Do Wider Neural Networks Really Help Adversarial Robustness?

Boxi Wu, Jinghui Chen, Deng Cai, Xiaofei He, Quanquan Gu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 Scopus citations


Adversarial training is a powerful type of defense against adversarial examples. Previous empirical results suggest that adversarial training requires wider networks for better performances. However, it remains elusive how does neural network width affect model robustness. In this paper, we carefully examine the relationship between network width and model robustness. Specifically, we show that the model robustness is closely related to the tradeoff between natural accuracy and perturbation stability, which is controlled by the robust regularization parameter λ. With the same λ, wider networks can achieve better natural accuracy but worse perturbation stability, leading to a potentially worse overall model robustness. To understand the origin of this phenomenon, we further relate the perturbation stability with the network’s local Lipschitzness. By leveraging recent results on neural tangent kernels, we theoretically show that wider networks tend to have worse perturbation stability. Our analyses suggest that: 1) the common strategy of first fine-tuning λ on small networks and then directly use it for wide model training could lead to deteriorated model robustness; 2) one needs to properly enlarge λ to unleash the robustness potential of wider models fully. Finally, we propose a new Width Adjusted Regularization (WAR) method that adaptively enlarges λ on wide models and significantly saves the tuning time.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Number of pages14
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: Dec 6 2021Dec 14 2021

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


Dive into the research topics of 'Do Wider Neural Networks Really Help Adversarial Robustness?'. Together they form a unique fingerprint.

Cite this