mlsanityData to 14 Oct 2026

Adversarial Robustness of NTK Neural Networks

arXiv 2604.25965 ↗First posted 28 Apr 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

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 facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 32 of its 45 references that are in the map. First posted on arXiv 28 Apr 2026.

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References · 32

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2020Language Models are Few-Shot Learnerscited by 32,419
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  5. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  6. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  7. 2013Intriguing properties of neural networkscited by 5,155
  8. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  9. 2016Understanding deep learning requires rethinking generalizationcited by 1,674
  10. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,517
  11. 2019Adversarial Examples Are Not Bugs, They Are Featurescited by 953
  12. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
20 more
  1. 2019Benign Overfitting in Linear Regressioncited by 549
  2. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  3. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  4. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  5. 2019Deep ReLU network approximation of functions on a manifoldcited by 74
  6. 2019Convergence of Adversarial Training in Overparametrized Neural Networkscited by 58
  7. 2023On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domainscited by 31
  8. 2023Generalization Ability of Wide Neural Networks on ℝcited by 30
  9. 2023On the Optimality of Misspecified Spectral Algorithmscited by 28
  10. 2023Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimensioncited by 26
  11. 2021Convergence rates of deep ReLU networks for multiclass classificationcited by 21
  12. 2021Interpolation can hurt robust generalization even when there is no noisecited by 15
  13. 2023Robust Nonparametric Regression under Poisoning Attackcited by 11
  14. 2023Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approachcited by 9
  15. 2024The Surprising Harmfulness of Benign Overfitting for Adversarial Robustnesscited by 9
  16. 2024On the Impacts of the Random Initialization in the Neural Tangent Kernel Theorycited by 5
  17. 2025Adversarial learning for nonparametric regression: Minimax rate and adaptive estimationcited by 3
  18. 2024Minimax rates of convergence for nonparametric regression under adversarial attackscited by 2
  19. 2025Adversarial Robustness of Nonparametric Regressioncited by 1
  20. 2026On damage of interpolation to adversarial robustness in regressioncited by 1

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