{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/adversarial-robustness-of-stabilized","title":"Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradients","arxiv_id":"2009.13145","date":"2020-09-28","proceeding":null,"authors":["Yifei Huang","Yaodong Yu","Hongyang Zhang","Yi Ma","Yuan YAO"],"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.","url_abs":"https://arxiv.org/abs/2009.13145v2","url_pdf":"https://arxiv.org/pdf/2009.13145v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"adversarial-robustness-of-stabilized","repo_url":"https://github.com/yao-lab/SONet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"adversarial-defense","task_name":"Adversarial Defense"},{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"bottleneck-residual-block","method_name":"Bottleneck Residual Block"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"kaiming-initialization","method_name":"Kaiming Initialization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"residual-block","method_name":"Residual Block"},{"method_slug":"residual-connection","method_name":"Residual Connection"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2009.13145","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}