Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

TL;DR

This paper introduces a Riemannian geometry approach to unify multiple graph datasets into a smooth manifold, improving knowledge transfer and performance in graph foundation models through a novel theoretical framework and the GraphGlue system.

Contribution

It presents the neural manifold gluing theory and the GraphGlue framework, enabling systematic knowledge integration and transfer across diverse graph domains.

Findings

GraphGlue outperforms existing methods across multiple domains.

Larger datasets lead to smoother manifolds and better transferability.

Empirical validation of the geometric scaling law.

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.