Abstract: Computational models of neural map formation can be considered on at least three different levels of abstraction: detailed models including neural activity dynamics, weight dynamics which abstract from the the neural activity dynamics by an adiabatic approximation, and objective functions from which weight dynamics may be derived as gradient flows. In this paper we present an example of how an objective function can be derived from detailed non-linear neural dynamics. A systematic investigation reveals how different weight dynamics introduced previously can be derived from objective functions generated from a few prototypical terms. This includes dynamic link matching as a special case of neural map formation. We focus in particular on the role of coordinate transformations to derive different weight dynamics from the same objective function. Coordinate transformations are also important in deriving normalization rules from constraints. Several examples illustrate how objective functions can help in understanding, generating, and comparing different models of neural map formation. The techniques used in this analysis may also be useful in investigating other types of neural dynamics.
Keywords: neural map formation, objective functions, constraints, coordinate transformations