A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation

arXiv:2606.03315v1
Announcement Type: New

Abstract:

Graph foundation models (GFMs) are designed to acquire transferable knowledge from a wide variety of graphs, enabling effective generalization to previously unseen graphs and tasks. However, achieving cross-graph transfer is significantly more difficult for graphs than for text or images because graphs do not possess a common vocabulary or a regular spatial grid. This difficulty stems primarily from feature discrepancies and, even more critically, from the heterogeneous nature of graph structures.

Current approaches to enhancing transferability typically focus on harmonizing feature spaces or introducing structural tokens and vocabularies. Yet, existing topology-aware methods remain limited. Structural tokens tend to be discrete, and structural vocabularies frequently depend on predefined substructures like trees and cycles. Such limited coverage often fails to capture richer relational patterns that exist across different graphs. Furthermore, graph signals comprise both high-frequency local patterns and smoother low-frequency components, each necessitating distinct propagation behaviors. In raw graph signals, these elements are often intertwined, a spectral perspective that has been largely overlooked in current GFM research.

To overcome these obstacles, we introduce SPG, a graph foundation model that integrates spectral parsing with prototype-guided spatial propagation. SPG utilizes learnable Chebyshev filters to decompose node features into various spectral responses, thereby mitigating the mismatch between frequency-specific graph signals and their corresponding propagation behaviors. Subsequently, it employs a Gromov-Wasserstein prototype geometry to extract transferable pairwise relationships—extending beyond predefined substructures—into a unified structural space. This learned prototype geometry is then projected back into a prototype-guided propagation operator. Experimental results confirm consistent enhancements in cross-domain generalization performance.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC