ODNet: Opinion Dynamics-Inspired Neural Message Passing for Graphs and Hypergraphs

Neural message passing serves as a cornerstone framework in graph neural networks, providing a clear and intuitive mathematical guideline for the propagation and aggregation of information among interconnected nodes within graphs. Throughout this process, node representations undergo dynamic updates, considering both the individual states and connections of neighboring nodes. Concurrently, social networks, as prominent forms of interconnected data, form dynamic systems that achieve stability through continuous internal communications and opinion exchanges among social actors along their social ties. Drawing upon the shared concepts between these two domains, our study establishes an explicit connection between message passing and opinion dynamics in sociology. Moreover, we introduce a novel continuous message passing scheme termed ODNet, which integrates bounded confidence to refine the influence weight of local nodes for message propagation. By adjusting the similarity cutoffs of bounded confidence and influence weights within ODNet, we define opinion exchange rules that align with the characteristics of neural message passing and can effectively mitigate the oversmoothing issue. We extend the framework to hypergraphs and formulate corresponding continuous message passing rules, which reveal a close association with particle dynamics. Empirically, we showcase that ODNet enhances prediction performance across various social networks presented as homophilic graphs, heterophilic graphs, and hypergraphs. Notably, our proposed ODNet outperforms existing GNNs with its straightforward construction and robust theoretical foundation.