深层前馈网络的单调同伦学习算法

本文研究前馈神经网络的结构以及快速二阶学习算法，首先提出一种能和适应分布网络结构的深层前馈网络模型，并利用构造性方法证明了该网络的通有逼近性质，为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性，数值实例显示了该方法的高效性与大范围收敛性，深层前馈网络模型具有自适应分布网络结构，高度非线性逼近性以及可实现快速学习算法等特点。

THE MONOTONE HOMOTOPY LEARNING ALGORITHM FOR DEEPLY LAYERED FEEDFORWARD NEURAL NETWORKS

This paper studies the feed forward neural network structures and their fast second order learning algorithm. In section 2 we propose a deeply layered feedforward network at which the structure can be located adaptively, and prove its universal approximation property by a construction method. To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method,to train the weights of the network. The numerical example shows the effectiveness and global convergence of the method. The deeply layered forward neural network has some chracteristics such as the adaptive structure location,highly nonlinear approximate capacity and fast learning.