Deep learning models are widely deployed in safety-critical domains, but remain vulnerable to adversarial attacks. In this paper, we study the adversarial robustness of NTK neural networks in the context of nonparametric regression. We establish minimax optimal rates for adversarial regression in Sobolev spaces and then show that NTK neural networks, trained via gradient flow with early stopping, can achieve this optimal rate. However, in the overfitting regime, we prove that the minimum norm interpolant is vulnerable to adversarial perturbations.

翻译：深度学习模型被广泛部署于安全关键领域，但始终面临对抗攻击的脆弱性。本文在非参数回归背景下研究NTK神经网络的对抗鲁棒性。我们建立了Sobolev空间中对抗回归的极小极大最优速率，并证明通过梯度流结合早停法训练的NTK神经网络能达到该最优速率。然而，在过拟合机制中，我们证明最小范数插值器易受对抗扰动的影响。