Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models Article Swipe

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Li Sun , Zhenhao Huang , Ming Zhang , Philip S. Yu · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2510.17457

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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preprint

Landing Page

http://arxiv.org/abs/2510.17457

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https://arxiv.org/pdf/2510.17457

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green

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https://openalex.org/W4415964566

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OpenAlex ID

https://openalex.org/W4415964566

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DOI

https://doi.org/10.48550/arxiv.2510.17457

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Title

Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models

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preprint

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Publication year

2025

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2025-10-20

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Authors

Li Sun, Zhenhao Huang, Ming Zhang, Philip S. Yu

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https://arxiv.org/abs/2510.17457

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https://arxiv.org/pdf/2510.17457

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Yes

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green

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https://arxiv.org/pdf/2510.17457

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