Dynamical-functional neural networks for time series prediction

We study time series prediction capabilities of a new type of artificial neural networks, called dynamical-functional artificial neural networks (D-FANNs). These are two-layer neural systems in which the synaptic weights are “functions” rather than numbers, and where the action of a synapse on a signal passing through it takes place in the form of a scalar product in L² between the functional weight and the signal. The functional weights of the first layer of a D-FANN are modeled as the impulse responses of a set of linear time-invariant differential dynamical systems. We consider only the special discrete case when these impulse responses are the set of discrete signals corresponding to the discrete cosine transform. The time series prediction performance of this D-FANN model is demonstrated on a speech signal with high dynamics