Expectation-Complete Graph Representations with Homomorphisms

Welke, Pascal and Thiessen, Maximilian and Jogl, Fabian and Gärtner, Thomas (2023) Expectation-Complete Graph Representations with Homomorphisms. Other. Arxiv.

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Abstract

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 Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.