Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation

2026-07-08

AI Summary

Existing hypergraph neural networks struggle to effectively capture predictive uncertainty inherent in high-order relationships, particularly failing to model the evolution of uncertainty induced by structural changes in node–hyperedge associations. This work proposes HyperNSD, which for the first time introduces stochastic differential equations (SDEs) into hypergraph representation learning. By employing learnable drift and diffusion functions, HyperNSD models hypergraph embeddings as a structure-aware stochastic process that intrinsically unifies deterministic dynamics with structural ambiguity and noise. The method enjoys strong theoretical guarantees—including well-posedness, perturbation stability, permutation equivariance, and numerical convergence—and achieves significant improvements in out-of-distribution detection and misclassification identification across multiple benchmarks, while maintaining competitive predictive accuracy, thereby enabling trustworthy high-order representation learning.

Abstract

Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored. Unlike pairwise graphs, uncertainty in hypergraphs arises not only from noisy attributes and ambiguous labels, but also from variations in node-hyperedge incidence structures and complex higher-order dependencies. Existing approaches mainly estimate uncertainty from final predictions or rely on computationally expensive ensembles and Bayesian inference, limiting their ability to capture uncertainty evolution during representation learning. In this paper, we propose Hypergraph Neural Stochastic Diffusion(HyperNSD), a stochastic differential equation framework for uncertainty estimation on hypergraphs. HyperNSD models hypergraph representations as stochastic processes evolving over node-hyperedge incidence structures. A learnable drift function captures deterministic higher-order diffusion dynamics, while a learnable stochastic forcing function characterizes structural ambiguity and representation noise. Predictive uncertainty is directly quantified through the variability of stochastic representation trajectories, providing an intrinsic uncertainty measure beyond post-hoc confidence scores. We formulate HyperNSD with neural drift and diffusion networks, enabling joint learning of prediction and uncertainty propagation. Theoretical analyses establish well posedness, perturbation stability,permutation equivariance, and numerical convergence of the proposed stochastic dynamics. Experiments on multiple hypergraph benchmarks demonstrate that HyperNSD achieves reliable uncertainty estimation for out-of-distribution and misclassification detection while preserving competitive prediction accuracy. These results provide a principled stochastic-dynamical framework for trustworthy higher-order representation learning.

Problem

• hypergraph
• uncertainty estimation
• higher-order relations
• stochastic differential equation
• representation learning

Innovation

• Hypergraph Neural Networks
• Stochastic Differential Equations
• Uncertainty Estimation
• Higher-order Relations
• Stochastic Representation Learning