Research
Message-Passing Graph Persistence (MGP) enhances GNN expressivity with topology-aware descriptors
The paper introduces Message-Passing Graph Persistence (MGP), a family of topological descriptors that integrates message passing into graph filtrations, updating node embeddings at each step and linking them to persistence events. MGP is proven to be invariant under graph isomorphism and strictly more expressive than existing PH-based descriptors. Experiments on expressivity benchmarks and graph classification/regression datasets show MGP outperforms other PH-based descriptors on most datasets.
Graph Neural NetworksTopological Data AnalysisPersistent Homology