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., hyperbolic tangent, do not improve adversarial robustness since input vectors of the function (pre-logit vectors) can have large norms. From the theoretical findings, we develop the new bounded function. The addition of our function improves adversarial robustness because it makes logit and pre-logit vectors have small norms. Since our method only adds one activation function before softmax, it is easy to combine our method with adversarial training. Our experiments demonstrate that our method is comparable to logit regularization methods in terms of accuracies on adversarially perturbed datasets without adversarial training. Furthermore, it is superior or comparable to logit regularization methods and a recent defense method (TRADES) when using adversarial training.
In this paper, we develop improved techniques for defending against adversarial examples at scale. First, we implement the state of the art version of adversarial training at unprecedented scale on ImageNet and investigate whether it remains effective in this setting - an important open scientific question (Athalye et al., 2018). Next, we introduce enhanced defenses using a technique we call logit pairing, a method that encourages logits for pairs of examples to be similar. When applied to clean examples and their adversarial counterparts, logit pairing improves accuracy on adversarial example…
Adversarial defenses train deep neural networks to be invariant to the input perturbations from adversarial attacks. Almost all defense strategies achieve this invariance through adversarial training i.e. training on inputs with adversarial perturbations. Although adversarial training is successful at mitigating adversarial attacks, the behavioral differences between adversarially-trained (AT) models and standard models are still poorly understood. Motivated by a recent study on learning robustness without input perturbations by distilling an AT model, we explore what is learned during adversa…
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…
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.
Saarland University（萨尔兰大学）；University of Tübingen（蒂宾根大学）
Recently, Kannan et al. [2018] proposed several logit regularization methods to improve the adversarial robustness of classifiers. We show that the computationally fast methods they propose - Clean Logit Pairing (CLP) and Logit Squeezing (LSQ) - just make the gradient-based optimization problem of crafting adversarial examples harder without providing actual robustness. We find that Adversarial Logit Pairing (ALP) may indeed provide robustness against adversarial examples, especially when combined with adversarial training, and we examine it in a variety of settings. However, the increase in a…
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…
Ghent University（根特大学）；Ghent University Global Campus（根特大学全球校区）
Detecting adversarial examples currently stands as one of the biggest challenges in the field of deep learning. Adversarial attacks, which produce adversarial examples, increase the prediction likelihood of a target class for a particular data point. During this process, the adversarial example can be further optimized, even when it has already been wrongly classified with 100% confidence, thus making the adversarial example even more difficult to detect. For this kind of adversarial examples, which we refer to as over-optimized adversarial examples, we discovered that the logits of the model …
Generating and eliminating adversarial examples has been an intriguing topic in the field of deep learning. While previous research verified that adversarial attacks are often fragile and can be defended via image-level processing, it remains unclear how high-level features are perturbed by such attacks. We investigate this issue from a new perspective, which purely relies on logits, the class scores before softmax, to detect and defend adversarial attacks. Our defender is a two-layer network trained on a mixed set of clean and perturbed logits, with the goal being recovering the original pred…
Beijing Jiaotong University（北京交通大学）；University of Science and Technology of China（中国科学技术大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Adversarial examples provide an opportunity as well as impose a challenge for understanding image classification systems. Based on the analysis of the adversarial training solution Adversarial Logits Pairing (ALP), we observed in this work that: (1) The inference of adversarially robust model tends to rely on fewer high-contribution features compared with vulnerable ones. (2) The training target of ALP doesn't fit well to a noticeable part of samples, where the logits pairing loss is overemphasized and obstructs minimizing the classification loss. Motivated by these observations, we design an …
Convolutional neural networks (CNNs) have achieved state-of-the-art performance on various tasks in computer vision. However, recent studies demonstrate that these models are vulnerable to carefully crafted adversarial samples and suffer from a significant performance drop when predicting them. Many methods have been proposed to improve adversarial robustness (e.g., adversarial training and new loss functions to learn adversarially robust feature representations). Here we offer a unique insight into the predictive behavior of CNNs that they tend to misclassify adversarial samples into the most…
Though deep neural networks have achieved the state of the art performance in visual classification, recent studies have shown that they are all vulnerable to the attack of adversarial examples. In this paper, we develop improved techniques for defending against adversarial examples. First, we propose an enhanced defense technique denoted Attention and Adversarial Logit Pairing(AT+ALP), which encourages both attention map and logit for the pairs of examples to be similar. When being applied to clean examples and their adversarial counterparts, AT+ALP improves accuracy on adversarial examples o…
Generative classifiers have been shown promising to detect illegal inputs including adversarial examples and out-of-distribution samples. Supervised Deep Infomax~(SDIM) is a scalable end-to-end framework to learn generative classifiers. In this paper, we propose a modification of SDIM termed SDIM-\emph{logit}. Instead of training generative classifier from scratch, SDIM-\emph{logit} first takes as input the logits produced any given discriminative classifier, and generate logit representations; then a generative classifier is derived by imposing statistical constraints on logit representations…
Generating Transferrable Adversarial Examples via Local Mixing and Logits Optimization for Remote Sensing Object Recognition
State Key Laboratory of Spatial Datum, College of Remote Sensing and Geoinformatics Engineering, Henan University（空间基准国家重点实验室、遥感与地理信息工程学院、河南大学）；School of Computer and Information Engineering, Henan University（计算机与信息工程学院、河南大学）；School of Automation Science and Electrical Engineering, Beihang University（自动化科学与电气工程学院、北京航空航天大学）
Despite having excellent performances for a wide variety of tasks, modern neural networks are unable to provide a reliable confidence value allowing to detect misclassifications. This limitation is at the heart of what is known as an adversarial example, where the network provides a wrong prediction associated with a strong confidence to a slightly modified image. Moreover, this overconfidence issue has also been observed for regular errors and out-of-distribution data. We tackle this problem by what we call introspection, i.e. using the information provided by the logits of an already pretrai…
We show that it is possible to predict which deep network has generated a given logit vector with accuracy well above chance. We utilize a number of networks on a dataset, initialized with random weights or pretrained weights, as well as fine-tuned networks. A classifier is then trained on the logit vectors of the trained set of this dataset to map the logit vector to the network index that has generated it. The classifier is then evaluated on the test set of the dataset. Results are better with randomly initialized networks, but also generalize to pretrained networks as well as fine-tuned one…
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…
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…
School of Big-Data Science, Zhejiang University of Science and Technology（浙江科技大学大数据学院）；Hangzhou Hikvision Digital Technology Co., Ltd.（杭州海康威视数字技术股份有限公司）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；School of Computer Science and Technology, Huizhou University（惠州学院计算机科学与技术学院）；Cyberspace Institute of Advanced Technology, Guangzhou University（广州大学先进技术网络空间学院）；CY Cergy Paris University（赛吉巴黎大学）
Adversarial training is wildly considered as one of the most effective way to defend against adversarial examples. However, existing adversarial training methods consume unbearable time, due to the fact that they need to generate adversarial examples in the large input space. To speed up adversarial training, we propose a novel adversarial training method that does not need to generate real adversarial examples. By adding perturbations to logits to generate Endogenous Adversarial Examples (EAEs) -- the adversarial examples in the latent space, the time consuming gradient calculation can be avo…
This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solv…
It is becoming increasingly clear that many machine learning classifiers are vulnerable to adversarial examples. In attempting to explain the origin of adversarial examples, previous studies have typically focused on the fact that neural networks operate on high dimensional data, they overfit, or they are too linear. Here we argue that the origin of adversarial examples is primarily due to an inherent uncertainty that neural networks have about their predictions. We show that the functional form of this uncertainty is independent of architecture, dataset, and training protocol; and depends onl…
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…
University of Central Florida（中佛罗里达大学）；École Normale Supérieure（巴黎高等师范学院）；INRIA（法国国家信息与自动化研究所）
White box adversarial perturbations are sought via iterative optimization algorithms most often minimizing an adversarial loss on a $l_p$ neighborhood of the original image, the so-called distortion set. Constraining the adversarial search with different norms results in disparately structured adversarial examples. Here we explore several distortion sets with structure-enhancing algorithms. These new structures for adversarial examples, yet pervasive in optimization, are for instance a challenge for adversarial theoretical certification which again provides only $l_p$ certificates. Because adv…
University of Science and Technology of China（中国科学技术大学）
Despite achieving great success, Deep Neural Networks (DNNs) are vulnerable to adversarial examples. How to accurately evaluate the adversarial robustness of DNNs is critical for their deployment in real-world applications. An ideal indicator of robustness is adversarial risk. Unfortunately, since it involves maximizing the 0-1 loss, calculating the true risk is technically intractable. The most common solution for this is to compute an approximate risk by replacing the 0-1 loss with a surrogate one. Some functions have been used, such as Cross-Entropy (CE) loss and Difference of Logits Ratio …
Isik University（伊希克大学）；University of Stavanger（斯塔万格大学）
In standard Deep Neural Network (DNN) based classifiers, the general convention is to omit the activation function in the last (output) layer and directly apply the softmax function on the logits to get the probability scores of each class. In this type of architectures, the loss value of the classifier against any output class is directly proportional to the difference between the final probability score and the label value of the associated class. Standard White-box adversarial evasion attacks, whether targeted or untargeted, mainly try to exploit the gradient of the model loss function to c…
Ghent University（根特大学）；Ghent University Global Campus（根特大学全球校区）
After the discovery of adversarial examples and their adverse effects on deep learning models, many studies focused on finding more diverse methods to generate these carefully crafted samples. Although empirical results on the effectiveness of adversarial example generation methods against defense mechanisms are discussed in detail in the literature, an in-depth study of the theoretical properties and the perturbation effectiveness of these adversarial attacks has largely been lacking. In this paper, we investigate the objective functions of three popular methods for adversarial example genera…
School of Computer Science and Technology, Huazhong University of Science and Technology（华中科技大学计算机科学与技术学院）；Computer Science Department, University of California, Los Angeles（加州大学洛杉矶分校计算机科学系）
Adversarial training is the most empirically successful approach in improving the robustness of deep neural networks for image classification.For text classification, however, existing synonym substitution based adversarial attacks are effective but not efficient to be incorporated into practical text adversarial training. Gradient-based attacks, which are very efficient for images, are hard to be implemented for synonym substitution based text attacks due to the lexical, grammatical and semantic constraints and the discrete text input space. Thereby, we propose a fast text adversarial attack …
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…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Institute for AI Industry Research (AIR), Tsinghua University（清华大学人工智能产业研究院（AIR））；Tsinghua University（清华大学）
Recent studies have shown that, like traditional machine learning, federated learning (FL) is also vulnerable to adversarial attacks. To improve the adversarial robustness of FL, federated adversarial training (FAT) methods have been proposed to apply adversarial training locally before global aggregation. Although these methods demonstrate promising results on independent identically distributed (IID) data, they suffer from training instability on non-IID data with label skewness, resulting in degraded natural accuracy. This tends to hinder the application of FAT in real-world applications wh…
Generative adversarial networks (GAN) have shown remarkable results in image generation tasks. High fidelity class-conditional GAN methods often rely on stabilization techniques by constraining the global Lipschitz continuity. Such regularization leads to less expressive models and slower convergence speed; other techniques, such as the large batch training, require unconventional computing power and are not widely accessible. In this paper, we develop an efficient algorithm, namely FastGAN (Free AdverSarial Training), to improve the speed and quality of GAN training based on the adversarial t…
Huazhong University of Science and Technology（华中科技大学）
A line of work has shown that natural text processing models are vulnerable to adversarial examples. Correspondingly, various defense methods are proposed to mitigate the threat of textual adversarial examples, eg, adversarial training, input transformations, detection, etc. In this work, we treat the optimization process for synonym substitution based textual adversarial attacks as a specific sequence of word replacement, in which each word mutually influences other words. We identify that we could destroy such mutual interaction and eliminate the adversarial perturbation by randomly substitu…
Adversarial training, a method for learning robust deep neural networks, constructs adversarial examples during training. However, recent methods for generating NLP adversarial examples involve combinatorial search and expensive sentence encoders for constraining the generated instances. As a result, it remains challenging to use vanilla adversarial training to improve NLP models' performance, and the benefits are mainly uninvestigated. This paper proposes a simple and improved vanilla adversarial training process for NLP models, which we name Attacking to Training (A2T). The core part of A2T …
Although Deep Neural Networks (DNNs) achieve excellent performance on many real-world tasks, they are highly vulnerable to adversarial attacks. A leading defense against such attacks is adversarial training, a technique in which a DNN is trained to be robust to adversarial attacks by introducing adversarial noise to its input. This procedure is effective but must be done during the training phase. In this work, we propose Augmented Random Forest (ARF), a simple and easy-to-use strategy for robustifying an existing pretrained DNN without modifying its weights. For every image, we generate rando…
Deep learning classifiers are known to be vulnerable to adversarial examples. A recent paper presented at ICML 2019 proposed a statistical test detection method based on the observation that logits of noisy adversarial examples are biased toward the true class. The method is evaluated on CIFAR-10 dataset and is shown to achieve 99% true positive rate (TPR) at only 1% false positive rate (FPR). In this paper, we first develop a classifier-based adaptation of the statistical test method and show that it improves the detection performance. We then propose Logit Mimicry Attack method to generate a…
University of Central Florida（中佛罗里达大学）；Centre de Recherche INRIA de Paris（法国国家信息与自动化研究所巴黎研究中心）
White box adversarial perturbations are generated via iterative optimization algorithms most often by minimizing an adversarial loss on a $\ell_p$ neighborhood of the original image, the so-called distortion set. Constraining the adversarial search with different norms results in disparately structured adversarial examples. Here we explore several distortion sets with structure-enhancing algorithms. These new structures for adversarial examples might provide challenges for provable and empirical robust mechanisms. Because adversarial robustness is still an empirical field, defense mechanisms s…
Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network reduces the 'space' in which adversarial examples exist. Guided by this intuition, we demonstrate that discretization greatly improves the robustness of DLNs against adversarial attacks. Specifically, discretizing the input space (or allowed pixel levels from 256 values or 8-bit to 4 values or 2-bit) extensively improves the adversarial robustness of DLNs for …
Université Paris-Dauphine, PSL Research University（巴黎多芬大学，PSL研究大学）；CNRS（法国国家科学研究中心）；Facebook AI Research（脸书人工智能研究院）
We introduce a new black-box attack achieving state of the art performances. Our approach is based on a new objective function, borrowing ideas from $\ell_\infty$-white box attacks, and particularly designed to fit derivative-free optimization requirements. It only requires to have access to the logits of the classifier without any other information which is a more realistic scenario. Not only we introduce a new objective function, we extend previous works on black box adversarial attacks to a larger spectrum of evolution strategies and other derivative-free optimization methods. We also highl…
