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.

翻译：我们提出一种类似2-WL的几何图同构测试，并证明该测试对$\mathbb{R}^3$中的欧几里得图具有完备性。随后，我们利用近期关于多重集嵌入的研究成果，设计了一种具有等价分离能力的几何图神经网络模型。实验验证表明，该模型能够有效区分极具挑战性的合成示例，并在化学性质预测问题中展现出其实用价值。