分析深度群卷积网络的泛化能力，揭示层数、参数量等对学习能力的影响。
On the VC dimension of deep group convolutional neural networks
- 通过上下界推导群卷积网络的VC维，研究其泛化能力
- 发现输入分辨率、层数和参数量显著影响学习能力
- 为理解群卷积网络泛化特性提供新视角，适合关注模型复杂度的研究者
我们通过推导上界和下界，研究了带有ReLU激活函数的群卷积神经网络（GCNNs）的泛化能力，重点关注层数、权重数量和输入维度等因素对Vapnik-Chervonenkis（VC）维的影响。进一步将所得边界与其它类型神经网络的结果进行比较。研究结果拓展了以往关于双层连续GCNNs VC维的工作，为理解GCNNs的泛化性质提供了新见解，尤其揭示了其对数据输入分辨率的依赖性。
原文摘要 · Abstract (English)
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.
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