Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation

Traditional Hypergraph Neural Networks (HGNNs) typically produce deterministic representations, which often leads to overconfident predictions when faced with noisy attributes, ambiguous labels, or structural shifts. This paper addresses the lack of intrinsic uncertainty estimation in existing HGNNs by proposing a stochastic dynamical framework that models how uncertainty evolves during the message-passing process.

HyperNSD treats node representations as stochastic processes evolving over the node-hyperedge incidence structure. The framework is defined by a Stochastic Differential Equation (SDE) consisting of two primary components:

• Neural Drift: A deterministic function that captures higher-order diffusion dynamics, modulating the flow of information between nodes and hyperedges based on local feature compatibility.
• Stochastic Forcing: A learnable function that introduces representation noise and structural ambiguity into the diffusion process, allowing the model to generate multiple stochastic trajectories.

By sampling these trajectories, the model quantifies predictive uncertainty through the variability of the resulting representations, rather than relying on post-hoc confidence scores or computationally expensive ensemble methods.

The authors provide theoretical guarantees for the proposed dynamics, including well-posedness, stability under perturbations, and numerical convergence. Experimental results across multiple benchmarks demonstrate that HyperNSD effectively detects out-of-distribution (OOD) samples and misclassifications while maintaining competitive predictive accuracy. The study highlights that modeling uncertainty directly within the incidence-aware diffusion process is superior to traditional methods that ignore the higher-order geometry of hypergraphs.