提出基于黎曼几何的局部消息传递机制，解决图模型深度增加时的信息衰减问题。
Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models
- 引入局部黎曼几何建模图结构，动态调整消息传递路径。
- 在256层深度下仍保持性能稳定，克服信息过度平滑与挤压。
- 适用于异质与同质图数据，适合构建深层图基础模型。
消息传递神经网络（MPNN）是图基础模型的核心组件，但存在过度平滑和过度挤压问题。现有方法多采用全局策略，虽在某些区域有效，却可能在其他区域造成负面影响，导致表达能力不足。本文通过全局度量——谱隙λ——重新审视过度挤压问题，证明λ增大将导致输入特征梯度消失，削弱消息传递效果。基于此理论洞察，我们提出一种局部自适应方法，将局部黎曼几何与MPNN结合，建立新型非齐次边界条件，同时缓解过度挤压与过度平滑。在此基础上，设计了具有局部瓶颈调整的GBN网络，并提供理论保证。在同质与异质图上的大量实验表明，GBN具有强表达能力；且当网络深度超过256层时，性能不下降。
原文摘要 · Abstract (English)
Message Passing Neural Networks (MPNNs) is the building block of graph foundation models, but fundamentally suffer from oversmoothing and oversquashing. There has recently been a surge of interest in fixing both issues. Existing efforts primarily adopt global approaches, which may be beneficial in some regions but detrimental in others, ultimately leading to the suboptimal expressiveness. In this paper, we begin by revisiting oversquashing through a global measure -- spectral gap $λ$ -- and prove that the increase of $λ$ leads to gradient vanishing with respect to the input features, thereby undermining the effectiveness of message passing. Motivated by such theoretical insights, we propose a \textbf{local} approach that adaptively adjusts message passing based on local structures. To achieve this, we connect local Riemannian geometry with MPNNs, and establish a novel nonhomogeneous boundary condition to address both oversquashing and oversmoothing. Building on the Robin condition, we design a GBN network with local bottleneck adjustment, coupled with theoretical guarantees. Extensive experiments on homophilic and heterophilic graphs show the expressiveness of GBN. Furthermore, GBN does not exhibit performance degradation even when the network depth exceeds $256$ layers.
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