Tools for connectionist modeling: The dynamical systems methodology

Some understanding of dynamical systems is essential to achieving competency in connectionist models. This mathematical background can be acquired either through a rigorous set of upper undergraduate and/or graduate formal courses or via disciplined self-teaching. As part of developing a course in connectionism, we feel that although certain very basic mathematical tools are most appropriately learned in their “pure” form (i.e., from mathematics textbooks and courses), more advanced exposure to dynamical systems theory can be given in the context of an introduction to connectionism. Students thus learn to write connectionist simulations by first writing programs for simulating arbitrary dynamical systems, then using them to learn some aspects of dynamical systems in general by simulating some special cases, and finally applying this technique to connectionist models of increasing complexity.