Bounds on the Vapnik-Chervonenkis Dimension of Graph Neural Networks with Pfaffian Activation Functions

The VC dimension of graph neural networks with Pfaffian activation functions, such as tanh, sigmoid, and arctangent, is bounded with respect to the network hyperparameters (number of parameters, layers, nodes, feature dimension) as well as the number of colors resulting from the 1-WL test on the graph domain.