This paper focuses on approximation and learning performance analysis for deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate $r$-smooth function, the approximation rates of deep convolutional neural networks with depth $L$ are of order $ (L^2/\log L)^{-2r/d} $, which is optimal up to a logarithmic factor. Furthermore, we deduce almost optimal learning rates for implementing empirical risk minimization over deep convolutional neural networks.

翻译：本文聚焦于采用零填充和最大池化的深度卷积神经网络的逼近与学习性能分析。我们证明，对于逼近$r$阶光滑函数，深度为$L$的深度卷积神经网络的逼近率阶数为$(L^2/\log L)^{-2r/d}$，该结果在对数因子意义下是渐进最优的。此外，我们推导出在深度卷积神经网络上实施经验风险最小化时，几乎最优的学习速率。