Graph Neural Networks with polynomial activations have limited expressivity

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 …

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