Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation

The paper introduces HyperNSD, a stochastic differential equation framework for uncertainty estimation in hypergraph neural networks. Hypergraph representations evolve as stochastic processes over node-hyperedge incidence structures. A learnable drift function models deterministic higher-order diffusion, while a stochastic forcing function captures structural ambiguity and representation noise. Uncertainty is estimated from variability across stochastic representation trajectories rather than only from post-hoc prediction confidence. The authors report theoretical results on well-posedness, perturbation stability, permutation equivariance, and numerical convergence. Experiments on multiple hypergraph benchmarks evaluate out-of-distribution and misclassification detection while retaining competitive predictive accuracy.