Graph Persistence goes Spectral
edge featuresglobal stabilitygraph modelsgraph neural networksgraph representation learninggraph structural informationlocal stabilitymessage-passingpersistent homologyph diagramsspectral informationtopological descriptortopological informationvertex featuresweisfeiler-leman hierarchy
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are increasingly employed for graph representation learning. In this context, recent works have proposed decorating classical PH diagrams with vertex and edge features for improved expressivity. However, these methods still fail to capture basic graph structural information. In this paper, we propose SpectRe