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Intriguing Properties of Adversarial Examples

arXiv.org Machine Learning

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 only on the statistics of the logit differences of the network, which do not change significantly during training. This leads to adversarial error having a universal scaling, as a power-law, with respect to the size of the adversarial perturbation. We show that this universality holds for a broad range of datasets (MNIST, CIFAR10, ImageNet, and random data), models (including state-of-the-art deep networks, linear models, adversarially trained networks, and networks trained on randomly shuffled labels), and attacks (FGSM, step l.l., PGD). Motivated by these results, we study the effects of reducing prediction entropy on adversarial robustness. Finally, we study the effect of network architectures on adversarial sensitivity. To do this, we use neural architecture search with reinforcement learning to find adversarially robust architectures on CIFAR10. Our resulting architecture is more robust to white \emph{and} black box attacks compared to previous attempts.


Bayesian Adversarial Learning

Neural Information Processing Systems

Deep neural networks have been known to be vulnerable to adversarial attacks, raising lots of security concerns in the practical deployment. Popular defensive approaches can be formulated as a (distributionally) robust optimization problem, which minimizes a "point estimate" of worst-case loss derived from either perdatum perturbationor adversary data-generating distribution within certain predefined constraints.This point estimate ignores potential test adversaries that are beyond the predefined constraints. The model robustness might deteriorate sharply in the scenario of stronger test adversarial data. In this work, a novel robust training framework is proposed to alleviate this issue, Bayesian Robust Learning, in which a distribution is put on the adversarial data-generating distribution to account for the uncertainty of the adversarial data-generating process. The uncertainty directly helps to consider the potential adversaries that are stronger than the point estimate in the cases of distributionally robust optimization. The uncertainty of model parameters is also incorporated to accommodate the full Bayesian framework. We design a scalable Markov Chain Monte Carlo sampling strategy to obtain the posterior distribution over model parameters. Various experiments are conducted to verify the superiority of BAL over existing adversarial training methods. The code for BAL is available at https://tinyurl.com/ycxsaewr.


Adversarial Reprogramming of Neural Networks

arXiv.org Machine Learning

Deep neural networks are susceptible to adversarial attacks. In computer vision, well-crafted perturbations to images can cause neural networks to make mistakes such as identifying a panda as a gibbon or confusing a cat with a computer. Previous adversarial examples have been designed to degrade performance of models or cause machine learning models to produce specific outputs chosen ahead of time by the attacker. We introduce adversarial attacks that instead reprogram the target model to perform a task chosen by the attacker---without the attacker needing to specify or compute the desired output for each test-time input. This attack is accomplished by optimizing for a single adversarial perturbation, of unrestricted magnitude, that can be added to all test-time inputs to a machine learning model in order to cause the model to perform a task chosen by the adversary when processing these inputs---even if the model was not trained to do this task. These perturbations can be thus considered a program for the new task. We demonstrate adversarial reprogramming on six ImageNet classification models, repurposing these models to perform a counting task, as well as two classification tasks: classification of MNIST and CIFAR-10 examples presented within the input to the ImageNet model.


Spatially Transformed Adversarial Examples

arXiv.org Machine Learning

Recent studies show that widely used deep neural networks (DNNs) are vulnerable to carefully crafted adversarial examples. Many advanced algorithms have been proposed to generate adversarial examples by leveraging the $\mathcal{L}_p$ distance for penalizing perturbations. Researchers have explored different defense methods to defend against such adversarial attacks. While the effectiveness of $\mathcal{L}_p$ distance as a metric of perceptual quality remains an active research area, in this paper we will instead focus on a different type of perturbation, namely spatial transformation, as opposed to manipulating the pixel values directly as in prior works. Perturbations generated through spatial transformation could result in large $\mathcal{L}_p$ distance measures, but our extensive experiments show that such spatially transformed adversarial examples are perceptually realistic and more difficult to defend against with existing defense systems. This potentially provides a new direction in adversarial example generation and the design of corresponding defenses. We visualize the spatial transformation based perturbation for different examples and show that our technique can produce realistic adversarial examples with smooth image deformation. Finally, we visualize the attention of deep networks with different types of adversarial examples to better understand how these examples are interpreted.


Adversarial Risk and the Dangers of Evaluating Against Weak Attacks

arXiv.org Machine Learning

This paper investigates recently proposed approaches for defending against adversarial examples and evaluating adversarial robustness. The existence of adversarial examples in trained neural networks reflects the fact that expected risk alone does not capture the model's performance against worst-case inputs. We motivate the use of adversarial risk as an objective, although it cannot easily be computed exactly. We then frame commonly used attacks and evaluation metrics as defining a tractable surrogate objective to the true adversarial risk. This suggests that models may be obscured to adversaries, by optimizing this surrogate rather than the true adversarial risk. We demonstrate that this is a significant problem in practice by repurposing gradient-free optimization techniques into adversarial attacks, which we use to decrease the accuracy of several recently proposed defenses to near zero. Our hope is that our formulations and results will help researchers to develop more powerful defenses.