Graph Neural Diffusion via Generalized Opinion Dynamics

TL;DR

This paper introduces GODNF, a novel diffusion-based GNN framework that models heterogeneous and dynamic diffusion processes, overcoming limitations of existing methods in adaptability, depth, and theoretical understanding.

Contribution

GODNF unifies opinion dynamics models into a trainable, flexible diffusion mechanism that captures heterogeneous and temporal diffusion patterns in graphs.

Findings

GODNF outperforms state-of-the-art GNNs in node classification.

Theoretical analysis confirms GODNF's ability to model diverse convergence behaviors.

Empirical results demonstrate improved influence estimation accuracy.

Abstract

There has been a growing interest in developing diffusion-based Graph Neural Networks (GNNs), building on the connections between message passing mechanisms in GNNs and physical diffusion processes. However, existing methods suffer from three critical limitations: (1) they rely on homogeneous diffusion with static dynamics, limiting adaptability to diverse graph structures; (2) their depth is constrained by computational overhead and diminishing interpretability; and (3) theoretical understanding of their convergence behavior remains limited. To address these challenges, we propose GODNF, a Generalized Opinion Dynamics Neural Framework, which unifies multiple opinion dynamics models into a principled, trainable diffusion mechanism. Our framework captures heterogeneous diffusion patterns and temporal dynamics via node-specific behavior modeling and dynamic neighborhood influence, while ensuring efficient and interpretable message propagation even at deep layers. We provide a rigorous theoretical analysis demonstrating GODNF's ability to model diverse convergence configurations. Extensive empirical evaluations of node classification and influence estimation tasks confirm GODNF's superiority over state-of-the-art GNNs.