Learning convergence of CMAC technique

CMAC is one useful learning technique that was developed two decades ago but yet lacks adequate theoretical foundation. Most past studies focused on development of algorithms, improvement of the CMAC structure, and applications. Given a learning problem, very little about the CMAC learning behavior such as the convergence characteristics, effects of hash mapping, effects of memory size, the error bound, etc. can be analyzed or predicted. In this paper, we describe the CMAC technique with mathematical formulation and use the formulation to study the CMAC convergence properties. Both information retrieval and learning rules are described by algebraic equations in matrix form. Convergence characteristics and learning behaviors for the CMAC with and without hash mapping are investigated with the use of these equations and eigenvalues of some derived matrices. The formulation and results provide a foundation for further investigation of this technique.