Study Establishes Optimal Adversarial Robustness Rates for NTK Neural Networks
Researchers have derived minimax optimal rates for adversarial robustness in Neural Tangent Kernel (NTK) neural networks applied to nonparametric regression in Sobolev spaces. The study shows that NTK networks trained with gradient flow and early stopping can achieve these optimal rates, but that minimum norm interpolation in the overfitting regime leaves models vulnerable to adversarial attacks. The findings provide a theoretical foundation for understanding when and why deep learning models fail under adversarial perturbations.
A preprint posted to arXiv investigates the adversarial robustness of Neural Tangent Kernel (NTK) neural networks within the framework of nonparametric regression. The authors establish minimax optimal convergence rates for adversarial regression problems defined over Sobolev spaces, providing a rigorous benchmark for evaluating model robustness. They demonstrate that NTK networks trained via gradient flow with early stopping can attain these optimal rates, suggesting a practical training strategy for robust models. However, the paper also proves that in the overfitting regime—specifically when using the minimum norm interpolant—networks become provably vulnerable to adversarial perturbations. This dual finding highlights a fundamental tension between interpolation-based training and robustness. The work contributes to the growing theoretical literature on adversarial machine learning by connecting classical statistical estimation theory with modern deep learning phenomena. The preprint has undergone at least one revision since its initial submission in April 2026.
What's missing
As a preprint, this work has not yet undergone formal peer review. The theoretical results are derived under NTK assumptions, which may not fully capture the behavior of finite-width or practically trained deep networks. The paper does not appear to include empirical validation on real-world datasets, leaving open questions about how well the theoretical rates translate to practice. The scope is limited to nonparametric regression and Sobolev spaces, so generalizability to classification tasks or other function classes is unclear.
What different sources said
- arXiv cs.LGCenter
Adversarial Robustness of NTK Neural Networks
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