Dynamics of Autoassociative Neural Networks

摘要

In this report, the dynamics of autoassociative analogue neural networks is analyzed theoretically. We found some characteristics that do not depend on the form of the output function of the neurons. The distance between the network state vector and the subspace II_1 spanned by given patterns decreases at an exponential rate. And, the network dynamics is a (mapped) gradient flow in II_1. Moreover, the dynamics outside II_1 is also a (mapped) gradient flow. This means that the network dynamics is neither periodic nor chaotic even if the output function of the neurons is not monotonic.