Continuous Graph Neural Networks

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.

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• Geometer: Graph Few-Shot Class-Incremental Learning via Prototype Representation
• STEER: Simple Temporal Regularization For Neural ODEs
• Structural Inference of Networked Dynamical Systems with Universal Differential Equations
• Revisiting Graph Convolutional Network on Semi-Supervised Node Classification from an Optimization Perspective
• CPMR: Context-Aware Incremental Sequential Recommendation with Pseudo-Multi-Task Learning
• Continuous-Depth Neural Models for Dynamic Graph Prediction
• Reversible and irreversible bracket-based dynamics for deep graph neural networks