression under the challenging scenario of having only adversarially corrupted data for training. We use the primal-dual witness paradigm to provide provable performance guarantees for the support of the estimated regression parameter vector to match the actual parameter. Our theoretical analysis shows the counter-intuitive result that an adversary can influence sample complexity by corrupting the irrelevant features, i.e., those corresponding to zero coefficients of the regression parameter vector, which, consequently, do not affect the depend…
State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against such examples. It is formulated as a min-max problem, searching for the best solution when the training data was corrupted by the worst-case attacks. For linear regression problems, adversarial training can be formulated as a convex problem. We use this reformulation to make two technical contributions: First, we formulate the training problem as an instance of robust regression to reveal its connection …
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carnegie Mellon University（卡内基梅隆大学）；University of Chicago（芝加哥大学）；Massachusetts Institute of Technology（麻省理工学院）
A wide range of machine learning applications such as privacy-preserving learning, algorithmic fairness, and domain adaptation/generalization among others, involve learning invariant representations of the data that aim to achieve two competing goals: (a) maximize information or accuracy with respect to a target response, and (b) maximize invariance or independence with respect to a set of protected features (e.g., for fairness, privacy, etc). Despite their wide applicability, theoretical understanding of the optimal tradeoffs -- with respect to accuracy, and invariance -- achievable by invari…
In this paper, we take a first step towards answering the question of how to design fair machine learning algorithms that are robust to adversarial attacks. Using a minimax framework, we aim to design an adversarially robust fair regression model that achieves optimal performance in the presence of an attacker who is able to add a carefully designed adversarial data point to the dataset or perform a rank-one attack on the dataset. By solving the proposed nonsmooth nonconvex-nonconcave minimax problem, the optimal adversary as well as the robust fairness-aware regression model are obtained. For…
University of California, Riverside（加州大学河滨分校）；Indian Institute of Science（印度科学研究所）
In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an abstain option, where the classifier abstains from making a decision when it has low confidence about the prediction. We propose metrics to quantify the nominal performance of a classifier with an abstain option and its robustness against adversarial perturbations. We show that there exist a tradeoff between the two metrics regardless of what method is used …
The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a z…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Cambridge（剑桥大学）
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting where the covariates are sub-Gaussian and uncontaminated; however, these estimators may fail when the covariates are either heavy-tailed or contain outliers. In this work, we show how to modify the Huber regression, least trimmed squares, and least absolute deviation estimators to obtain estimators which are simultaneously computationally and statistically effic…
Huazhong University of Science and Technology（华中科技大学）；University of California San Diego（加州大学圣地亚哥分校）
Machine learning has achieved great success in many applications, including electroencephalogram (EEG) based brain-computer interfaces (BCIs). Unfortunately, many machine learning models are vulnerable to adversarial examples, which are crafted by adding deliberately designed perturbations to the original inputs. Many adversarial attack approaches for classification problems have been proposed, but few have considered target adversarial attacks for regression problems. This paper proposes two such approaches. More specifically, we consider white-box target attacks for regression problems, wher…
We study the error of linear regression in the face of adversarial attacks. In this framework, an adversary changes the input to the regression model in order to maximize the prediction error. We provide bounds on the prediction error in the presence of an adversary as a function of the parameter norm and the error in the absence of such an adversary. We show how these bounds make it possible to study the adversarial error using analysis from non-adversarial setups. The obtained results shed light on the robustness of overparameterized linear models to adversarial attacks. Adding features migh…
Motivated by recent data analytics applications, we study the adversarial robustness of robust estimators. Instead of assuming that only a fraction of the data points are outliers as considered in the classic robust estimation setup, in this paper, we consider an adversarial setup in which an attacker can observe the whole dataset and can modify all data samples in an adversarial manner so as to maximize the estimation error caused by his attack. We characterize the attacker's optimal attack strategy, and further introduce adversarial influence function (AIF) to quantify an estimator's sensiti…
Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-dimensional geometry of adversarial examples. In particular, we highlight the importance of codimension: for low-dimensional data manifolds embedded in high-dimensional space there are many directions off the manifold in which to construct adversarial examples. Adversarial exampl…
EXE-Bench: Ranking the Tradeoffs of AI-based Windows Malware Detectors for Real-World Usability
University of Genova（热那亚大学）；Artificial Intelligence Research Institute (IIIA-CSIC)（西班牙国家研究委员会人工智能研究所）；CTU in Prague（布拉格捷克技术大学）；Sapienza University（罗马大学）；University of Cagliari（卡利亚里大学）
PAR-AdvGAN: Improving Adversarial Attack Capability with Progressive Auto-Regression AdvGAN
Suzhou University of Technology（苏州科技大学）；University of Technology Sydney（技术悉尼大学）；University of Malaya（马来亚大学）；Nanning Normal University（南宁师范学院）；University of New South Wales（新南威尔士大学）；The University of Sydney（悉尼大学）
Despite the tremendous success of deep neural networks in various learning problems, it has been observed that adding an intentionally designed adversarial perturbation to inputs of these architectures leads to erroneous classification with high confidence in the prediction. In this work, we propose a general framework based on the perturbation analysis of learning algorithms which consists of convex programming and is able to recover many current adversarial attacks as special cases. The framework can be used to propose novel attacks against learning algorithms for classification and regressi…
Provable Unrestricted Adversarial Training without Compromise with Generalizability
School of Computer Science, Sichuan University（四川大学计算机学院）；University of Maryland, College Park（马里兰大学帕克分校）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Tufts University（塔夫茨大学）；Arizona State University（亚利桑那州立大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Robust machine learning formulations have emerged to address the prevalent vulnerability of deep neural networks to adversarial examples. Our work draws the connection between optimal robust learning and the privacy-utility tradeoff problem, which is a generalization of the rate-distortion problem. The saddle point of the game between a robust classifier and an adversarial perturbation can be found via the solution of a maximum conditional entropy problem. This information-theoretic perspective sheds light on the fundamental tradeoff between robustness and clean data performance, which ultimat…
We explore adversarial robustness in the setting in which it is acceptable for a classifier to abstain---that is, output no class---on adversarial examples. Adversarial examples are small perturbations of normal inputs to a classifier that cause the classifier to give incorrect output; they present security and safety challenges for machine learning systems. In many safety-critical applications, it is less costly for a classifier to abstain on adversarial examples than to give incorrect output for them. We first introduce a novel objective function for adversarial robustness with an abstain op…
Duke University（杜克大学）；Hewlett Packard Labs（惠普实验室）；Air Force Research Lab（美国空军研究实验室）
Some recent works revealed that deep neural networks (DNNs) are vulnerable to so-called adversarial attacks where input examples are intentionally perturbed to fool DNNs. In this work, we revisit the DNN training process that includes adversarial examples into the training dataset so as to improve DNN's resilience to adversarial attacks, namely, adversarial training. Our experiments show that different adversarial strengths, i.e., perturbation levels of adversarial examples, have different working zones to resist the attack. Based on the observation, we propose a multi-strength adversarial tra…
University of California, Davis（加利福尼亚大学戴维斯分校）；University of California, Berkeley（加利福尼亚大学伯克利分校）
We present a probabilistic framework for studying adversarial attacks on discrete data. Based on this framework, we derive a perturbation-based method, Greedy Attack, and a scalable learning-based method, Gumbel Attack, that illustrate various tradeoffs in the design of attacks. We demonstrate the effectiveness of these methods using both quantitative metrics and human evaluation on various state-of-the-art models for text classification, including a word-based CNN, a character-based CNN and an LSTM. As as example of our results, we show that the accuracy of character-based convolutional netwo…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H. Milton Stewart工业与系统工程学院）；Beijing Institute of Spacecraft System Engineering（北京航天器系统工程研究所）；Department of Statistics, Purdue University（普渡大学统计系）
Because of the widespread existence of noise and data corruption, recovering the true regression parameters with a certain proportion of corrupted response variables is an essential task. Methods to overcome this problem often involve robust least-squares regression, but few methods perform well when confronted with severe adaptive adversarial attacks. In many applications, prior knowledge is often available from historical data or engineering experience, and by incorporating prior information into a robust regression method, we develop an effective robust regression method that can resist ada…
Center for Systems Biology, Massachusetts General Hospital（麻省总医院系统生物学中心）；Massachusetts Alzheimer’s Disease Research Center（马萨诸塞州阿尔茨海默病研究中心）；Massachusetts General Hospital（麻省总医院）
Automated disease detection in neuroimaging holds promise to improve the diagnostic ability of radiologists, but routinely collected clinical data frequently contains technical and demographic confounding factors that cause data to both differ between sites and be systematically associated with the disease of interest, thus negatively affecting the robustness of diagnostic models. There is a critical need for diagnostic deep learning models that can train on such imbalanced datasets without being influenced by these confounds. In this work, we introduce a novel deep learning architecture, MUCR…
