论文标题
使用深度卷积神经网络进行图像分类的统计学理论，在分层最大模型下具有跨凝结损失
Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss under the hierarchical max-pooling model
论文作者
论文摘要
事实证明，经过跨凝结损失训练的卷积神经网络（CNN）在对图像进行分类方面非常成功。近年来，已经进行了许多工作，以提高对神经网络的理论理解。然而，当这些网络经过交叉渗透损失训练时，这似乎有限，这主要是由于目标函数的无限性。在本文中，我们旨在通过分析通过跨透镜损失训练的CNN分类器的多余风险率来填补这一空白。在对A后验概率的平滑度和结构的合适假设下，证明这些分类器达到了与图像尺寸无关的收敛速率。这些速率与有关CNN的实际观察结果一致。
Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks. Nevertheless, it seems limited when these networks are trained with cross-entropy loss, mainly because of the unboundedness of the target function. In this paper, we aim to fill this gap by analyzing the rate of the excess risk of a CNN classifier trained by cross-entropy loss. Under suitable assumptions on the smoothness and structure of the a posteriori probability, it is shown that these classifiers achieve a rate of convergence which is independent of the dimension of the image. These rates are in line with the practical observations about CNNs.
