FILTERING, PREDICTION, AND LEARNING PROPERTIES OF ECE NEURAL NETWORKS

In this paper the capabilities of recurrent high order neural networks (RHONNs), whose synapses are adjusted according to the learning law p roposed in [19], [23], [24], are examined in 1) spatiotemporal pattern learning, recognition, and reproduction and 2) stochastic dynamical s ystem identification problems. The mathematical model describing the s tochastic disturbances that affect the spatiotemporal patterns or the system dynamics is quite general, and includes both additive and multi plicative stochastic disturbances. Under an extensive mathematical ana lysis, we show that, for any selection of the neural network's high or der terms, the prediction error converges to zero exponentially fast. Extensions are also made to the case where the energy coordinate equiv alent (ECE) RHONN's are used.