Is Distance Matrix Enough for Geometric Deep Learning?. (arXiv:2302.05743v3 [cs.LG] UPDATED)

Graph Neural Networks (GNNs) are often used for tasks involving the geometry
of a given graph, such as molecular dynamics simulation. Although the distance
matrix of a geometric graph contains complete geometric information, it has
been demonstrated that Message Passing Neural Networks (MPNNs) are insufficient
for learning this geometry. In this work, we expand on the families of
counterexamples that MPNNs are unable to distinguish from their distance
matrices, by constructing families of novel and symmetric geometric graphs. We
then …

arxiv deep learning dynamics exploit geometry gnns graph graph neural networks graphs information matrix molecular dynamics networks neural networks novel simulation work