Abstract

The study of opinion dynamics is an intriguing and challenging field that has attracted researchers from various disciplines. Opinion dynamics models aim to capture the intricate and dynamic nature of social interactions that shape the formation and evolution of opinions in human societies, and they have been proven valuable in investigating a wide range of phenomena, including political polarization, rumor propagation and emergence of consensus. Recently, there has been a growing interest in employing computational tools to model opinion dynamics, and within this realm, sheaf theory has emerged as a powerful mathematical framework. Sheaf theory enables the study of complex systems with both local and global interactions, treating opinions as mathematical entities associated with network nodes.

Bounded confidence, in the context of opinion dynamics, refers to a model where individuals are willing to adjust their opinions only if others’ opinions are sufficiently similar to their own. By incorporating bounded confidence into sheaf theory, it becomes possible to model and comprehend the emergence of opinion clusters, polarization, and the convergence or divergence of opinions within intricate social networks. An intriguing question arises: how does the integration of bounded confidence dynamics into a Sheaf Neural Network affect its expressiveness, signal diffusion, and ultimately its performance? Furthermore, what unique properties does it offer?