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Register a new userOn the Sensitivity of Adversarial Robustness to Input Data Distributions
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Added by
Gavin Weiguang Ding
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Neural networks are vulnerable to small adversarial perturbations. Existing literature largely focused on understanding and mitigating the vulnerability of learned models. In this paper, we demonstrate an intriguing phenomenon about the most popular robust training method in the literature, adversarial training: Adversarial robustness, unlike clean accuracy, is sensitive to the input data distribution. Even a semantics-preserving transformations on the input data distribution can cause a significantly different robustness for the adversarial trained model that is both trained and evaluated on the new distribution. Our discovery of such sensitivity on data distribution is based on a study which disentangles the behaviors of clean accuracy and robust accuracy of the Bayes classifier. Empirical investigations further confirm our finding. We construct semantically-identical variants for MNIST and CIFAR10 respectively, and show that standardly trained models achieve comparable clean accuracies on them, but adversarially trained models achieve significantly different robustness accuracies. This counter-intuitive phenomenon indicates that input data distribution alone can affect the adversarial robustness of trained neural networks, not necessarily the tasks themselves. Lastly, we discuss the practical implications on evaluating adversarial robustness, and make initial attempts to understand this complex phenomenon.
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We focus on the use of proxy distributions, i.e., approximations of the underlying distribution of the training dataset, in both understanding and improving the adversarial robustness in image classification. While additional training data helps in adversarial training, curating a very large number of real-world images is challenging. In contrast, proxy distributions enable us to sample a potentially unlimited number of images and improve adversarial robustness using these samples. We first ask the question: when does adversarial robustness benefit from incorporating additional samples from the proxy distribution in the training stage? We prove that the difference between the robustness of a classifier on the proxy and original training dataset distribution is upper bounded by the conditional Wasserstein distance between them. Our result confirms the intuition that samples from a proxy distribution that closely approximates training dataset distribution should be able to boost adversarial robustness. Motivated by this finding, we leverage samples from state-of-the-art generative models, which can closely approximate training data distribution, to improve robustness. In particular, we improve robust accuracy by up to 6.1% and 5.7% in $l_{infty}$ and $l_2$ threat model, and certified robust accuracy by 6.7% over baselines not using proxy distributions on the CIFAR-10 dataset. Since we can sample an unlimited number of images from a proxy distribution, it also allows us to investigate the effect of an increasing number of training samples on adversarial robustness. Here we provide the first large scale empirical investigation of accuracy vs robustness trade-off and sample complexity of adversarial training by training deep neural networks on 2K to 10M images.
advertorch is a toolbox for adversarial robustness research. It contains various implementations for attacks, defenses and robust training methods. advertorch is built on PyTorch (Paszke et al., 2017), and leverages the advantages of the dynamic computational graph to provide concise and efficient reference implementations. The code is licensed under the LGPL license and is open sourced at https://github.com/BorealisAI/advertorch .
Deep networks are well-known to be fragile to adversarial attacks. We conduct an empirical analysis of deep representations under the state-of-the-art attack method called PGD, and find that the attack causes the internal representation to shift closer to the false class. Motivated by this observation, we propose to regularize the representation space under attack with metric learning to produce more robust classifiers. By carefully sampling examples for metric learning, our learned representation not only increases robustness, but also detects previously unseen adversarial samples. Quantitative experiments show improvement of robustness accuracy by up to 4% and detection efficiency by up to 6% according to Area Under Curve score over prior work. The code of our work is available at https://github.com/columbia/Metric_Learning_Adversarial_Robustness.
Despite their unmatched performance, deep neural networks remain susceptible to targeted attacks by nearly imperceptible levels of adversarial noise. While the underlying cause of this sensitivity is not well understood, theoretical analyses can be simplified by reframing each layer of a feed-forward network as an approximate solution to a sparse coding problem. Iterative solutions using basis pursuit are theoretically more stable and have improved adversarial robustness. However, cascading layer-wise pursuit implementations suffer from error accumulation in deeper networks. In contrast, our new method of deep pursuit approximates the activations of all layers as a single global optimization problem, allowing us to consider deeper, real-world architectures with skip connections such as residual networks. Experimentally, our approach demonstrates improved robustness to adversarial noise.
Deep learning models are prone to being fooled by imperceptible perturbations known as adversarial attacks. In this work, we study how equipping models with Test-time Transformation Ensembling (TTE) can work as a reliable defense against such attacks. While transforming the input data, both at train and test times, is known to enhance model performance, its effects on adversarial robustness have not been studied. Here, we present a comprehensive empirical study of the impact of TTE, in the form of widely-used image transforms, on adversarial robustness. We show that TTE consistently improves model robustness against a variety of powerful attacks without any need for re-training, and that this improvement comes at virtually no trade-off with accuracy on clean samples. Finally, we show that the benefits of TTE transfer even to the certified robustness domain, in which TTE provides sizable and consistent improvements.
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