On the VC dimension of deep group convolutional neural networks
Machine Learning
2024-10-22 v1 Statistics Theory
Machine Learning
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2410.15800,
title = {On the VC dimension of deep group convolutional neural networks},
author = {Anna Sepliarskaia and Sophie Langer and Johannes Schmidt-Hieber},
journal= {arXiv preprint arXiv:2410.15800},
year = {2024}
}