Adversarial Robustness of NTK Neural Networks
Minimax optimal rates for adversarial regression in Sobolev spaces, but overfitting leaves models vulnerable.
Yuxuan Hou's recent paper, 'Adversarial Robustness of NTK Neural Networks,' tackles a critical challenge in deep learning: vulnerability to adversarial attacks. The study focuses on neural tangent kernel (NTK) networks, which approximate infinitely wide neural networks, within the context of nonparametric regression. Hou establishes minimax optimal rates for adversarial regression in Sobolev spaces, a theoretical framework for functions with smoothness constraints.
Crucially, the paper shows that NTK networks trained via gradient flow with early stopping can achieve these optimal rates, providing a theoretical guarantee for robustness. However, in the overfitting regime, where models perfectly fit training data (minimum norm interpolant), the networks become highly vulnerable to adversarial perturbations. This highlights a fundamental trade-off between fitting and robustness. The findings offer actionable insights for practitioners: early stopping is key to balancing performance and security in safety-critical applications like autonomous driving or medical imaging.
- NTK neural networks achieve minimax optimal rates for adversarial regression in Sobolev spaces when trained with gradient flow and early stopping.
- Overfitting, specifically the minimum norm interpolant, significantly increases vulnerability to adversarial attacks.
- The paper establishes theoretical foundations for robust deep learning deployment in safety-critical domains.
Why It Matters
Theoretical proof that early stopping in NTK networks balances accuracy and adversarial robustness, guiding safer AI deployment.