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

Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?