# Causal Spherical Hypergraph Networks for Modelling Social Uncertainty

arXiv: https://arxiv.org/abs/2506.17840 · HTML: https://mlsanity.com/paper/2506.17840/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 21 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Analysing How People Orient to and Spread Rumours in Social Media by Looking at Conversational Threads](https://mlsanity.com/paper/1511.07487/) (2015)
- [Self-supervised Hypergraph Representation Learning for Sociological Analysis](https://mlsanity.com/paper/2212.11440/) (2022)
- [CI-GNN: A Granger Causality-Inspired Graph Neural Network for Interpretable Brain Network-Based Psychiatric Diagnosis](https://mlsanity.com/paper/2301.01642/) (2023)
- [Breaking Down Financial News Impact: A Novel AI Approach with Geometric Hypergraphs](https://mlsanity.com/paper/2409.00438/) (2024)

## Built on by (most cited first, 5 of 5)

- [ManifoldMind: Dynamic Hyperbolic Reasoning for Trustworthy Recommendations](https://mlsanity.com/paper/2507.02014/) (2025)
- [RicciFlowRec: A Geometric Root Cause Recommender Using Ricci Curvature on Financial Graphs](https://mlsanity.com/paper/2508.09334/) (2025)
- [From News to Returns: A Granger-Causal Hypergraph Transformer on the Sphere](https://mlsanity.com/paper/2510.04357/) (2025)
- [SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry](https://mlsanity.com/paper/2603.01168/) (2026)
- [GLANCE: Graph Logic Attention Network with Cluster Enhancement for Heterophilous Graph Representation Learning](https://mlsanity.com/paper/2507.18521/) (2025)

## Abstract (arXiv)

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.