In this paper, we study the generalization performance of min $\ell_2$-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.

翻译：在本文中,我们研究了二层神经网络神经相近内核(NTK)模型的超常性能。我们发现,根据地面真相功能,高装NTK模型的测试错误显示了不同于具有简单Fourier或Gaussian特征的其他超度线性模型“双白”的特征。具体地说,对于一类可学习功能,我们提供了一个新的超常性错误的上限,它接近于一个小的有限值,即使神经元数量接近于无限值。这种限制值随着培训样品的数量进一步减少,为美元。对于这一类以外的功能,我们提供了更低的通用性错误约束,即使美元和美元都是大的,也不会降低到零。