title: The learning problem of multi-layer neural networks.
abstract: This manuscript considers the learning problem of multi-layer neural networks (MNNs) with an activation function which comes from cellular neural networks. A systematic investigation of the partition of the parameter space is provided. Furthermore, the recursive formula of the transition matrix of an MNN is obtained. By implementing the well-developed tools in the symbolic dynamical systems, the topological entropy of an MNN can be computed explicitly. A novel phenomenon, the asymmetry of a topological diagram that was seen in Ban, Chang, Lin, and Lin (2009) [J. Differential Equations 246, pp. 552-580, 2009], is revealed.
authors.affiliation: Department of Applied Mathematics, National Dong Hwa University, Hualien 970003, Taiwan, ROC. jcban@mail.ndhu.edu.tw
authors.forename: Jung-Chao
authors.initials: JC
authors.lastname: Ban
authors.forename: Chih-Hung
authors.initials: CH
authors.lastname: Chang
mesh_terms: D000465:Algorithms; D019277:Entropy; D007858:Learning; D008959:Models, Neurological; D016571:Neural Networks, Computer
keywords: Learning problem; Linear separation; Multi-layer neural networks; Sofic shift; Topological entropy