Learning periodic signals with recurrent neural networks

A class of recurrent neural network configurations that are related to control systems have been introduced. The main result states that this class of recurrent neural networks generates a limit cycle for a broad range of parameter values. When the parameters of the network cross a specified area in the parameter space, the origin becomes an asymptotic equilibrium point. The fact that the recurrent network possesses a stable limit cycle enhances the robustness properties of the network. This stable limit cycle can be achieved by a suitable choice of the parameters of the network and is independent of the initial condition of the network. A recurrent neural network is made to learn and replicate a desired periodic signal within a certain class. This learning is achieved by using a gradient descent algorithm to adjust the internal parameters of the recurrent network. Further research is necessary in order to understand the behaviour of recurrent networks with neural units formed from other transfer functions. It is expected that many different choices for the transfer function of the neurons will give networks enjoying similar properties.