Structure-Centric Graph Foundation Model via Geometric Bases

Researchers propose Structure-Centric Graph Foundation Models (SCGFM), a novel approach that treats graph topology as the primary source of transferable knowledge using geometric bases and Gromov-Wasserstein distances. The method addresses key limitations in existing graph foundation models by handling structural heterogeneity and incompatible node feature spaces, demonstrating improved generalization across both in-domain and cross-domain graph tasks.

The development of Structure-Centric Graph Foundation Models represents a meaningful advancement in transfer learning for graph neural networks. Previous graph foundation models struggled with fundamental incompatibilities when applying learned representations across different graph domains—inconsistent node feature dimensions, varying structural patterns, and heterogeneous topologies created barriers to meaningful knowledge transfer. SCGFM reframes this problem by prioritizing graph structure itself as the core transferable signal, rather than attempting to harmonize incompatible feature spaces directly.

This approach builds on the mathematical foundation of optimal transport theory, specifically Gromov-Wasserstein distances, which enable comparison and alignment of different metric measure spaces without requiring direct correspondence. By learning a shared set of geometric bases that define a universal structural coordinate system, the model can map diverse graph topologies into a common representational space. The structure-aware feature re-encoding mechanism then handles node-level features flexibly, without assuming fixed dimensionality or requiring dataset-specific preprocessing.

For the AI and machine learning community, this work addresses a practical bottleneck in foundation model development. Graph-structured data appears across domains—molecular structures, social networks, recommendation systems, and knowledge graphs—but cross-domain transfer has remained elusive. Demonstrated improvements on both graph-level and node-level tasks suggest the approach has genuine utility beyond academic benchmarks.

The architecture's flexibility regarding feature spaces makes it particularly relevant for real-world deployment scenarios where data preprocessing pipelines vary significantly across organizations. Future developments will likely focus on scaling these methods to larger graphs and validating performance on domain-specific transfer tasks.

• →SCGFM treats graph topology as primary transferable knowledge using learnable geometric bases and optimal transport theory.
• →The method eliminates assumptions about fixed node feature dimensions, enabling flexible cross-domain knowledge transfer.
• →Gromov-Wasserstein distance-based alignment creates structure-aligned latent representations accommodating heterogeneous graph topologies.
• →Experimental results show strong generalization on both in-domain and cross-domain graph and node-level tasks.
• →The approach reduces preprocessing requirements, potentially lowering barriers to deploying graph foundation models in production systems.