RUI: A Proposal for Research on Computing with Neural Models of Computation

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The last two decades have seen a resurgence in the interest of investigating various neural models of computation. Researchers from various fields such as mathematics, computer science, cognitive science and biology are either trying to analyze the capabilities and limitations of various neural models, or proposing extensions or modifications of current neural models to make these models more consistent with applications in biology, control theory, pattern recognition and other related areas. Recent advanced mathematical techniques using results on semi- algebraic sets, model theory, statistical methods and theory of real numbers have enabled researchers to answer many theoretical questions about neural models which were previously open. This project continues further investigation of the capabilities and limitations of various neural models, either from a theoretical point of view using some of the advanced mathematical techniques mentioned in the references, or from an experimental point of view. The ultimate objective is to be able to provide further insight into the working mechanisms of these models, and to modify or extend existing models whenever appropriate. The theoretical investigations to be carried out in this project will also be valuable in various practical application of neural models. This project involves interaction with undergraduate students which should prepare them for possible graduate studies in mathematics, computer science and theoretical biology.