Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

TL;DR

This paper introduces permutation equivariant neural graph CDEs that efficiently model dynamic graphs, reducing parameters and enhancing performance in both simulated and real-world tasks.

Contribution

It proposes a novel permutation equivariant extension of Graph Neural CDEs, improving efficiency and generalization in dynamic graph representation learning.

Findings

Reduced parameter count without loss of accuracy

Improved performance in interpolation tasks

Enhanced generalization in real-world dynamic graph tasks

Abstract

Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios.