In an attempt to better understand structural benefits and generalization power of deep neural networks, we firstly present a novel graph theoretical formulation of neural network models, including fully connected, residual network~(ResNet) and densely connected networks~(DenseNet). Secondly, we extend the error analysis of the population risk for two layer network~\cite{ew2019prioriTwo} and ResNet~\cite{e2019prioriRes} to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained. These estimates are a priori in nature since they depend sorely on the information prior to the training process, in particular, the bounds for the estimation errors are independent of the input dimension.
翻译:为了更好地了解深神经网络的结构效益和普及力,我们首先提出神经网络模型的新颖图表理论公式,包括完全连接、剩余网络~(ResNet)和紧密连接网络~(DenseNet)等。 其次,我们将两个层网络(cite{ew2019priori2}和ResNet ⁇ cite{e2019prioriRes})的人口风险错误分析扩展至DenseNet,并进一步表明对于满足某些温和条件的神经网络,可以获得类似的估计。这些估计具有先验性,因为它们非常依赖培训过程之前的信息,特别是估计错误的界限独立于输入层面。