Ockham's Razor Modeling of the Matrisome Channels of the Basal Ganglia Thalamocortical Loops

A functional model of the basal ganglia-thalamocortical (BTC) loops is described. In our modeling effort, we try to minimize the complexity of our starting hypotheses. For that reason, we call this type of modeling Ockham's razor modeling. We have the additional constraint that the starting assumptions should not contradict experimental findings about the brain. First assumption: The brain lacks direct representation of paths but represents directions (called speed fields in control theory). Then control should be concerned with speed-field tracking (SFT). Second assumption: Control signals are delivered upon differencing in competing parallel channels of the BTC loops. This is modeled by extending SFT with differencing that gives rise to the robust Static and Dynamic State (SDS) feedback-controlling scheme. Third assumption: Control signals are expressed in terms of a gelatinous medium surrounding the limbs. This is modeled by expressing parameters of motion in parameters of the external space. We show that corollaries of the model fit properties of the BTC loops. The SDS provides proper identification of motion related neuronal groups of the putamen. Local minima arise during the controlling process that works in external space. The model explains the presence of parallel channels as the means to avoiding such local minima. Stability conditions of the SDS predict that the initial phase of learning is mostly concerned with selection of sign for the inverse dynamics. The model provides a scalable controller. State description in external space instead of configurational space reduces the dimensionality problem. Falsifying experiment is suggested. Computer experiments demonstrate the feasibility of the approach. We argue that the resulting scheme has a straightforward connectionist representation exhibiting population coding and Hebbian learning properties.