Title: Neighborhood Sampling Does Not Learn the Same Graph Neural Network
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: graph neural network, neighborhood sampling, neural tangent kernel, Gaussian process posterior inference

Abstract: Neighborhood sampling is an important ingredient in the training of large-scale graph neural networks. It suppresses the exponential growth of the neighborhood size across network layers and maintains feasible memory consumption and time costs. While it becomes a standard implementation in practice, its systemic behaviors are less understood. We conduct a theoretical analysis by using the tool of neural tangent kernels, which characterize the (analogous) training dynamics of neural networks based on their infinitely wide counterparts---Gaussian processes (GPs). We study several established neighborhood sampling approaches and the corresponding posterior GP. With limited samples, the posteriors are all different, although they converge to the same one as the sample size increases. Moreover, the posterior covariance, which lower-bounds the mean squared prediction error, is uncomparable, aligning with observations that no sampling approach dominates.

TL;DR: We analyze the training dynamics of graph neural networks under neighborhood sampling by using graph neural tangent kernels.