Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to be learned, in an optimization framework. The proposed framework can be applied to any of the existing networks such as ResNet, DenseNet or Fractional-DNN. This framework is shown to help overcome the vanishing and exploding gradient issues. Stability of some of the existing continuous DNNs such as Fractional-DNN is also studied. The proposed approach is applied to an ill-posed 3D-Maxwell's equation.

翻译：深神经网络(DNN)中的地物传播可与非线性离散动态系统相关联。本文的新颖之处在于将离散参数(时间级级)在优化框架内的层次和层次上各异,需要学习。拟议框架可适用于ResNet、DenseNet或Freactional-DNN等任何现有网络。这一框架显示有助于克服消失和爆炸的梯度问题。还研究了Freactional-DNN等一些现有连续的DNN的稳定性。拟议方法适用于一个错误的 3D-Maxwell等式。