VC dimensions of group convolutional neural networks
This addresses theoretical understanding of generalization in invariant neural networks for researchers, but it is incremental as it builds on existing VC dimension analysis.
The paper tackled the generalization capacity of group convolutional neural networks by estimating their VC dimensions, finding that two-parameter families can have infinite VC dimension for infinite groups with appropriate kernels, despite group invariance.
We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and appropriately chosen convolutional kernels, already two-parameter families of convolutional neural networks have an infinite VC dimension, despite being invariant to the action of an infinite group.