A Regularized Inverse QR Decomposition Based Recursive Least Squares Algorithm for the CMAC Neural Network

Abstract

The Cerebellar Model Articulation Controller (CMAC) neural network is an associative memory that is biologically inspired by the cerebellum, which is found in the brains of animals. The standard CMAC uses the least mean squares algorithm (LMS) to train the weights. Recently, the recursive least squares (RLS) algorithm was proposed as a superior algorithm for training the CMAC online as it can converge in one epoch, and does not require tuning of a learning rate. However, the RLS algorithm was found to be very computationally demanding. In this work, the RLS computation time is reduced by using an inverse QR decomposition based RLS (IQR-RLS) algorithm which is also parallelized for multi-core CPUs. Furthermore, this work shows how the IQR-RLS algorithm may be regularized which greatly improves the generalization capabilities of the CMAC.