To address this shortcoming of weak convergence, D. Aldous [

Augmenting these graph models with topological features via persistent homology (PH) has gained prominence, but identifying the class of attributed graphs that PH can recognize remains open. We introduce a novel concept of color-separating sets to provide a complete resolution to this important problem.

This state of the art was recently critiqued by O'Bray et al.

SSL based on persistent homology (PH), a mathematical tool for modeling topological features of data that persist across multiple scales.

Many works have studied neural execution in different domains before [45, 23, 24, 31, 33, 42]. With the rapid development of GNNs in graph representation learning, learning graph algorithms with GNNs has attracted researchers' attention [39, 38, 41]. These works exploit GNNs to approximate certain classes of graph algorithms, such as parallel algorithms (e.g., Breadth-First-Search) and sequential algorithms (e.g., Dijkstra).

However,computing extendedpersistent homologysummaries remainsslowfor large and dense graphs and can be aserious bottleneck for the learning pipeline.