State evaluation functions and Lyapunov functions for neural networks

✍ Scribed by Youichi Kobuchi

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 711 KB
• Volume: 4
• Category: Article
• ISSN: 0893-6080
• DOI: 10.1016/0893-6080(91)90046-8

✦ Synopsis

For (I nettvork of binary State elements. consider functions from the set of State configurations into the .set of reul nurnberv. We first characterize the existenc~c of such .state evaluation f~rnctions through the properties on their difference flmctions. A method to restore the originul state eluluation fllnction from their difference fitnctions is also shown. A stute evaluation function is u Lyapunov fllnction for Some network if' the ,function ,ulae decrease.s us the system undergoes stute chuqes. Then NY apply the results for networks of' McCulloch-Pitts type model nelirons to see when there cun be L!apLtno~ firnctions. In the simplest lineur unulysis, the wleight mutrix W qf' the network hus non-negative diugonul elements and must be yuasi-symmetric with respect to u positive diagonal matrix C, that is. CW must he .syrnrnetric. We hu\se ulso deri~ed, us another example. more complicated conditions under wahich neurul networks hu~.e Lytrplrnol, ,flulctions.