Graph Neural Diffusion via Generalized Opinion Dynamics

2025-08-15

AI Summary

Existing diffusion-based graph neural networks suffer from three key limitations: (1) homogeneous and static diffusion processes that poorly adapt to diverse graph structures; (2) depth constraints imposed by computational overhead and diminished interpretability in deeper architectures; and (3) lack of theoretical guarantees on convergence. To address these, we propose GODNF—a Generalized Opinion Dynamics-based Neural Framework—that models heterogeneous diffusion and dynamic neighborhood influence via generalized opinion dynamics, enabling personalized node behavior modeling and adaptive neighborhood aggregation. GODNF introduces a trainable diffusion mechanism grounded in rigorous convergence analysis, thereby transcending the constraints of conventional diffusion paradigms. Extensive experiments demonstrate that GODNF achieves state-of-the-art performance on node classification and influence estimation tasks, while simultaneously offering enhanced expressivity, computational efficiency, structural interpretability, and robustness across heterogeneous graph topologies.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

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.

Problem

• Addressing homogeneous diffusion limitations in GNNs
• Overcoming depth constraints and interpretability issues
• Providing theoretical convergence analysis for diffusion models

Innovation

• Unifies opinion dynamics into trainable diffusion
• Models heterogeneous diffusion via node-specific behavior
• Ensures efficient interpretable propagation in deep layers