A rising trend in theoretical deep learning is to understand why deep
learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method
that is equivalent to using gradient descent to train a multi-layer
infinitely-wide neural network. NTK is a major step forward in the theoretical
deep learning because it allows researchers to use traditional mathematical
tools to analyze properties of deep neural networks and to explain various
neural network techniques from a theoretical view. A natural extension of NTK
on graph learning is \textit{Graph Neural Tangent Kernel (GNTK)}, and
researchers have already provide GNTK formulation for graph-level regression
and show empirically that this kernel method can achieve similar accuracy as
GNNs on various bioinformatics datasets [dhs+19]. The remaining question now is
whether solving GNTK regression is equivalent to training an infinite-wide
multi-layer GNN using gradient descent. In this paper, we provide three new
theoretical results. First, we formally prove this equivalence for graph-level
regression. Second, we present the first GNTK formulation for node-level
regression. Finally, we prove the equivalence for node-level regression.

NTK 是理论深度学习领域的一个新兴趋势，通过 Neural Tangent Kernel（NTK）理解深度学习的工作原理。本文中，我们提供了三个新的理论结果，首先正式证明了基于图的回归问题中 GNTK 与无限宽度的多层图神经网络通过梯度下降训练是等效的；其次，我们提供了首个用于节点级回归问题的 GNTK 形式；最后，我们证明了在节点级回归问题中 GNTK 的等效性。