On the VC dimension of deep group convolutional neural networks

TL;DR

This paper analyzes the VC dimension of Group Convolutional Neural Networks (GCNNs) with ReLU, providing bounds that relate network complexity to factors like layers, weights, and input size, enhancing understanding of their generalization.

Contribution

It extends previous VC dimension bounds for GCNNs to multiple layers and input resolutions, offering new insights into their generalization capabilities.

Findings

Derived upper and lower bounds for VC dimension of GCNNs.

Compared VC bounds of GCNNs with other neural network types.

Showed how input resolution affects GCNN generalization.

Abstract

We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such as the number of layers, weights, and input dimension affect the VC dimension. We further compare the derived bounds to those known for other types of neural networks. Our findings extend previous results on the VC dimension of continuous GCNNs with two layers, thereby providing new insights into the generalization properties of GCNNs, particularly regarding the dependence on the input resolution of the data.