defense 2026

Adversarial Robustness of NTK Neural Networks

Yuxuan Hou 1,2

1 Qiuzhen College

2 Tsinghua University

0 citations
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Published on arXiv

2604.25965

Input Manipulation Attack

OWASP ML Top 10 — ML01

Key Finding

NTK networks with early stopping achieve minimax optimal adversarial robustness rates in Sobolev spaces, while overfitted minimum norm interpolants are provably vulnerable

NTK with Early Stopping

Novel technique introduced

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.

Key Contributions

  • Establishes minimax optimal rates for adversarial regression in Sobolev spaces
  • Proves NTK neural networks with gradient flow and early stopping achieve optimal adversarial robustness
  • Demonstrates that minimum norm interpolants (overfitting regime) are provably vulnerable to adversarial perturbations

🛡️ Threat Analysis

Input Manipulation Attack

Paper analyzes adversarial robustness of neural networks against input perturbations in the adversarial regression setting, establishing both defense guarantees (early stopping achieves optimal robustness) and vulnerability results (overfitting regime is vulnerable).

Details

Domains
tabular
Model Types
traditional_ml
Threat Tags
inference_timeuntargeted
Applications
nonparametric regression
Read PDF arXiv

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