Title: Is Transferability of Common Substructures Realizable? A Riemannian Graph Foundation Model Utilizing Neural Vector Bundles

Abstract:

The pretraining-adaptation paradigm has driven a revolution in foundation models, with recent research extending this success to the graph domain. While graphs are characterized by complex structural patterns, the mechanisms behind their structural transferability remain insufficiently understood. Previous studies have focused on common substructures within discrete frameworks, prompting a fundamental inquiry: Can these common substructures be effectively transferred? This theoretical aspect has seen limited exploration. To address this, our work pivots toward acquiring transferable structures by examining functional behavior. We theoretically establish a link between transferable substructures and the intrinsic geometry of the representation space, a feature that has rarely been characterized. Leveraging Riemannian geometry, we introduce a framework for learning graph intrinsic geometry named Neural Vector Bundle, which facilitates the parsing of intrinsic geometry using local coordinates. Utilizing this foundation, we propose GAUGE, a pretrainable neural architecture that constructs the vector bundle by flattening geometrically compatible local coordinates. Additionally, we introduce a novel Dirichlet loss function designed to quantify the effort required for transfer. Our empirical evaluations demonstrate GAUGE’s superior expressiveness in demanding tasks, such as zero-shot link prediction and graph isomorphism.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC