Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

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.

The key contributions are listed as follows.

1. Problem. We investigate the theoretical underpinnings of multi-domain graph pre-training and study a foundational problem of how knowledge is integrated and transferred across different domains.
2. Theory. We introduce a fresh differential-geometric perspective for systematically understanding knowledge transfer and propose the theory of neural manifold gluing, which consistently integrates multi-domain graphs into a unified, smooth Riemannian manifold via “gluing”.
3. Methodology. We propose a GRAPHGLUE framework based on the above theory that supports batched pre-training for large-scale graphs and incorporates a natural metric to quantify transferability.
4. Experiment. We evaluate GRAPHGLUEin cross-domain transfer learning and empirically demonstrate its geometric scaling law.