A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation
2026-06-02 • Machine Learning
Machine Learning
AI summaryⓘ
The authors focus on making graph foundation models better at understanding and transferring knowledge between different kinds of graphs, which is hard because graphs vary a lot in structure and features. They introduce SPG, a model that separates graph information into frequency parts to better match how patterns spread in graphs. They also create a shared structural space using a method called Gromov-Wasserstein prototype geometry to capture relationships that go beyond simple patterns. Their approach improves performance when applying models to new, unseen graphs.
graph foundation modelsgraph structureChebyshev filtersspectral graph theoryGromov-Wasserstein distanceprototype geometrygraph signal processingcross-domain generalizationspatial propagationstructural tokens
Authors
Ankang Yang, Jitao Zhao, Dongxiao He, Liang Yang, Di Jin, Weixiong Zhang
Abstract
Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks. Unlike text and images, graphs lack a shared vocabulary or regular spatial grid, making cross-graph transfer challenging. This challenge comes from both feature discrepancies and, more critically, diverse graph structures. Existing GFMs mainly improve transferability by unifying feature spaces or incorporating structural tokens and vocabularies. However, existing topology-aware designs still have limitations. Structural tokens are usually discrete, while structural vocabularies often rely on predefined substructures such as trees and cycles, whose limited coverage may miss richer relational patterns across graphs. Moreover, graph signals contain both high-frequency local patterns and smoother low-frequency patterns, which require different propagation behaviors. These components are often entangled in raw graph signals, while this spectral perspective is rarely explored in existing GFMs. To address these challenges, we propose SPG, a graph foundation model with spectral parsing and prototype-guided spatial propagation. SPG applies learnable Chebyshev filters to decompose node features into multiple spectral responses, reducing the mismatch between frequency-specific graph signals and propagation behaviors. It then constructs a Gromov-Wasserstein prototype geometry to distill transferable pairwise relations beyond predefined substructures into a shared structural space. The learned prototype geometry is further projected back as a prototype-guided propagation operator. Experiments demonstrate consistent improvements in cross-domain generalization.