On the VC dimension of deep group convolutional neural networks
This work provides theoretical insights into the generalization properties of GCNNs, which is important for researchers in machine learning theory, but it is incremental as it extends previous results on VC dimension.
The authors tackled the problem of understanding the generalization capabilities of Group Convolutional Neural Networks (GCNNs) by deriving upper and lower bounds for their VC dimension, showing how factors like layers and input dimension affect it, and comparing these bounds to other neural networks.
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.