Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger

2026-02-28

AI Summary

This work addresses the limitation of conventional hypergraph neural networks, which rely on the homophily assumption and struggle to model long-range dependencies in heterophilous hypergraphs. From a Riemannian geometric perspective, the authors propose an adaptive local heat exchanger equipped with Robin boundary conditions and a source term, thereby linking the over-smoothing problem to hypergraph bottlenecks and establishing a locally adaptive regularization mechanism. The method theoretically guarantees both effective long-range dependency modeling and discriminative representation learning, while maintaining linear computational complexity. Extensive experiments demonstrate that the proposed model achieves state-of-the-art performance on both homophilous and heterophilous hypergraph benchmarks, confirming its effectiveness and strong generalization capability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Hypergraphs are the natural description of higher-order interactions among objects, widely applied in social network analysis, cross-modal retrieval, etc. Hypergraph Neural Networks (HGNNs) have become the dominant solution for learning on hypergraphs. Traditional HGNNs are extended from message passing graph neural networks, following the homophily assumption, and thus struggle with the prevalent heterophilic hypergraphs that call for long-range dependence modeling. In this paper, we achieve heterophily-agnostic message passing through the lens of Riemannian geometry. The key insight lies in the connection between oversquashing and hypergraph bottleneck within the framework of Riemannian manifold heat flow. Building on this, we propose the novel idea of locally adapting the bottlenecks of different subhypergraphs. The core innovation of the proposed mechanism is the design of an adaptive local (heat) exchanger. Specifically, it captures the rich long-range dependencies via the Robin condition, and preserves the representation distinguishability via source terms, thereby enabling heterophily-agnostic message passing with theoretical guarantees. Based on this theoretical foundation, we present a novel Heat-Exchanger with Adaptive Locality for Hypergraph Neural Network (HealHGNN), designed as a node-hyperedge bidirectional systems with linear complexity in the number of nodes and hyperedges. Extensive experiments on both homophilic and heterophilic cases show that HealHGNN achieves the state-of-the-art performance.

Problem

• heterophily
• hypergraph neural networks
• long-range dependencies
• oversquashing
• Riemannian geometry

Innovation

• Heterophily-Agnostic
• Riemannian Geometry
• Hypergraph Neural Networks
• Heat Flow
• Adaptive Local Exchanger