Expectation-Complete Graph Representations with Homomorphisms
Pascal Welke,u00a0Maximilian Thiessen,u00a0Fabian Jogl,u00a0Thomas Gu00e4rtner
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lovu00e1szu2019 characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.
