VC dimensions of group convolutional neural networks

TL;DR

This paper investigates the VC dimensions of group convolutional neural networks, revealing that certain networks can have infinite VC dimension even with invariance to infinite groups, impacting their generalization understanding.

Contribution

It provides precise estimates for the VC dimensions of simple group convolutional neural networks and highlights cases with infinite VC dimension despite invariance.

Findings

Infinite VC dimension for certain networks with infinite groups

VC dimension estimates for specific group convolutional neural networks

Invariance does not necessarily limit VC dimension

Abstract

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.