An extension to the Hayashi coupled oscillator network training rule

A variety of recurrent network architectures have been developed and applied to the problem of time series prediction. One particularly interesting network was developed by Hayashi (1994). Hayashi presented a network of coupled oscillators and a training rule for the network. His derivation was based on continuous mathematics and provided a mechanism for updating the weights into the output nodes. The work presented here gives an alternative derivation of Hayashi´s learning rule based on discrete mathematics as well an extension to the learning rule which allows for updating of all weights in the network