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 probable false classes. This inspires us to propose a new Probabilistically Compact (PC) loss with logit constraints which can be used as a drop-in replacement for cross-entropy (CE) loss to improve CNN's adversarial robustness. Specifically, PC loss enlarges the probability gaps between true class and false classes meanwhile the logit constraints prevent the gaps from being melted by a small perturbation. We extensively compare our method with the state-of-the-art using large scale datasets under both white-box and black-box attacks to demonstrate its effectiveness. The source codes are available from the following url: https://github.com/xinli0928/PC-LC.
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 …
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.
Xiamen University（厦门大学）；University of Trento（特伦托大学）
Previous works have extensively studied the transferability of adversarial samples in untargeted black-box scenarios. However, it still remains challenging to craft targeted adversarial examples with higher transferability than non-targeted ones. Recent studies reveal that the traditional Cross-Entropy (CE) loss function is insufficient to learn transferable targeted adversarial examples due to the issue of vanishing gradient. In this work, we provide a comprehensive investigation of the CE loss function and find that the logit margin between the targeted and untargeted classes will quickly ob…
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…
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…
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…
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…
Towards Adversarial Robustness via Debiased High-Confidence Logit Alignment
Department of Artificial Intelligence, Xiamen University（厦门大学人工智能学院）；College of Information Science and Technology, Jinan University（济南大学信息科学与技术学院）；Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University（教育部多媒体可信感知与高效计算重点实验室，厦门大学）
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…
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…
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）
Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness th…
It begins with a boundary: A geometric view on probabilistically robust learning
University of Würzburg（维尔茨堡大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of California Santa Barbara（加利福尼亚大学圣巴巴拉分校）；Colorado School of Mines（科罗拉多矿业学院）；University of Utah（犹他大学）
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）
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…
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…
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院）
Efficient and effective attacks are crucial for reliable evaluation of defenses, and also for developing robust models. Projected Gradient Descent (PGD) attack has been demonstrated to be one of the most successful adversarial attacks. However, the effect of the standard PGD attack can be easily weakened by rescaling the logits, while the original decision of every input will not be changed. To mitigate this issue, in this paper, we propose Scale-Invariant Adversarial Attack (SI-PGD), which utilizes the angle between the features in the penultimate layer and the weights in the softmax layer to…
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…
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…
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）
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…
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…
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 Colorado Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校）
Deep neural networks (DNNs) provide state-of-the-art results on various tasks and are widely used in real world applications. However, it was discovered that machine learning models, including the best performing DNNs, suffer from a fundamental problem: they can unexpectedly and confidently misclassify examples formed by slightly perturbing otherwise correctly recognized inputs. Various approaches have been developed for efficiently generating these so-called adversarial examples, but those mostly rely on ascending the gradient of loss. In this paper, we introduce the novel logits optimized ta…
Zhejiang University of Science and Technology（浙江科技学院）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Zhejiang University（浙江大学）；INSA De Rennes（雷恩国立应用科学学院）；CNRS（法国国家科学研究中心）
Adversarial training, as one of the most effective defense methods against adversarial attacks, tends to learn an inclusive decision boundary to increase the robustness of deep learning models. However, due to the large and unnecessary increase in the margin along adversarial directions, adversarial training causes heavy cross-over between natural examples and adversarial examples, which is not conducive to balancing the trade-off between robustness and natural accuracy. In this paper, we propose a novel adversarial training scheme to achieve a better trade-off between robustness and natural a…
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…
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…
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 …
National University of Singapore（新加坡国立大学）；Huawei International（华为国际）
Deep neural networks are vulnerable to adversarial attacks. In this paper, we take the role of investigators who want to trace the attack and identify the source, that is, the particular model which the adversarial examples are generated from. Techniques derived would aid forensic investigation of attack incidents and serve as deterrence to potential attacks. We consider the buyers-seller setting where a machine learning model is to be distributed to various buyers and each buyer receives a slightly different copy with same functionality. A malicious buyer generates adversarial examples from a…
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…
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…
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…
