Structure-Centric Graph Foundation Model via Geometric Bases

2026-05-09

AI Summary

Existing graph foundation models struggle with cross-graph domain transfer due to structural heterogeneity and incompatibility in node feature spaces. This work proposes a topology-centric, structure-aligned framework that models graphs as metric measure spaces, introducing learnable geometric bases to construct a shared structural coordinate system and employing Gromov–Wasserstein distance to align cross-graph structures. Concurrently, a structure-aware feature recoding mechanism enables unified representation of heterogeneous features without requiring fixed-dimensional inputs. The proposed approach demonstrates exceptional in-domain and cross-domain generalization performance on both graph-level and node-level tasks, significantly outperforming current graph foundation models.

Abstract

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov-Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Problem

• graph foundation models
• structural heterogeneity
• feature incompatibility
• transferable representations
• graph topology

Innovation

• graph foundation model
• geometric bases
• Gromov-Wasserstein alignment
• structure-aware representation
• metric measure space