Causal Spherical Hypergraph Networks for Modelling Social Uncertainty

Abstract: Human social behaviour is governed by complex interactions shaped by uncertainty, causality, and group dynamics. We propose Causal Spherical Hypergraph Networks (Causal-SphHN), a principled framework for socially grounded prediction that jointly models higher-order structure, directional influence, and epistemic uncertainty. Our method represents individuals as hyperspherical embeddings and group contexts as hyperedges, capturing semantic and relational geometry. Uncertainty is quantified via Shannon entropy over von Mises-Fisher distributions, while temporal causal dependencies are identified using Granger-informed subgraphs. Information is propagated through an angular message-passing mechanism that respects belief dispersion and directional semantics. Experiments on SNARE (offline networks), PHEME (online discourse), and AMIGOS (multimodal affect) show that Causal-SphHN improves predictive accuracy, robustness, and calibration over strong baselines. Moreover, it enables interpretable analysis of influence patterns and social ambiguity. This work contributes a unified causal-geometric approach for learning under uncertainty in dynamic social environments.