On the Generalization Power of Overfitted Two-Layer Neural Tangent Kernel Models
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In this paper, we study the generalization performance of min ℓ_2-norm overfitting solutions for the neural tangent kernel (NTK) model of a two-layer neural network. We show that, depending on the ground-truth function, the test error of overfitted NTK models exhibits characteristics that are different from the "double-descent" of other overparameterized linear models with simple Fourier or Gaussian features. Specifically, for a class of learnable functions, we provide a new upper bound of the generalization error that approaches a small limiting value, even when the number of neurons p approaches infinity. This limiting value further decreases with the number of training samples n. For functions outside of this class, we provide a lower bound on the generalization error that does not diminish to zero even when n and p are both large.
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