CMAC learning is governed by a single parameter

A Fourier analysis of the learning algorithm in the Cerebellar Model Articulation Controller (CMAC) is presented. It is proved that CMAC is capable of learning any discrete input-output mapping by Fourier analysis. The convergence rates are obtained for the different frequencies, which are governed by a single parameter M-the size of the receptive fields of the neurons. This complements an earlier result that CMAC always learns with arbitrary accuracy. The approach offers new insights into the nature of the leaning mechanism in CMAC. The analysis provides mathematical rigor and structure for a neural-network-learning model with simple and intuitive mechanisms