Graph Neural Networks with polynomial activations have limited expressivity. (arXiv:2310.13139v4 [cs.LG] UPDATED)

The expressivity of Graph Neural Networks (GNNs) can be entirely
characterized by appropriate fragments of the first order logic. Namely, any
query of the two variable fragment of graded modal logic (GC2) interpreted over
labeled graphs can be expressed using a GNN whose size depends only on the
depth of the query. As pointed out by [Barcelo & Al., 2020, Grohe, 2021], this
description holds for a family of activation functions, leaving the
possibibility for a hierarchy of logics expressible …

arxiv cs.lg gnn gnns graph graph neural networks graphs interpreted logic modal networks neural networks polynomial query