[论文解读] Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger

Li Sun, Ming Zhang+6 more|arXiv (Cornell University)|Feb 28, 2026

Advanced Graph Neural Networks被引用 0

一句话总结

HealHGNN 引入一种基于自适应局部换热的超图神经网络，基于 Robin 边界条件与源项实现自适应本地换热，在同质和异质超图上均实现强性能和线性复杂度。

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.

研究动机与目标

• 在同时存在同质与异质的超图上推动学习，解决 HGNN 的过平滑与过挤压问题。
• 开发一个统一、几何信息驱动的消息传递机制，使其本地适应子超图结构。
• 提出自适应局部换换器（Robin 型边界控制+源项），实现信息流的平衡与特征保持。
• 创建 HealHGNN，一种节点-超边双向模型，具有线性复杂度，便于大规模学习。
• 在谱属性、瓶颈与能量动力学之间提供理论保证，与异性亲和性无关的传播相联系。

提出的方法

• 将超图扩散建模为黎曼热扩散，以将瓶颈与过挤压与特征谱间隙联系起来。
• 通过 Robin 边界条件引入自适应局部换换器，以控制子超图之间的信息通量。
• 通过源项引入能量，保持节点特征差异并防止过平滑。
• 将节点与超边传播耦合，形成具有可学习边界与耦合参数的双向扩散系统。
• 推导节点级、Jacobi 迭代风格的更新，节点数+超边数的线性复杂度。
• 给出使用拉普拉斯算子和双向传输算子（P_V→V、P_E→V 等）的简洁的节点/超边更新公式。

Figure 1 . (A). Traditional dynamics in HGNN. (B). Illustration of our adaptive heat exchanger; bd denotes boundary nodes.

实验结果

研究问题

• RQ1 RQ1：HealHGNN 是否能在大规模的同质与异质超图上工作？
• RQ2 RQ2：该方法是否在实现长距离传播的同时缓解过挤压？
• RQ3 RQ3：在堆叠深层层数时，该方法是否能缓解过平滑？
• RQ4 RQ4：所提出的 Robin 边界和源项组件对性能有多关键？

主要发现

• HealHGNN 在同质超图上实现了有竞争力的结果，在异质超图上实现了明显提升。
• 在 Senate 数据集上，HealHGNN 比次优方法高出 5%。
• 该模型在多种真实世界和异质超图上展示了最先进或接近最先进的性能。
• 实验结果支持异性亲和性无关的设计，验证了在不牺牲局部区分度的情况下捕捉长程依赖。
• 该方法在节点和超边数量上的线性复杂度使得可扩展的大规模超图学习成为可能。

Figure 2 . Overall architecture of the proposed heat kernel based hypergraph neural network.