This paper studies the performance of deep convolutional neural networks (DCNNs) with zero-padding in feature extraction and learning. After verifying the roles of zero-padding in enabling translation-equivalence, and pooling in its translation-invariance driven nature, we show that with similar number of free parameters, any deep fully connected networks (DFCNs) can be represented by DCNNs with zero-padding. This demonstrates that DCNNs with zero-padding is essentially better than DFCNs in feature extraction. Consequently, we derive universal consistency of DCNNs with zero-padding and show its translation-invariance in the learning process. All our theoretical results are verified by numerical experiments including both toy simulations and real-data running.

本研究通过验证零填充在特征提取和学习中的作用，以及池化在其平移不变性驱动的性质中的作用，表明具有相似自由参数的深度全连接网络可以通过零填充的DCNNs来表示，从而证明了零填充的DCNNs在特征提取方面优于DFCNs。因此，我们推导出了具有零填充的DCNNs的普遍一致性，并展示了它在学习过程中的平移不变性。所有的理论结果都通过包括玩具模拟和真实数据运行的数值实验证实。

带零填充的深度卷积神经网络：特征提取与学习