On the VC dimension of deep group convolutional neural networks

Equivariant neural networks outperform traditional deep neural networks on a number of tasks. The theoretical understanding of their generalization properties remains, however, limited. In this paper, we analyze the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function through the lens of Vapnik-Chervonenkis (VC) dimension theory. By deriving upper and lower bounds, we investigate how the network architecture affects the VC dimension.