论文标题
深层卷积神经网络的学习能力
Learning Ability of Interpolating Deep Convolutional Neural Networks
论文作者
论文摘要
经常观察到过度参数化的神经网络概括了。关于这种现象，现有的理论工作主要致力于线性设置或完全连接的神经网络。本文研究了重要的神经网络，深度卷积神经网络（DCNNS）的学习能力，在不同参数和过度参数的环境下。我们建立了文献中提出的参数或功能变量结构限制的范围内的DCNN的第一个学习率。我们还表明，通过将良好定义的层添加到非插值DCNN中，我们可以获得一些插值DCNN，这些DCNN可以维持非交流DCNN的良好学习率。该结果是通过为DCNN设计的新型网络加深方案而实现的。我们的工作提供了理论上的验证DCNN的概括性过高。
It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under both underparameterized and overparameterized settings. We establish the first learning rates of underparameterized DCNNs without parameter or function variable structure restrictions presented in the literature. We also show that by adding well-defined layers to a non-interpolating DCNN, we can obtain some interpolating DCNNs that maintain the good learning rates of the non-interpolating DCNN. This result is achieved by a novel network deepening scheme designed for DCNNs. Our work provides theoretical verification of how overfitted DCNNs generalize well.
