Abstract

We study a model for learning periodic signals in recurrent neural networks proposed by Doya and Yoshizawa [7] that can be considered as a model for temporal pattern memory in animal motoric systems. A network receives an external oscillatory input and adjusts its weights so that this signal can be reproduced approximately as the network output after some time. We use tools from adaptive control theory to derive an algorithm for weight matrices with special structure. If the input is generated by a network of the same structure the algorithm converges globally and does not exhibit the deficiencies of the back-propagation based approach of Doya and Yoshizawa under a persistency of excitation condition. This simple algorithm can also be used for open loop identification under quite restrictive assumptions. The persistency of excitation condition cannot be proven even for the matrices with special structure but for a 3d system. For higher dimensional systems we give connections to the the...

Citations