论文标题
深卷积神经网络的最佳收敛速率：添加脊功能
Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functions
论文作者
论文摘要
卷积神经网络在许多应用中表现出令人印象深刻的能力，尤其是与分类任务相关的功能。但是，对于回归问题，尚未完全了解卷积结构的能力，需要进一步研究。在本文中，我们考虑了深层卷积神经网络的平均误差分析。我们表明，对于添加脊功能，卷积神经网络随后是一个具有relu激活功能的完全连接的层可以达到最佳的迷你最大速率（最多可达对数系数）。输入维度仅出现在收敛速率的常数中。这项工作显示了卷积神经网络的统计最佳性，并可能阐明了为什么卷积神经网络能够在高维输入方面表现良好。
Convolutional neural networks have shown impressive abilities in many applications, especially those related to the classification tasks. However, for the regression problem, the abilities of convolutional structures have not been fully understood, and further investigation is needed. In this paper, we consider the mean squared error analysis for deep convolutional neural networks. We show that, for additive ridge functions, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal mini-max rates (up to a log factor). The input dimension only appears in the constant of convergence rates. This work shows the statistical optimality of convolutional neural networks and may shed light on why convolutional neural networks are able to behave well for high dimensional input.
