On the Expressive Power of Sparse Geometric MPNNs

Understand

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions.

• Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances.
• However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes.
• In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors.