无异质性偏见的超图神经网络与黎曼局部交换器
Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger
AI总结：
本文提出HealHGNN，通过黎曼几何和自适应局部交换器实现异质性无关的超图神经网络，提升长距离依赖建模和表示区分性。
摘要：
超图是描述对象间高阶相互作用的自然描述，广泛应用于社交网络分析、跨模态检索等领域。超图神经网络（HGNN）已成为学习超图的主导解决方案。传统HGNN是基于消息传递图神经网络扩展而来的，遵循同质性假设，因此在普遍存在的异质性超图中挣扎，这些超图需要长距离依赖建模。在本文中，我们通过黎曼几何的视角实现了异质性无关的消息传递。关键洞察在于框架内超压缩和超图瓶颈之间的联系。在此基础上，我们提出了在不同子超图中本地适应瓶颈的新理念。所提出机制的核心创新是设计了自适应的局部（热）交换器。具体来说，它通过Robin条件捕捉丰富的长距离依赖，通过源项保持表示区分性，从而实现具有理论保证的异质性无关消息传递。基于这一理论基础，我们提出了一个新的具有自适应局部性的超图神经网络（HealHGNN），设计为节点-超边双向系统，具有线性复杂度。在同质性和异质性案例上的广泛实验表明，HealHGNN实现了最先进的性能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
