Review for NeurIPS paper: When Do Neural Networks Outperform Kernel Methods?

Summary and Contributions: This paper mainly studies the approximation error of random feature model, neural tangent kernel model, and two-layer neural network model, for non-uniform data distribution. Specifically, an "effective dimension" is defined to characterize the informative dimension of the data, which depend on both the dimension used to generate the target (d0) and the noise level on other dimensions. For RF and NT model, the approximation error bounds depends on the effective dimension. While for NN model, the bounds only depends on d0. This difference between two types of models can help understand the performance different between kernel methods and two-layer neural networks.