Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger
arXiv:2603.00599v1 Announce Type: new 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
arXiv:2603.00599v1 Announce Type: new 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.
Executive Summary
The article proposes a novel approach to hypergraph neural networks (HGNNs) by leveraging Riemannian geometry to achieve heterophily-agnostic message passing. The authors introduce a Heat-Exchanger with Adaptive Locality for Hypergraph Neural Network (HealHGNN), which enables long-range dependence modeling and preserves representation distinguishability. The proposed mechanism is based on the connection between oversquashing and hypergraph bottleneck within the framework of Riemannian manifold heat flow. The authors demonstrate the effectiveness of HealHGNN through extensive experiments on both homophilic and heterophilic cases, achieving state-of-the-art performance. The article contributes significantly to the field of HGNNs, providing a novel solution to the prevalent heterophilic hypergraphs.
Key Points
- ▸ Heterophily-agnostic message passing through Riemannian geometry
- ▸ Adaptive local heat exchanger for long-range dependence modeling
- ▸ Preservation of representation distinguishability
- ▸ HealHGNN architecture with linear complexity
Merits
Strength in theoretical foundation
The proposed mechanism is grounded in Riemannian manifold heat flow, providing a solid theoretical foundation for heterophily-agnostic message passing.
Demerits
Complexity of implementation
The adaptive local heat exchanger may require significant computational resources and expertise to implement, potentially limiting its adoption in practice.
Expert Commentary
The article makes a significant contribution to the field of HGNNs by providing a novel solution to the prevalent heterophilic hypergraphs. The proposed mechanism is well-grounded in Riemannian manifold heat flow, and the extensive experiments demonstrate its effectiveness. However, the complexity of implementation may be a limitation in practice. The article has implications for both practical applications and policy decisions, highlighting the importance of considering heterophily in HGNNs.
Recommendations
- ✓ Further investigation into the applicability of the proposed approach to other domains, such as recommendation systems and natural language processing.
- ✓ Development of more efficient implementation methods to reduce the computational complexity of the adaptive local heat exchanger.