Implicit differential analysis for cortical models

摘要

Large cortical models based on differential equations may require significant computations to converge, in addition to the computations required to simulate learning. Fortunately, sensitivity analysis for such models can be done using the implicit function theorem (IFT), as shown by McFadden in 1993 for a model with "virtual lateral inhibition" (VLI) in which inhibition is based on competition for activation, rather than on direct reduction of activation levels. The current work reviews recent neurobiological work on the nature of inhibition, and also reports new results on numerical issues that arise in the analysis of VLI models of cortical networks. The IFT technique is at least an order of magnitude faster than numerical ODE solvers. A new explanation for inhibition based on energy resource sharing is proposed.