Expectation-Complete Graph Representations with Homomorphisms
This work addresses a fundamental limitation in graph representation learning for applications requiring high expressiveness and efficiency, though it appears incremental as it builds on existing homomorphism-based characterizations.
The paper tackles the problem of distinguishing non-isomorphic graphs efficiently by proposing novel random graph embeddings that can be computed in expected polynomial time and are expectation-complete, achieving competitive results on benchmark graph learning tasks.
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 Lovász' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.