Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels

TL;DR

This paper introduces Graph Neural Tangent Kernels (GNTKs), combining the expressive power of GNNs with the theoretical guarantees and training simplicity of graph kernels, demonstrating strong empirical performance.

Contribution

The paper proposes GNTKs, a new class of graph kernels that represent infinitely wide GNNs trained by gradient descent, unifying GNN expressiveness with kernel advantages.

Findings

GNTKs achieve strong performance on graph classification tasks.

GNTKs provably learn smooth functions on graphs.

GNTKs inherit the full expressive power of GNNs.

Abstract

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to infinitely wide multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.