Expectation-Complete Graph Representations with Homomorphisms

Pascal Welke, Maximilian Thiessen, Fabian Jogl, Thomas Gärtner
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36910-36925, 2023.

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-welke23a, title = {Expectation-Complete Graph Representations with Homomorphisms}, author = {Welke, Pascal and Thiessen, Maximilian and Jogl, Fabian and G\"{a}rtner, Thomas}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36910--36925}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/welke23a/welke23a.pdf}, url = {https://proceedings.mlr.press/v202/welke23a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Expectation-Complete Graph Representations with Homomorphisms %A Pascal Welke %A Maximilian Thiessen %A Fabian Jogl %A Thomas Gärtner %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-welke23a %I PMLR %P 36910--36925 %U https://proceedings.mlr.press/v202/welke23a.html %V 202 %X 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.
APA
Welke, P., Thiessen, M., Jogl, F. & Gärtner, T.. (2023). Expectation-Complete Graph Representations with Homomorphisms. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36910-36925 Available from https://proceedings.mlr.press/v202/welke23a.html.

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