How do high-level specifications of the brain relate to variational approaches?

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). In this article, we describe how the variational framework, which encountered a large success in modeling computer vision tasks, has some interesting relationships, at a mesoscopic scale, with computational neuroscience. We focus on cortical map computations such that "what is to be done" can be represented as a variational approach, i.e., an optimization problem defined over a continuous functional space. In particular, generalizing some existing results, we show how a general variational approach can be solved by an analog neural network with a given architecture and conversely. Numerical experiments are provided as an illustration of this general framework, which is a promising framework for modeling macro-behaviors in computational neuroscience.