Modeling Cortical Maps with Feed-Backs

High-level specification of how the brain represents and categorizes the causes of its sensory input allows to link "what is to be done" (perceptual task) with "how to do it" (neural network calculation). More precisely, a general class of cortical map computations can be specified representing what is to be done as an optimization problem, in order to derive the related neural network parameters considering regularization mechanisms (implemented using so-called partial-differential-equations). The present contribution revisits this framework with three add-ons. It is generalized to a larger class of (non-linear) map computations, including winner-take-all mechanisms. The capability to represent standard "analog" neural network and guaranty their convergence, providing their weights are local and unbiased, is made explicit. The fact that not only one but several cortical maps can interact, with feed-backs, in a stable way is shown. Two experiments are provided as an illustration of this general framework.