Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradients

• URL: http://arxiv.org/abs/2009.13145v2
• Date: Wed, 2 Jun 2021 04:14:08 GMT
• Title: Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradients
• Authors: Yifei Huang, Yaodong Yu, Hongyang Zhang, Yi Ma, Yuan Yao
• Abstract summary: We introduce a provably stable architecture for Neural Ordinary Differential Equations (ODEs) which achieves non-trivial adversarial robustness under white-box attacks. Inspired by dynamical system theory, we design a neural stabilized ODE network named SONet whose ODE blocks are skew-symmetric and proved to be input-output stable. With natural training, SONet can achieve comparable robustness with the state-of-the-art adversarial defense methods, without sacrificing natural accuracy.
• Score: 30.560531008995806
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we introduce a provably stable architecture for Neural Ordinary Differential Equations (ODEs) which achieves non-trivial adversarial robustness under white-box adversarial attacks even when the network is trained naturally. For most existing defense methods withstanding strong white-box attacks, to improve robustness of neural networks, they need to be trained adversarially, hence have to strike a trade-off between natural accuracy and adversarial robustness. Inspired by dynamical system theory, we design a stabilized neural ODE network named SONet whose ODE blocks are skew-symmetric and proved to be input-output stable. With natural training, SONet can achieve comparable robustness with the state-of-the-art adversarial defense methods, without sacrificing natural accuracy. Even replacing only the first layer of a ResNet by such a ODE block can exhibit further improvement in robustness, e.g., under PGD-20 ($\ell_\infty=0.031$) attack on CIFAR-10 dataset, it achieves 91.57\% and natural accuracy and 62.35\% robust accuracy, while a counterpart architecture of ResNet trained with TRADES achieves natural and robust accuracy 76.29\% and 45.24\%, respectively. To understand possible reasons behind this surprisingly good result, we further explore the possible mechanism underlying such an adversarial robustness. We show that the adaptive stepsize numerical ODE solver, DOPRI5, has a gradient masking effect that fails the PGD attacks which are sensitive to gradient information of training loss; on the other hand, it cannot fool the CW attack of robust gradients and the SPSA attack that is gradient-free. This provides a new explanation that the adversarial robustness of ODE-based networks mainly comes from the obfuscated gradients in numerical ODE solvers.

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