# SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry

arXiv: https://arxiv.org/abs/2603.01168 · HTML: https://mlsanity.com/paper/2603.01168/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [Causal Inference under Networked Interference and Intervention Policy Enhancement](https://mlsanity.com/paper/2002.08506/) (2020)
- [Robust Multi-Agent Reinforcement Learning with State Uncertainty](https://mlsanity.com/paper/2307.16212/) (2023)
- [Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation](https://mlsanity.com/paper/2112.07184/) (2021)
- [Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty](https://mlsanity.com/paper/2311.08309/) (2023)
- [Self-supervised Hypergraph Representation Learning for Sociological Analysis](https://mlsanity.com/paper/2212.11440/) (2022)
- [A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications](https://mlsanity.com/paper/2111.01968/) (2021)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [CI-GNN: A Granger Causality-Inspired Graph Neural Network for Interpretable Brain Network-Based Psychiatric Diagnosis](https://mlsanity.com/paper/2301.01642/) (2023)
- [Identifying Possible Rumor Spreaders on Twitter: A Weak Supervised Learning Approach](https://mlsanity.com/paper/2010.07647/) (2020)
- [Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes](https://mlsanity.com/paper/2203.03060/) (2022)
- [Using Embeddings for Causal Estimation of Peer Influence in Social Networks](https://mlsanity.com/paper/2205.08033/) (2022)
- [MA-DPR: Manifold-aware Distance Metrics for Dense Passage Retrieval](https://mlsanity.com/paper/2509.13562/) (2025)
- [Geodesic Causal Inference](https://mlsanity.com/paper/2406.19604/) (2024)
- [Causal Spherical Hypergraph Networks for Modelling Social Uncertainty](https://mlsanity.com/paper/2506.17840/) (2025)
- [Causal Inference under Network Interference Using a Mixture of Randomized Experiments](https://mlsanity.com/paper/2309.00141/) (2023)
- [vMF-Contact: Uncertainty-aware Evidential Learning for Probabilistic Contact-grasp in Noisy Clutter](https://mlsanity.com/paper/2411.03591/) (2024)
- [Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA](https://mlsanity.com/paper/2411.00259/) (2024)
- [From News to Returns: A Granger-Causal Hypergraph Transformer on the Sphere](https://mlsanity.com/paper/2510.04357/) (2025)
- [A solution for the mean parametrization of the von Mises-Fisher distribution](https://mlsanity.com/paper/2404.07358/) (2024)
- [Higher-order Interaction Matters: Dynamic Hypergraph Neural Networks for Epidemic Modeling](https://mlsanity.com/paper/2503.20114/) (2025)

## Built on by (most cited first, 1 of 1)

- [Noise Floor Audit for Agent Benchmarks](https://mlsanity.com/paper/2608.22331/) (2026)

## Abstract (arXiv)

Reliable decision-making in complex multi-agent systems requires calibrated predictions and interpretable uncertainty. We introduce SphUnc, a unified framework combining hyperspherical representation learning with structural causal modeling. The model maps features to unit hypersphere latents using von Mises-Fisher distributions, decomposing uncertainty into epistemic and aleatoric components through information-geometric fusion. A structural causal model on spherical latents enables directed influence identification and interventional reasoning via sample-based simulation. Empirical evaluations on social and affective benchmarks demonstrate improved accuracy, better calibration, and interpretable causal signals, establishing a geometric-causal foundation for uncertainty-aware reasoning in multi-agent settings with higher-order interactions.