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This paper addresses the theoretical gap in graph foundation models by linking transferable substructures to the intrinsic geometry of representation spaces. The authors introduce a Riemannian geometry-based framework, Neural Vector Bundle, which utilizes local coordinates and a novel Dirichlet loss to measure transfer effort. Empirical results demonstrate that this approach significantly improves expressiveness in challenging tasks like zero-shot link prediction and graph isomorphism.
Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
arXiv:2606.03270v1 Announce Type: cross Abstract: Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework called Neural Vector Bundle, which enables parsing intrinsic geometry with local coordinates. Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.
Title:Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
Abstract:Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework called Neural Vector Bundle, which enables parsing intrinsic geometry with local coordinates. Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.03270 [cs.LG]
(or arXiv:2606.03270v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.03270 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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