Continuous Graph Neural Networks

TL;DR

This paper introduces continuous graph neural networks (CGNN), a novel framework that models node dynamics continuously over time, improving depth and long-range dependency capture while being robust to over-smoothing.

Contribution

We propose a new continuous dynamics formulation for graph neural networks, extending discrete models with a theoretical basis and demonstrating enhanced depth and performance.

Findings

CGNN outperforms baseline methods on node classification tasks.

The approach is robust to over-smoothing, enabling deeper networks.

Theoretical analysis supports the continuous dynamics model.

Abstract

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.