Basis function models of the CMAC network

An interpretation of the Cerebellar Model Articulation Controller (CMAC) network as a member of the General Memory Neural Network (GMNN) architecture is presented. The usefulness of this approach stems from the fact that, within the GMNN formalism, CMAC can be treated as a particular form of a basis function network, where the basis function is inherently dependent on the type of input quantization present in the network mapping. Furthermore, considering the relative regularity of input-space quantization performed by CMAC, we are able to derive an expected (or average) form of the basis function characteristic of this network. Using this basis form, it is possible to create basis-functions models of CMAC mapping, as well as to gain more insight into its performance. The developments are supported by numerical simulations.