论文标题
控制映射的流形，以了解深度学习
Control on the Manifolds of Mappings with a View to the Deep Learning
论文作者
论文摘要
对人工神经网络（ANN）的深入学习可以视为特定类别的插值问题。目的是找到一个神经网络，其输入输出图在有限或无限训练集上近似于所需的地图。我们的想法包括将输入输出图作为近似值，这是由非线性连续时间控制系统产生的。在限制中，该控制系统可以看作是一个连续层的网络，每个网络都标记为时间变量。每个时间瞬间的控件值是图层的参数。
Deep learning of the Artificial Neural Networks (ANN) can be treated as a particular class of interpolation problems. The goal is to find a neural network whose input-output map approximates well the desired map on a finite or an infinite training set. Our idea consists of taking as an approximant the input-output map, which arises from a nonlinear continuous-time control system. In the limit such control system can be seen as a network with a continuum of layers, each one labelled by the time variable. The values of the controls at each instant of time are the parameters of the layer.
