Dirichlet Energy Constrained Learning for Deep Graph Neural Networks

TL;DR

This paper introduces a Dirichlet energy-based framework to enable deep graph neural networks, effectively preventing over-smoothing and achieving state-of-the-art results with many layers.

Contribution

It proposes a theoretical principle based on Dirichlet energy to guide deep GNN training, leading to the design of the EGNN framework.

Findings

EGNN achieves state-of-the-art performance with deep layers.

Dirichlet energy constraints effectively prevent over-smoothing.

Theoretical analysis guides the design of deep GNNs.

Abstract

Graph neural networks (GNNs) integrate deep architectures and topological structure modeling in an effective way. However, the performance of existing GNNs would decrease significantly when they stack many layers, because of the over-smoothing issue. Node embeddings tend to converge to similar vectors when GNNs keep recursively aggregating the representations of neighbors. To enable deep GNNs, several methods have been explored recently. But they are developed from either techniques in convolutional neural networks or heuristic strategies. There is no generalizable and theoretical principle to guide the design of deep GNNs. To this end, we analyze the bottleneck of deep GNNs by leveraging the Dirichlet energy of node embeddings, and propose a generalizable principle to guide the training of deep GNNs. Based on it, a novel deep GNN framework -- EGNN is designed. It could provide lower and upper constraints in terms of Dirichlet energy at each layer to avoid over-smoothing. Experimental results demonstrate that EGNN achieves state-of-the-art performance by using deep layers.