Inaba, Hiroshi (Tokyo Denki Univ.), Shoji, Yoshimitsu (Ikegami Tsushinki Corp.)

Stable Fixed Point Assignment Problems in Neural Networks

Scheduled for presentation during the Regular Session "Neural Networks I" (TuP01), Tuesday, July 25, 2006, 15:20−15:45, Room B2

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 27, 2023

Abstract

The problem of assigning a prescribed set of vectors to locally asymptotically stable fixed points of a system arises in implementing associative memory using a neural network. This paper discusses this problem for neural networks of the discrete state space type in the framework of systems and control theory. Although the so-called orthogonal projection method is reasonably powerful and widely used to construct such a network for associative memory, there is yet another important problem to be investigated. That is the problem of how to avoid fictitious fixed points created around desired fixed points or how to enlarge and /or adjust the domains of attraction of desired fixed points. Firstly a generalized orthogonal projection method is studied, and secondary introducing a state feedback structure in to a neural network it is shown that it is possible to design a control law such that without changing the already assigned fixed points each fixed point achieves a maximum convergence margin to improve the capability as associative memory. Finally, to illustrate the results, numerical examples for associative memory are worked out.