Structure-Centric Graph Foundation Model via Geometric Bases

TL;DR

This paper introduces SCGFM, a novel graph foundation model that aligns diverse graph structures using geometric bases and Gromov-Wasserstein distances, enabling better transferability across heterogeneous graph domains.

Contribution

It proposes a structure-centric approach with learnable geometric bases and a structure-aware feature re-encoding mechanism for improved transferability and handling of heterogeneous graph data.

Findings

Outperforms existing GFM approaches on various tasks.

Demonstrates strong in-domain and cross-domain generalization.

Effectively handles structural heterogeneity and feature incompatibility.

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.