Training convolutional neural networks (CNNs) with a strict Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients and stable training. While $1$-Lipschitz CNNs can be designed by enforcing a $1$-Lipschitz constraint on each layer, training such networks requires each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. A layer with this property is said to be Gradient Norm Preserving (GNP). In this work, we introduce a procedure to certify the robustness of $1$-Lipschitz CNNs by relaxing the orthogonalization of the last linear layer of the network that significantly advances the state of the art for both standard and provable robust accuracies on CIFAR-100 (gains of $4.80\%$ and $4.71\%$, respectively). We further boost their robustness by introducing (i) a novel Gradient Norm preserving activation function called the Householder activation function (that includes every $\mathrm{GroupSort}$ activation) and (ii) a certificate regularization. On CIFAR-10, we achieve significant improvements over prior works in provable robust accuracy ($5.81\%$) with only a minor drop in standard accuracy ($-0.29\%$). Code for reproducing all experiments in the paper is available at \url{https://github.com/singlasahil14/SOC}.
Michigan State University（密歇根州立大学）；Argonne National Laboratory（阿贡国家实验室）；Brookhaven National Laboratory（布鲁克海文国家实验室）
Robust machine learning models with accurately calibrated uncertainties are crucial for safety-critical applications. Probabilistic machine learning and especially the Bayesian formalism provide a systematic framework to incorporate robustness through the distributional estimates and reason about uncertainty. Recent works have shown that approximate inference approaches that take the weight space uncertainty of neural networks to generate ensemble prediction are the state-of-the-art. However, architecture choices have mostly been ad hoc, which essentially ignores the epistemic uncertainty from…
We introduce SPLASH units, a class of learnable activation functions shown to simultaneously improve the accuracy of deep neural networks while also improving their robustness to adversarial attacks. SPLASH units have both a simple parameterization and maintain the ability to approximate a wide range of non-linear functions. SPLASH units are: 1) continuous; 2) grounded (f(0) = 0); 3) use symmetric hinges; and 4) the locations of the hinges are derived directly from the data (i.e. no learning required). Compared to nine other learned and fixed activation functions, including ReLU and its varian…
Defense Innovation Institute, Chinese Academy of Military Science（中国人民解放军军事科学院国防科技创新研究院）；School of Artificial Intelligence, Xidian University（西安电子科技大学人工智能学院）
The robustness of deep neural networks (DNN) models has attracted increasing attention due to the urgent need for security in many applications. Numerous existing open-sourced tools or platforms are developed to evaluate the robustness of DNN models by ensembling the majority of adversarial attack or defense algorithms. Unfortunately, current platforms do not possess the ability to optimize the architectures of DNN models or the configuration of adversarial attacks to further enhance the robustness of models or the performance of adversarial attacks. To alleviate these problems, in this paper,…
Facebook AI Research（Facebook人工智能研究院）；LAMSADE, Université Paris-Dauphine（巴黎多芬大学LAMSADE实验室）；Institut LIST, CEA, Université Paris-Saclay（巴黎萨克雷大学CEA LIST研究所）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of statistical learning theory and information theory. To this aim, we introduce a new notion of robustness for randomized classifiers, enforcing local Lipschitzness using probability metrics. Equipped with this definition, we make two new contributions. The first one consists in devising a new upper bound on the adversarial generalization gap of randomized class…
Recent work argues that robust training requires substantially larger datasets than those required for standard classification. On CIFAR-10 and CIFAR-100, this translates into a sizable robust-accuracy gap between models trained solely on data from the original training set and those trained with additional data extracted from the "80 Million Tiny Images" dataset (TI-80M). In this paper, we explore how generative models trained solely on the original training set can be leveraged to artificially increase the size of the original training set and improve adversarial robustness to $\ell_p$ norm-…
Technion - Israel Institute of Technology（以色列理工学院）
We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a $d$-dimensional ball to arbitrary accuracy with only 2 layers and $\mathcal{O}(1)$ neurons, where a 2-layer deterministic network was shown to require $Ω(e^d)$ neurons, an exponential improvement (arXiv:1610.09887). We prove a highly non-trivial result, that for almost any classification problem, there exists a trivially simple network that solves it given a suff…
Neither Adversarial Training Nor Purification: Emergent Adversarial Robustness from Oscillatory Predictive Learning
Ecole polytechnique（巴黎综合理工学院）；Ecole Nationale des Ponts et Chaussées（巴黎国立路桥学校）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）
While many defences against adversarial examples have been proposed, finding robust machine learning models is still an open problem. The most compelling defence to date is adversarial training and consists of complementing the training data set with adversarial examples. Yet adversarial training severely impacts training time and depends on finding representative adversarial samples. In this paper we propose to train models on output spaces with large class separation in order to gain robustness without adversarial training. We introduce a method to partition the output space into class proto…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Do all adversarial examples have the same consequences? An autonomous driving system misclassifying a pedestrian as a car may induce a far more dangerous -- and even potentially lethal -- behavior than, for instance, a car as a bus. In order to better tackle this important problematic, we introduce the concept of hierarchical adversarial robustness. Given a dataset whose classes can be grouped into coarse-level labels, we define hierarchical adversarial examples as the ones leading to a misclassification at the coarse level. To improve the resistance of neural networks to hierarchical attacks,…
Randomized smoothing is a general technique for computing sample-dependent robustness guarantees against adversarial attacks for deep classifiers. Prior works on randomized smoothing against L_1 adversarial attacks use additive smoothing noise and provide probabilistic robustness guarantees. In this work, we propose a non-additive and deterministic smoothing method, Deterministic Smoothing with Splitting Noise (DSSN). To develop DSSN, we first develop SSN, a randomized method which involves generating each noisy smoothing sample by first randomly splitting the input space and then returning a …
We propose a principled framework that combines adversarial training and provable robustness verification for training certifiably robust neural networks. We formulate the training problem as a joint optimization problem with both empirical and provable robustness objectives and develop a novel gradient-descent technique that can eliminate bias in stochastic multi-gradients. We perform both theoretical analysis on the convergence of the proposed technique and experimental comparison with state-of-the-arts. Results on MNIST and CIFAR-10 show that our method can consistently match or outperform …
Verifiable training has shown success in creating neural networks that are provably robust to a given amount of noise. However, despite only enforcing a single robustness criterion, its performance scales poorly with dataset complexity. On CIFAR10, a non-robust LeNet model has a 21.63% error rate, while a model created using verifiable training and a L-infinity robustness criterion of 8/255, has an error rate of 57.10%. Upon examination, we find that when labeling visually similar classes, the model's error rate is as high as 61.65%. We attribute the loss in performance to inter-class similari…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Self-supervised Contrastive Learning (CL) has been recently shown to be very effective in preventing deep networks from overfitting noisy labels. Despite its empirical success, the theoretical understanding of the effect of contrastive learning on boosting robustness is very limited. In this work, we rigorously prove that the representation matrix learned by contrastive learning boosts robustness, by having: (i) one prominent singular value corresponding to each sub-class in the data, and significantly smaller remaining singular values; and (ii) {a large alignment between the prominent singula…
Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. However, their performance often significantly lags behind that of heuristic methods to enforce Lipschitz constraints where the resulting CNN is not \textit{provably} 1-Lipschitz. In this work, we reduce this gap by introducing (a…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Recent studies show that training deep neural networks (DNNs) with Lipschitz constraints are able to enhance adversarial robustness and other model properties such as stability. In this paper, we propose a layer-wise orthogonal training method (LOT) to effectively train 1-Lipschitz convolution layers via parametrizing an orthogonal matrix with an unconstrained matrix. We then efficiently compute the inverse square root of a convolution kernel by transforming the input domain to the Fourier frequency domain. On the other hand, as existing works show that semi-supervised training helps improve e…
A major drawback of adversarially robust models, in particular for large scale datasets like ImageNet, is the extremely long training time compared to standard ones. Moreover, models should be robust not only to one $l_p$-threat model but ideally to all of them. In this paper we propose Extreme norm Adversarial Training (E-AT) for multiple-norm robustness which is based on geometric properties of $l_p$-balls. E-AT costs up to three times less than other adversarial training methods for multiple-norm robustness. Using E-AT we show that for ImageNet a single epoch and for CIFAR-10 three epochs a…
Diverse data augmentation strategies are a natural approach to improving robustness in computer vision models against unforeseen shifts in data distribution. However, the ability to tailor such strategies to inoculate a model against specific classes of corruptions or attacks -- without incurring substantial losses in robustness against other classes of corruptions -- remains elusive. In this work, we successfully harden a model against Fourier-based attacks, while producing superior-to-AugMix accuracy and calibration results on both the CIFAR-10-C and CIFAR-100-C datasets; classification erro…
Despite its popularity, deep neural networks are easily fooled. To alleviate this deficiency, researchers are actively developing new training strategies, which encourage models that are robust to small input perturbations. Several successful robust training methods have been proposed. However, many of them rely on strong adversaries, which can be prohibitively expensive to generate when the input dimension is high and the model structure is complicated. We adopt a new perspective on robustness and propose a novel training algorithm that allows a more effective use of adversaries. Our method i…
Improving Mixup Calibration with Wasserstein Distributionally Robust Optimization
Department of Mathematics & Statistics（数学与统计学系）；Boston University（波士顿大学）；Department of Electrical and Computer Engineering, Division of Systems Engineering（电气与计算机工程系，系统工程 division）；Department of Biomedical Engineering（生物医学工程系）；Faculty of Computing & Data Sciences（计算与数据科学学院）
Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustness
AI Research Lab, Department of Computer Science, University of South Dakota（人工智能研究实验室、计算机科学系、南达科他大学）；School of Information and Artificial Intelligence, Yangzhou University（信息与人工智能学院、扬州大学）；Department of Computer Science and Software Engineering, Auburn University（计算机科学与软件工程系、阿伯丁大学）
Adversarial training (AT) and its variants have spearheaded progress in improving neural network robustness to adversarial perturbations and common corruptions in the last few years. Algorithm design of AT and its variants are focused on training models at a specified perturbation strength $ε$ and only using the feedback from the performance of that $ε$-robust model to improve the algorithm. In this work, we focus on models, trained on a spectrum of $ε$ values. We analyze three perspectives: model performance, intermediate feature precision and convolution filter sensitivity. In each, we ident…
New York University（纽约大学）；Facebook AI Research（Facebook人工智能研究）；CIFAR（加拿大高级研究所（CIFAR））
We propose a retrieval-augmented convolutional network and propose to train it with local mixup, a novel variant of the recently proposed mixup algorithm. The proposed hybrid architecture combining a convolutional network and an off-the-shelf retrieval engine was designed to mitigate the adverse effect of off-manifold adversarial examples, while the proposed local mixup addresses on-manifold ones by explicitly encouraging the classifier to locally behave linearly on the data manifold. Our evaluation of the proposed approach against five readily-available adversarial attacks on three datasets--…
University of Groningen（格罗宁根大学）；University of Malaga（马拉加大学）
We propose a new layer in Convolutional Neural Networks (CNNs) to increase their robustness to several types of noise perturbations of the input images. We call this a push-pull layer and compute its response as the combination of two half-wave rectified convolutions, with kernels of opposite polarity. It is based on a biologically-motivated non-linear model of certain neurons in the visual system that exhibit a response suppression phenomenon, known as push-pull inhibition. We validate our method by substituting the first convolutional layer of the LeNet-5 and WideResNet architectures with ou…
Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics
Carnegie Mellon University（卡内基梅隆大学）；AT&T Chief Data Office（AT&T首席数据办公室）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Michigan（密歇根大学）
Center for Artificial Intelligence Research, University of Agder（阿格德大学人工智能研究中心）
In this article, we introduce a novel variant of the Tsetlin machine (TM) that randomly drops clauses, the key learning elements of a TM. In effect, TM with drop clause ignores a random selection of the clauses in each epoch, selected according to a predefined probability. In this way, additional stochasticity is introduced in the learning phase of TM. To explore the effects drop clause has on accuracy, training time, interpretability and robustness, we conduct extensive experiments on nine benchmark datasets in natural language processing~(NLP) (IMDb, R8, R52, MR and TREC) and image classific…
Cornell University（康奈尔大学）；Facebook AI Research（Facebook 人工智能研究院）
Neural network robustness has become a central topic in machine learning in recent years. Most training algorithms that improve the model's robustness to adversarial and common corruptions also introduce a large computational overhead, requiring as many as ten times the number of forward and backward passes in order to converge. To combat this inefficiency, we propose BulletTrain $-$ a boundary example mining technique to drastically reduce the computational cost of robust training. Our key observation is that only a small fraction of examples are beneficial for improving robustness. BulletTra…
Nanyang Technological University（南洋理工大学）；AI3, A * STAR（新加坡科技研究局AI3）
Adversarial perturbations are imperceptible changes to input pixels that can change the prediction of deep learning models. Learned weights of models robust to such perturbations are previously found to be transferable across different tasks but this applies only if the model architecture for the source and target tasks is the same. Input gradients characterize how small changes at each input pixel affect the model output. Using only natural images, we show here that training a student model's input gradients to match those of a robust teacher model can gain robustness close to a strong baseli…
Recently, adversarial training has been incorporated in self-supervised contrastive pre-training to augment label efficiency with exciting adversarial robustness. However, the robustness came at a cost of expensive adversarial training. In this paper, we show a surprising fact that contrastive pre-training has an interesting yet implicit connection with robustness, and such natural robustness in the pre trained representation enables us to design a powerful robust algorithm against adversarial attacks, RUSH, that combines the standard contrastive pre-training and randomized smoothing. It boost…
We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Successful adoption of deep learning (DL) in the wild requires models to be: (1) compact, (2) accurate, and (3) robust to distributional shifts. Unfortunately, efforts towards simultaneously meeting these requirements have mostly been unsuccessful. This raises an important question: Is the inability to create Compact, Accurate, and Robust Deep neural networks (CARDs) fundamental? To answer this question, we perform a large-scale analysis of popular model compression techniques which uncovers several intriguing patterns. Notably, in contrast to traditional pruning approaches (e.g., fine tuning …
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）
In this work, we evaluate adversarial robustness in the context of transfer learning from a source trained on CIFAR 100 to a target network trained on CIFAR 10. Specifically, we study the effects of using robust optimisation in the source and target networks. This allows us to identify transfer learning strategies under which adversarial defences are successfully retained, in addition to revealing potential vulnerabilities. We study the extent to which features learnt by a fast gradient sign method (FGSM) and its iterative alternative (PGD) can preserve their defence properties against black a…
Texas A&M University（得克萨斯农工大学）；MIT-IBM Watson AI Lab, IBM Research（麻省理工学院-IBM沃森人工智能实验室，IBM研究院）；Microsoft Dynamics 365 AI Research（微软Dynamics 365人工智能研究院）
Pretrained models from self-supervision are prevalently used in fine-tuning downstream tasks faster or for better accuracy. However, gaining robustness from pretraining is left unexplored. We introduce adversarial training into self-supervision, to provide general-purpose robust pre-trained models for the first time. We find these robust pre-trained models can benefit the subsequent fine-tuning in two ways: i) boosting final model robustness; ii) saving the computation cost, if proceeding towards adversarial fine-tuning. We conduct extensive experiments to demonstrate that the proposed framewo…
Beihang University（北京航空航天大学）；Beijing Advanced Innovation Center for Big Data-Based Precision Medicine（北京大数据精准医疗高精尖创新中心）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；UBTECH Sydney Artificial Intelligence Centre（优必选悉尼人工智能中心）；The University of Sydney（悉尼大学）
In practice, deep neural networks have been found to be vulnerable to various types of noise, such as adversarial examples and corruption. Various adversarial defense methods have accordingly been developed to improve adversarial robustness for deep models. However, simply training on data mixed with adversarial examples, most of these models still fail to defend against the generalized types of noise. Motivated by the fact that hidden layers play a highly important role in maintaining a robust model, this paper proposes a simple yet powerful training algorithm, named \emph{Adversarial Noise P…
University of Southern California（南加州大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
We study the problem of training machine learning models incrementally with batches of samples annotated with noisy oracles. We select each batch of samples that are important and also diverse via clustering and importance sampling. More importantly, we incorporate model uncertainty into the sampling probability to compensate for poor estimation of the importance scores when the training data is too small to build a meaningful model. Experiments on benchmark image classification datasets (MNIST, SVHN, CIFAR10, and EMNIST) show improvement over existing active learning strategies. We introduce …
Optimal Transport Regularized Divergences: Application to Adversarial Robustness
Department of Mathematics（数学系）；Texas State University（德克萨斯州立大学）；School of Information Systems and Management（信息系统与管理学院）；University of South Florida（佛罗里达州立大学）
Sapienza University of Rome（罗马大学）；Department of Computer Science（计算机科学系）
In this technical report, we evaluate the adversarial robustness of a very recent method called "Geometry-aware Instance-reweighted Adversarial Training"[7]. GAIRAT reports state-of-the-art results on defenses to adversarial attacks on the CIFAR-10 dataset. In fact, we find that a network trained with this method, while showing an improvement over regular adversarial training (AT), is biasing the model towards certain samples by re-scaling the loss. Indeed, this leads the model to be susceptible to attacks that scale the logits. The original model shows an accuracy of 59% under AutoAttack - wh…
Consistency regularization is a commonly-used technique for semi-supervised and self-supervised learning. It is an auxiliary objective function that encourages the prediction of the network to be similar in the vicinity of the observed training samples. Hendrycks et al. (2020) have recently shown such regularization naturally brings test-time robustness to corrupted data and helps with calibration. This paper empirically studies the relevance of consistency regularization for training-time robustness to noisy labels. First, we make two interesting and useful observations regarding the consiste…
Optimal transport (OT) based distributional robust optimisation (DRO) has received some traction in the recent past. However, it is at a nascent stage but has a sound potential in robustifying the deep learning models. Interestingly, OT barycenters demonstrate a good robustness against adversarial attacks. Owing to the computationally expensive nature of OT barycenters, they have not been investigated under DRO framework. In this work, we propose a new barycenter, namely Beckman barycenter, which can be computed efficiently and used for training the network to defend against adversarial attack…
Seoul National University（首尔国立大学）；Seoul, Korea（韩国首尔（注意：根据要求，地址信息不应提取为机构，此处可能是误判，正确机构应为Seoul National University相关部分））
Adversarial training is a defense technique that improves adversarial robustness of a deep neural network (DNN) by including adversarial examples in the training data. In this paper, we identify an overlooked problem of adversarial training in that these adversarial examples often have different semantics than the original data, introducing unintended biases into the model. We hypothesize that such non-semantics-preserving (and resultingly ambiguous) adversarial data harm the robustness of the target models. To mitigate such unintended semantic changes of adversarial examples, we propose seman…
Adversarial training and its variants have become de facto standards for learning robust deep neural networks. In this paper, we explore the landscape around adversarial training in a bid to uncover its limits. We systematically study the effect of different training losses, model sizes, activation functions, the addition of unlabeled data (through pseudo-labeling) and other factors on adversarial robustness. We discover that it is possible to train robust models that go well beyond state-of-the-art results by combining larger models, Swish/SiLU activations and model weight averaging. We demon…
Google Research（谷歌研究院）；Department of Computer Science, Rutgers University（罗格斯大学计算机科学系）；Department of Computer Science, Northwestern University（西北大学计算机科学系）
Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time. In this work we highlight the benefits of natural low rank representations that often exist for real data such as images, for training neural networks with certified robustness guarantees. Our first contribution is for certified robustness to perturbations measured in $\ell_2$ norm. We exploit low rank data representations to provide improved guarantees over state-of-the-art randomized smoothing-based approaches on standard benchmark datasets such as CIFAR-10 and C…
Stylized Synthetic Augmentation further improves Corruption Robustness
Institute of Industrial Automation and Software Engineering, University of Stuttgart, Stuttgart, Germany（工业自动化与软件工程学院，斯图加特大学，斯图加特，德国）；Federal Institute for Occupational Safety and Health (BAuA)（联邦职业安全与健康研究所）
Adversarial training is the de facto most promising defense against adversarial examples. Yet, its passive nature inevitably prevents it from being immune to unknown attackers. To achieve a proactive defense, we need a more fundamental understanding of adversarial examples, beyond the popular bounded threat model. In this paper, we provide a causal viewpoint of adversarial vulnerability: the cause is the spurious correlation ubiquitously existing in learning, i.e., the confounding effect, where attackers are precisely exploiting these effects. Therefore, a fundamental solution for adversarial …
