Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach

Published: 16 Jan 2024, Last Modified: 05 Mar 2024ICLR 2024 posterEveryoneRevisionsBibTeX
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: NTK, neural tangent kernels, adversarial training, robust overfitting
Submission Guidelines: I certify that this submission complies with the submission instructions as described on
TL;DR: We present a theoretical explanation of robust overfitting for DNNs and design the first adversarial training algorithm for infinite-width DNNs.
Abstract: Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental to the robustness of DNNs. This paper presents a theoretical explanation of robust overfitting for DNNs. Specifically, we non-trivially extend the neural tangent kernel (NTK) theory to AT and prove that an adversarially trained wide DNN can be well approximated by a linearized DNN. Moreover, for squared loss, closed-form AT dynamics for the linearized DNN can be derived, which reveals a new AT degeneration phenomenon: a long-term AT will result in a wide DNN degenerates to that obtained without AT and thus cause robust overfitting. Based on our theoretical results, we further design a method namely Adv-NTK, the first AT algorithm for infinite-width DNNs. Experiments on real-world datasets show that Adv-NTK can help infinite-width DNNs enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. The code is available at
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
Supplementary Material: zip
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: societal considerations including fairness, safety, privacy
Submission Number: 2578