We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN. These results allow us to introduce an expected classifier (EC), and to give probabilistic upper bound for the classification error of the EC. We also state the optimal number of layers for the SDNN via an optimal stopping procedure. We apply our analysis to a stochastic version of a feedforward neural network with ReLU activation function.

翻译：本文给出了随机深度神经网络（SDNN）隐藏层输出以及整个SDNN输出的浓度不等式。这些结论使我们能够引入一个期望分类器（EC），并为该EC的分类误差提供概率上界。此外，我们还通过最优停止过程确定了SDNN的最优层数。我们将分析应用于采用ReLU激活函数的前馈神经网络的随机版本。