Filtering, prediction, and learning properties of ECE neural networks

The capabilities of recurrent high order neural networks (RHONNs), whose synapses are adjusted according to the learning law proposed in Kosmatopoulos and Christodoulou (1992), and Koostmatopoulos, Christodoulou, and Ioannou (1993) are examined in 1) spatiotemporal pattern learning, recognition, and reproduction and 2) stochastic dynamical system identification problems. The mathematical model describing the stochastic disturbances that affect the spatiotemporal patterns or the system dynamics is quite general, and includes both additive and multiplicative stochastic disturbances. Under an extensive mathematical analysis, the authors show that, for any selection of the neural network´s high order terms, the prediction error converges to zero exponentially fast. Extensions are also made to the case where the energy coordinate equivalent (ECE) RHONN´s are used