An electrodynamical perspective on neural field theory

S. Amari (1983) has proposed a field theory to study the self-organizing properties of neural fields, which are a continuum approximation to neural nets. The authors consider a special case of a two-dimensional neural field for which it is possible to obtain explicit solutions of the field equations. From these they derive evidence for the use of a Mexican hat style connectivity between neuronal regions and prove the existence of a topology preserving map between the input space and the neural field. The approach is based on an analogy between the neural field theory and the field theory of electrodynamics. The approach is illustrated by analyzing a recent work on a topological variant of a Hopfield net for solving the path finding problem in a maze