Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning

Torben Berndt, Benjamin Walker, Tiexin Qin, Jan Stühmer, Andrey Kormilitzin

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 Neu-
ral 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 represen-
tational 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.