Global Dynamics in Neural Networks
Stan Franklin
Max Garzon
Department of Mathematical Sciences and Institute for Intelligent Systems
Memphis State University, Memphis, TN 38152, USA
Abstract
The Hedlund-Richardsod Theorem states that a global mapping from configuration space to itself can be realized by a Euclidean 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 finite or infinite configuration space via neural networks is established. It follows that, under natural hypotheses, a uniform limit of global dynamics is a global dynamics. We also give sufficient conditions for the global dynamics of a neural network to be realized by a cellular automaton.
