Towards Deep Learning Models Resistant to Adversarial Attacks (1706.06083v4)

Published 19 Jun 2017 in stat.ML, cs.LG, and cs.NE

Abstract: Recent work has demonstrated that deep neural networks are vulnerable to adversarial examples---inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much of the prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against any adversary. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest the notion of security against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models. Code and pre-trained models are available at https://github.com/MadryLab/mnist_challenge and https://github.com/MadryLab/cifar10_challenge.

Authors (5)

Aleksander Madry (86 papers)
Aleksandar Makelov (4 papers)
Ludwig Schmidt (80 papers)
Dimitris Tsipras (22 papers)
Adrian Vladu (24 papers)

Citations (11,100)

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Summary

Abstract

Deep learning models, especially deep neural networks, suffer from a vulnerability to adversarial attacks—inputs that are slightly altered to cause the network to misclassify them. These adversarial inputs challenge the security features of deep learning applications, demonstrating that the affected models do not robustly grasp the underlying concepts they were trained to identify. This paper examines the adversarial robustness of deep neural networks through the lens of robust optimization and proposes using a saddle point (min-max) formulation to provide a structured perspective on creating models resistant to these attacks.

Adversarial Robustness

The introduction of deep learning in security-sensitive systems such as autonomous vehicles and malware detection has highlighted the necessity for models resistant to adversarial attacks. Although current classifiers perform well on benign inputs, they are susceptible to adversarial manipulation. The paper investigates the use of a principled min-max optimization framework for robustness, offering a unified view on existing adversarial example literature and suggesting optimal strategies for both constructing and defending against adversarial examples.

Methodology

The authors present an empirical exploration of the optimization landscape with the following findings:

Despite its non-convex and non-concave nature, the saddle point problem formed by adversarial-robust optimization is tractable.
Higher model capacity, implying a more complex decision boundary, is needed to withstand adversarial examples reliably.
Networks trained using Projected Gradient Descent (PGD) as an adversary achieved significantly greater resistance to adversarial examples on MNIST and CIFAR10 datasets.

Contributions and Experimental Results

The paper makes major strides in robustifying deep learning models:

Demonstrating tractable solutions to adversarial optimization via first-order methods.
Establishing the importance of network capacity in enhancing adversarial robustness.
Presenting robust training methods that notably improve a network's resilience against a spectrum of adversarial attacks.

For MNIST and CIFAR10 trained models, accuracy benchmarks show remarkable resistance to the strongest test adversarial attacks and even higher accuracy against weaker, black-box, or transfer attacks. The paper concludes with an invitation to the research community to further evaluate the robustness of the proposed models through public challenges, providing links to the accompanying code repositories.

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GitHub - MadryLab/cifar10_challenge: A challenge to explore adversarial robustness of neural networks on CIFAR10. (498 stars)

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