Habituation rules for a theory of the cerebellar cortex

A quantitative model of cerebellar cortical function is described with a complete formalization based on (i) the topology of cerebellar cortical neuronal network, (ii) some particular synaptic properties of cell classes in cerebellum cortex, and (iii) the dynamics of excitation in this network. For (i), a construction of functional classes around one Purkinje cell is given and their existence is discussed. For (ii), as in Marr-Albus model, the modifiability of synapses between parallel fibres and Purkinje cell is assumed. But the formalization permits to consider the consequences of such a property at the level of glomerulus (with granule cells) which is known as a complex transformation system. For (iii) habituation rules are assumed. It is shown that this method leads to some interesting properties in the functioning of cerebellar cortex. Particularly, emitting frequency along a Purkinje cell axon results from a discrimination by the system between transformed input signals and an external noise due to all other contexts, and learning could be considered as the result of a conflict between a set of patterns and the transformed input signals. This model could be a basis for future numerical simulations.