Sparse Geometric MPNNs Achieve Generic Separation with Connected Graphs

A recent study published on arXiv (2407.02025) examines the capabilities of message-passing neural networks (MPNNs) in relation to geometric graphs, where the features of nodes represent positions in 3D space. Previous research indicated that these models could distinguish between generic pairs of non-isomorphic geometric graphs, but those findings were based on the assumption of fully connected graphs, where every node is aware of all others. In reality, nodes typically have access only to a limited set of nearest neighbors. This paper reveals that message-passing networks with rotation equivariant features can separate non-isomorphic geometric graphs, provided the graph remains connected. If only invariant intermediate features are utilized, separation is assured for generically globally rigid graphs. These results are significant for fields like chemistry and other sciences that frequently utilize geometric graph data. The research team announced their findings as a replace-cross type on arXiv.