Global Dynamics in Neural Networks II
Max Garzon
Stan Franklin
Memphis State University, Memphis, TN 38152 USA
Abstract
Determining just what tasks are computable by neural networks is of fundamental importance in neural computing. The configuration space of several models of parallel computation is essentially the Cantor middle-third set of real numbers. The Hedlund--Richardson theorem states that a transformation from the Cantor set to itself can be realized as the global dynamics of a cellular automaton if and only if it takes the quiescent configuration to itself, commutes with shifts, and is continuous in the product topology. An analogous theorem characterizing the realizability of self-mappings of the Cantor set as net-input global dynamics of neural networks has recently been established. Here we give a characterization of such realizability as the more natural activation global dynamics of neural networks. We also present such a characterization for realizability via global dynamics of more general automata networks. This dynamical systems approach to neural computing allows precise formulations of significant problems about the computational power of neural networks.
