神经网络稳定性的逻辑分析

A Logical Analysis for Stability of Neural Networks

神经网络稳定性分析的传统方法是采用权矩阵的定量分析。本文提出一种基于推理和矛盾分析的逻辑分析法，并阐明导致网络不稳定的局部结构因素，这有利于神经网络的分析和设计。本文首先给出了二值神经网络（ＢＮＮ）的逻辑分析理论，然后对ＢＮＮ的稳定性给予定性分析，最后分别讨论了全约束规则和半约束规则形成矛盾环的情况。分析表明：神经网络不稳定的必要条件是网络中存在矛盾环。因此，有可能通过分析局部结构来研究网络的整体行为。

Traditional approaches for the analysis of stability of neural networks are quanti tative such as analysis of weight matrixes.This paper presents a logical method based on inference and contradiction analysis and reveals what partial/local structures are unstable factors,which is useful in the design and analysis of neural networks.In the paper,a logical theory of binary neural networks(BNNs) is first presented.Then,the qualitative analysis of the stability of BNNs is given.Finally,the formation of contradiction loops with full-constraint and semi-constraint rules is discussed.The analysis indicates that the existence of contradictory loops inside BNNs is a neces sary condition for BNNs to be unstable,so that it is possible to study the global properties of net works by only analyzing their partial/local structures.