Weights Behavior in the Solution Space of the Cerebellar Model Articulation Controller (CMAC) learning
Muhamad Iradat Achmad, Adhi Susanto, Hanung Adinugroho · Zenodo (CERN European Organization for Nuclear Research) · 2014
CMAC is an artificial neural network which represents the cerebellum model. This network has the capability to learn fast and to store information locally. The important aspect of learning capability is weights convergence. In line with that, this paper presents weights behavior in the solution space of CMAC learning. First, CMAC learning was formulated into the least square problem. Second, the least square solutions including LU, QR, and SVD methods were examined. Third, the LMS algorithm of CMAC learning was presented to compute the least square solution iteratively. In the implementation, sequential image “Claire” were used to arrange the dataset in which the row, column, and frame numbers are the network input and the corresponding pixel value is the desired output. Results show that the LMS solution with zero weights initialization converges to the SVD solution. The order of methods based on the norm values from smallest to largest are SVD, LMS, QR, and LU respectively. In the solution space, the LU, QR, and LMS weights with random initialization are segmented into subspaces based on CMAC generalization values. Weights on the same subspace have a uniform distance to the corresponding SVD subspace. In addition, the speed and stability of the weight training influenced by the convergence parameter µ in which the higher the value of µ, the faster the speed of weight convergence, and the more erratic the weight convergence tracking.