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The adversarial vulnerability of neural nets, and subsequent techniques tocreate robust models have attracted significant attention; yet we still lack afull understanding of this phenomenon. Here, we study adversarial examples oftrained neural networks through analytical tools afforded by recent theoryadvances connecting neural networks and kernel methods, namely the NeuralTangent Kernel (NTK), following a growing body of work that leverages the NTKapproximation to successfully analyze important deep learning phenomena anddesign algorithms for new applications. We show how NTKs allow to generateadversarial examples in a ``training-free'' fashion, and demonstrate that theytransfer to fool their finite-width neural net counterparts in the ``lazy''regime. We leverage this connection to provide an alternative view on robustand non-robust features, which have been suggested to underlie the adversarialbrittleness of neural nets. Specifically, we define and study features inducedby the eigendecomposition of the kernel to better understand the role of robustand non-robust features, the reliance on both for standard classification andthe robustness-accuracy trade-off. We find that such features are surprisinglyconsistent across architectures, and that robust features tend to correspond tothe largest eigenvalues of the model, and thus are learned early duringtraining. Our framework allows us to identify and visualize non-robust yetuseful features. Finally, we shed light on the robustness mechanism underlyingadversarial training of neural nets used in practice: quantifying the evolutionof the associated empirical NTK, we demonstrate that its dynamics falls muchearlier into the ``lazy'' regime and manifests a much stronger form of the wellknown bias to prioritize learning features within the top eigenspaces of thekernel, compared to standard training.

What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness?