Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

TL;DR

A fresh Riemannian geometry perspective is proposed, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer and presents the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence.

Abstract

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

Figures (8)

• Figure 1: An illustration of manifold gluing. The domains are distinguished by colors.
• Figure 2: An Illustration of GraphGlue Framework.
• Figure 3: GTM vs Test Task Loss.
• Figure 4: Effect of including distinct domains during pre-training.
• Figure 5: Geometric scaling law on (a) Computers and (b) Reddit datasets.

Theorems & Definitions (18)

• Definition 4.1: $(k,M)$-sparse perturbation
• Definition 4.2: Adaptive Orthogonal Frame, AOF
• Theorem 4.3: Upper bound of Tangent Vector Length, Appendix \ref{['proof. relation of perturbation']}
• Definition 4.4: Edge Tangent Translation
• Theorem 4.5: Tangent Edge Translation as Isometry, Appendix \ref{['proof. isometry']}
• Theorem 4.6: Existence of Global Metric, Appendix \ref{['proof. global_metric']}
• Definition 4.7: Holonomy Map and Holonomy Loss
• Theorem 4.8: Triangle Triviality, Appendix \ref{['proof. triangle']}
• Theorem 4.9: Ricci Curvature Estimation, Appendix \ref{['proof. curv']}
• Definition 4.10: $k$-order Smoothness and Curvature Loss