On associative motor learning by the cerebellar cortex: from Purkinje unit to network with variational learning rules

This paper is an attempt to describe the ability of the cerebellar cortical network to coordinate movement on the basis of the continuous behavior of individual neural networks, the so-called "Purkinje units." The problem is considered from the point of view of a hierarchical network with two levels of organization: the level of Purkinje units including Purkinje, star and basket cells, and the level of granule cells and Golgi cells which is a network with a specific architecture. We suggest that the coordination of movements is based on a new class of learning rules between Purkinje units, called variational learning rules (VLR), which are mathematically deduced from the dynamics of a Purkinje unit. This network is driven by two functions H0 and H, defined for each Purkinje unit, which depend on external signals for this unit. Specifically, the proposed interpretation of the coordination of movement depends on three main features: (i) The definition of a unit of function, the Purkinje unit, made up of a Purkinje cell and closely associated cells and connections; (ii) a new learning rule called the "Variational Learning Rule" (VLR), operating at the level of the Purkinje units; (iii) the interpretation of the coordination of movements in terms of excitatory and inhibitory interactions between Purkinje units. An emergent property of the model is that Purkinje units occur in groups which act in opposition in the sense that when the output of one group increases, that of the other decreases.