离散型神经网络的数学理论(Ⅰ)——网络状态图

The mathematical fundamentals of discrete neural networks(Ⅰ) network state graphs

该系列文章重新系统地研究了离散型神经网络的数学理论．此文属首篇，引入了一种新的研究工具——网络状态图．对于离散神经网络而言，通过引入网络状态图，可以很清楚地看到该网络的运行机理：网络是否收敛，网络有多少个稳定吸引子，有多少个环吸引子，并能清楚地反映各类吸引子的吸引域．在这篇文章里，比较详细地讨论了网络状态图的一些基本性质，诸如网络的分支数等于网络稳定吸引子与环吸引子数目之和；对称离散神经网络、反对称离散神经网络在全并行运行条件下网络状态图的结构特征等．

The mathematical fundamentals of discrete neural networks are systematically studied in this series of papers. By introducing the network state graph for discrete neural networks, we can know clearly the running construction such as the number of stable states and cyclic stable states, and the field of stable states. In this paper, we study in detail some basic properties of network state graphs such as the number of components of a network which is equal to the sum of the numbers of stable states and cyclic stable state, and the network state graphs of symmetrical and antisymmetrical discrete neural networks in a fully parallel mode.