Complete Neural Networks for Euclidean Graphs

We propose a 2-WL-like geometric graph isomorphism test and prove it is complete when applied to Euclidean Graphs in $\mathbb{R}^3$. We then use recent results on multiset embeddings to devise an efficient geometric GNN model with equivalent separation power. We verify empirically that our GNN model is able to separate particularly challenging synthetic examples, and demonstrate its usefulness for a chemical property prediction problem.