Regularization with Latent Space Virtual Adversarial Training
Philips Co-Creation Center（飞利浦共创中心）；University of Tsukuba（筑波大学）；I Dragon Corporation（I Dragon公司）；The Tokyo Foundation for Policy Research（东京政策研究基金会）；Lowe’s Services India Pvt. Ltd.（劳氏印度服务私人有限公司）
Virtual Adversarial Training (VAT) has shown impressive results among recently developed regularization methods called consistency regularization. VAT utilizes adversarial samples, generated by injecting perturbation in the input space, for training and thereby enhances the generalization ability of a classifier. However, such adversarial samples can be generated only within a very small area around the input data point, which limits the adversarial effectiveness of such samples. To address this problem we propose LVAT (Latent space VAT), which injects perturbation in the latent space instead of the input space. LVAT can generate adversarial samples flexibly, resulting in more adverse effects and thus more effective regularization. The latent space is built by a generative model, and in this paper, we examine two different type of models: variational auto-encoder and normalizing flow, specifically Glow. We evaluated the performance of our method in both supervised and semi-supervised learning scenarios for an image classification task using SVHN and CIFAR-10 datasets. In our evaluation, we found that our method outperforms VAT and other state-of-the-art methods.
Adversarial training (AT) has proven to be one of the most effective ways to defend Deep Neural Networks (DNNs) against adversarial attacks. However, the phenomenon of robust overfitting, i.e., the robustness will drop sharply at a certain stage, always exists during AT. It is of great importance to decrease this robust generalization gap in order to obtain a robust model. In this paper, we present an in-depth study towards the robust overfitting from a new angle. We observe that consistency regularization, a popular technique in semi-supervised learning, has a similar goal as AT and can be us…
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 …
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.
Adversarial training (AT) methods have been found to be effective against adversarial attacks on deep neural networks. Many variants of AT have been proposed to improve its performance. Pang et al. [1] have recently shown that incorporating hypersphere embedding (HE) into the existing AT procedures enhances robustness. We observe that the existing AT procedures are not designed for the HE framework, and thus fail to adequately learn the angular discriminative information available in the HE framework. In this paper, we propose integrating HE into AT with regularization terms that exploit the r…
Compared with standard supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. A recently proposed method, virtual adversarial training (VAT), smartly performs adversarial training without label information to impose a local smoothness on the classifier, which is especially beneficial to semi-supervised learning. In this work, we propose tangent-normal adversarial regularization (TNAR) as an extension of VAT by taking the data manifold into consideration. The proposed TNAR is composed by two complementary parts, the tangent adversarial…
In this paper we propose a new family of algorithms, ATENT, for training adversarially robust deep neural networks. We formulate a new loss function that is equipped with an additional entropic regularization. Our loss function considers the contribution of adversarial samples that are drawn from a specially designed distribution in the data space that assigns high probability to points with high loss and in the immediate neighborhood of training samples. Our proposed algorithms optimize this loss to seek adversarially robust valleys of the loss landscape. Our approach achieves competitive (or…
McGill University（麦吉尔大学）；ETS Montreal（蒙特利尔高等技术学院）；Université Paris-Saclay（巴黎萨克雷大学）；CentraleSupélec（中央理工-高等电力学院）；International Laboratory on Learning Systems（国际学习系统实验室）
Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce FIRE, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the bina…
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…
It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial training methods are most effective. However, most of these methods treat the training samples independently and demand a tremendous amount of samples to train a robust network, while ignoring the latent structural information among these samples. In this work, we propose a novel Local Structure Preserving (LSP) regularization, which aims to preserve the lo…
We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks. Specifically, we prove that $\ell_p$-norm constrained projected gradient ascent based adversarial training with an $\ell_q$-norm loss on the logits of clean and perturbed inputs is equivalent to data-dependent (p, q) operator norm regularization. This fundamental connection confirms the long-standing argument that a network's sensitivity to adversarial examples is tied to its spectral properties and hints at novel ways to robustify and defend against adversarial attacks. We p…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more robust (adversarially trained) models are more generalizable. On the other hand, there is a lack of theoretical understanding of their fundamental connections. In this paper, we explore the relationship between regularization and domain transferability considering different factors such as norm regularization and data augmentations (DA). We propose a general the…
Improving Adversarial Robustness of Attribution via Implicit Regularization
Department of Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden（瑞典皇家理工学院计算机科学系）；Science for Life Laboratory, Stockholm, Sweden（瑞典斯德哥尔摩科学生命实验室）；Department of Computer Science, Brown University, USA（美国布朗大学计算机科学系）
Many previous proposals for adversarial training of deep neural nets have included di- rectly modifying the gradient, training on a mix of original and adversarial examples, using contractive penalties, and approximately optimizing constrained adversarial ob- jective functions. In this paper, we show these proposals are actually all instances of optimizing a general, regularized objective we call DataGrad. Our proposed DataGrad framework, which can be viewed as a deep extension of the layerwise contractive au- toencoder penalty, cleanly simplifies prior work and easily allows extensions such a…
Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Beihang University（北京航空航天大学）；University of Ottawa（渥太华大学）
Recent researches have suggested that the predictive accuracy of neural network may contend with its adversarial robustness. This presents challenges in designing effective regularization schemes that also provide strong adversarial robustness. Revisiting Vicinal Risk Minimization (VRM) as a unifying regularization principle, we propose Adversarial Labelling of Perturbed Samples (ALPS) as a regularization scheme that aims at improving the generalization ability and adversarial robustness of the trained model. ALPS trains neural networks with synthetic samples formed by perturbing each authenti…
Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation over Transformation (EOT) attack. We investigate the effect of the adversarial attacks using proxy gradients on randomized neural networks and demonstrate that it highly relies on the directional distribution of the loss gradients of the randomized neural network. We show in particular that proxy gradients are less effective when the gradients are more scattere…
We propose a Regularization framework based on Adversarial Transformations (RAT) for semi-supervised learning. RAT is designed to enhance robustness of the output distribution of class prediction for a given data against input perturbation. RAT is an extension of Virtual Adversarial Training (VAT) in such a way that RAT adversarialy transforms data along the underlying data distribution by a rich set of data transformation functions that leave class label invariant, whereas VAT simply produces adversarial additive noises. In addition, we verified that a technique of gradually increasing of per…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Adversarial training is a common approach to improving the robustness of deep neural networks against adversarial examples. In this work, we propose a novel regularization approach as an alternative. To derive the regularizer, we formulate the adversarial robustness problem under the robust optimization framework and approximate the loss function using a second-order Taylor series expansion. Our proposed second-order adversarial regularizer (SOAR) is an upper bound based on the Taylor approximation of the inner-max in the robust optimization objective. We empirically show that the proposed met…
Semi-supervised learning (SSL) partially circumvents the high cost of labeling data by augmenting a small labeled dataset with a large and relatively cheap unlabeled dataset drawn from the same distribution. This paper offers a novel interpretation of two deep learning-based SSL approaches, ladder networks and virtual adversarial training (VAT), as applying distributional smoothing to their respective latent spaces. We propose a class of models that fuse these approaches. We achieve near-supervised accuracy with high consistency on the MNIST dataset using just 5 labels per class: our best mode…
We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT)…
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…
State-of-the-art deep neural networks (DNNs) are highly effective at tackling many real-world tasks. However, their wide adoption in mission-critical contexts is hampered by two major weaknesses - their susceptibility to adversarial attacks and their opaqueness. The former raises concerns about the security and generalization of DNNs in real-world conditions, whereas the latter impedes users' trust in their output. In this research, we (1) examine the effect of adversarial robustness on interpretability and (2) present a novel approach for improving the interpretability of DNNs that is based o…
Adversarial training is widely used to improve the robustness of deep neural networks to adversarial attack. However, adversarial training is prone to overfitting, and the cause is far from clear. This work sheds light on the mechanisms underlying overfitting through analyzing the loss landscape w.r.t. the input. We find that robust overfitting results from standard training, specifically the minimization of the clean loss, and can be mitigated by regularization of the loss gradients. Moreover, we find that robust overfitting turns severer during adversarial training partially because the grad…
Deep neural networks have lately shown tremendous performance in various applications including vision and speech processing tasks. However, alongside their ability to perform these tasks with such high accuracy, it has been shown that they are highly susceptible to adversarial attacks: a small change in the input would cause the network to err with high confidence. This phenomenon exposes an inherent fault in these networks and their ability to generalize well. For this reason, providing robustness to adversarial attacks is an important challenge in networks training, which has led to extensi…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；DeepMind（深度思维）
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the geometry of the classification landscape and decision boundaries. We show in particular that adversarial training leads to a significant decrease in the curvature of the loss surface with respect to inputs, leading to a drastically more "linear" behaviour of the network. Using a locally quadratic approximation, we provide theoretical evidence…
McGill University（麦吉尔大学）；University of Minnesota（明尼苏达大学）
In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networks. The adversarial robustness regularization combines adversarial training, which we show to be equivalent to Total Variation regularization, with Lipschitz regularization. We demonstrate empirically that the regularized models are more robust, and that gradient norms of images …
In this paper, we consider a generic probabilistic discriminative learner from the functional viewpoint and argue that, to make it learn well, it is necessary to constrain its hypothesis space to a set of non-trivial piecewise constant functions. To achieve this goal, we present a scalable unsupervised regularization framework. On the theoretical front, we prove that this framework is conducive to a factually confident and smooth discriminative model and connect it to an adversarial Taboo game, spectral clustering and virtual adversarial training. Experimentally, we take deep neural networks a…
Rutgers University（罗格斯大学）；Google Research（谷歌研究院）；University of Delaware（特拉华大学）
Adversarial data augmentation has shown promise for training robust deep neural networks against unforeseen data shifts or corruptions. However, it is difficult to define heuristics to generate effective fictitious target distributions containing "hard" adversarial perturbations that are largely different from the source distribution. In this paper, we propose a novel and effective regularization term for adversarial data augmentation. We theoretically derive it from the information bottleneck principle, which results in a maximum-entropy formulation. Intuitively, this regularization term enco…
Institute for Theoretical Studies（理论研究所）；Stanford University（斯坦福大学）；ETH Zurich（苏黎世联邦理工学院）
This work provides theoretical and empirical evidence that invariance-inducing regularizers can increase predictive accuracy for worst-case spatial transformations (spatial robustness). Evaluated on these adversarially transformed examples, we demonstrate that adding regularization on top of standard or adversarial training reduces the relative error by 20% for CIFAR10 without increasing the computational cost. This outperforms handcrafted networks that were explicitly designed to be spatial-equivariant. Furthermore, we observe for SVHN, known to have inherent variance in orientation, that rob…
Recent works have shown that the input domain of any machine learning classifier is bound to contain adversarial examples. Thus we can no longer hope to immune classifiers against adversarial examples and instead can only aim to achieve the following two defense goals: 1) making adversarial examples harder to find, or 2) weakening their adversarial nature by pushing them further away from correctly classified data points. Most if not all the previously suggested defense mechanisms attend to just one of those two goals, and as such, could be bypassed by adaptive attacks that take the defense me…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；AITRICS
Adversarial training (AT) is currently one of the most successful methods to obtain the adversarial robustness of deep neural networks. However, the phenomenon of robust overfitting, i.e., the robustness starts to decrease significantly during AT, has been problematic, not only making practitioners consider a bag of tricks for a successful training, e.g., early stopping, but also incurring a significant generalization gap in the robustness. In this paper, we propose an effective regularization technique that prevents robust overfitting by optimizing an auxiliary `consistency' regularization lo…
Peking University（北京大学）；Beijing Institute of Big Data Research (BIBDR)（北京大数据研究院）
The effectiveness of Graph Convolutional Networks (GCNs) has been demonstrated in a wide range of graph-based machine learning tasks. However, the update of parameters in GCNs is only from labeled nodes, lacking the utilization of unlabeled data. In this paper, we apply Virtual Adversarial Training (VAT), an adversarial regularization method based on both labeled and unlabeled data, on the supervised loss of GCN to enhance its generalization performance. By imposing virtually adversarial smoothness on the posterior distribution in semi-supervised learning, VAT yields improvement on the Symmetr…
Electrocardiogram (ECG) is the most widely used diagnostic tool to monitor the condition of the human heart. By using deep neural networks (DNNs), interpretation of ECG signals can be fully automated for the identification of potential abnormalities in a patient's heart in a fraction of a second. Studies have shown that given a sufficiently large amount of training data, DNN accuracy for ECG classification could reach human-expert cardiologist level. However, despite of the excellent performance in classification accuracy, DNNs are highly vulnerable to adversarial noises that are subtle change…
We present batch virtual adversarial training (BVAT), a novel regularization method for graph convolutional networks (GCNs). BVAT addresses the shortcoming of GCNs that do not consider the smoothness of the model's output distribution against local perturbations around the input. We propose two algorithms, sample-based BVAT and optimization-based BVAT, which are suitable to promote the smoothness of the model for graph-structured data by either finding virtual adversarial perturbations for a subset of nodes far from each other or generating virtual adversarial perturbations for all nodes with …
Institute for Advanced Computer Studies（高级计算机研究所）；University of Maryland（马里兰大学）
Adversarial training has been successfully applied to build robust models at a certain cost. While the robustness of a model increases, the standard classification accuracy declines. This phenomenon is suggested to be an inherent trade-off. We propose a model that employs feature prioritization by a nonlinear attention module and $L_2$ feature regularization to improve the adversarial robustness and the standard accuracy relative to adversarial training. The attention module encourages the model to rely heavily on robust features by assigning larger weights to them while suppressing non-robust…
While great progress has been made at making neural networks effective across a wide range of visual tasks, most models are surprisingly vulnerable. This frailness takes the form of small, carefully chosen perturbations of their input, known as adversarial examples, which represent a security threat for learned vision models in the wild -- a threat which should be responsibly defended against in safety-critical applications of computer vision. In this paper, we advocate for and experimentally investigate the use of a family of logit regularization techniques as an adversarial defense, which ca…
In semi-supervised learning, virtual adversarial training (VAT) approach is one of the most attractive method due to its intuitional simplicity and powerful performances. VAT finds a classifier which is robust to data perturbation toward the adversarial direction. In this study, we provide a fundamental explanation why VAT works well in semi-supervised learning case and propose new techniques which are simple but powerful to improve the VAT method. Especially we employ the idea of Bad GAN approach, which utilizes bad samples distributed on complement of the support of the input data, without a…
In spite of achieving revolutionary successes in machine learning, deep convolutional neural networks have been recently found to be vulnerable to adversarial attacks and difficult to generalize to novel test images with reasonably large geometric transformations. Inspired by a recent neuroscience discovery revealing that primate brain employs disentangled shape and appearance representations for object recognition, we propose a general disentangled deep autoencoding regularization framework that can be easily applied to any deep embedding based classification model for improving the robustnes…
South China University of Technology（华南理工大学）；Pazhou Lab（琶洲实验室）
The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be {\it $ε$-adversarially robust} (AR); that is, to require the model not to change predicted labels when any given input examples are perturbed within a certain range. However, it is observed that such methods would lead to standard performance degradation, i.e., the degradation on natural examples. In this work, we study the degradation through the regularization perspective. We identify quanti…
Adversarial training is one of the strongest defenses against adversarial attacks, but it requires adversarial examples to be generated for every mini-batch during optimization. The expense of producing these examples during training often precludes adversarial training from use on complex image datasets. In this study, we explore the mechanisms by which adversarial training improves classifier robustness, and show that these mechanisms can be effectively mimicked using simple regularization methods, including label smoothing and logit squeezing. Remarkably, using these simple regularization m…
Anhui University（安徽大学）；The University of Western Australia（西澳大学）；Swansea University（斯旺西大学）
Deep neural networks (DNNs) are known to be vulnerable to adversarial examples that are crafted with imperceptible perturbations, i.e., a small change in an input image can induce a mis-classification, and thus threatens the reliability of deep learning based deployment systems. Adversarial training (AT) is often adopted to improve robustness through training a mixture of corrupted and clean data. However, most of AT based methods are ineffective in dealing with transferred adversarial examples which are generated to fool a wide spectrum of defense models, and thus cannot satisfy the generaliz…
Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore, can be to used to design robust DNNs. In this work, this problem is studied through the lens of compression which is captured by the low-rank structure of weight matrices. It is first shown that adversarial training tends to promote simultaneously low-rank and sparse structure in the weight matrices of neural networks. This is measured through the notions of e…
We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as virtual adversarial training (VAT). The LDS of a model at an input datapoint is defined as the KL-divergence based robustness of the model distribution against local perturbation around the datapoint. VAT resembles adversarial training, but distinguishes itself in that it determines the adversarial direction from the model distribution alone without using the lab…
Deep neural networks (DNNs) have a high capacity to completely memorize noisy labels given sufficient training time, and its memorization, unfortunately, leads to performance degradation. Recently, virtual adversarial training (VAT) attracts attention as it could further improve the generalization of DNNs in semi-supervised learning. The driving force behind VAT is to prevent the models from overfitting data points by enforcing consistency between the inputs and the perturbed inputs. This strategy could be helpful in learning from noisy labels if it prevents neural models from learning noisy s…
We propose a method for improving adversarial robustness by addition of a new bounded function just before softmax. Recent studies hypothesize that small logits (inputs of softmax) by logit regularization can improve adversarial robustness of deep learning. Following this hypothesis, we analyze norms of logit vectors at the optimal point under the assumption of universal approximation and explore new methods for constraining logits by addition of a bounded function before softmax. We theoretically and empirically reveal that small logits by addition of a common activation function, e.g., hyper…
