On the role of anatomy in learning by the cerebellar cortex

The properties due to the location of neurons, synapses, and possibly even synaptic channels, in neuron networks are still unknown. Our preliminary results suggest that not only the interconnections but also the relative positions of the different elements in the network are of importance in the learning process in the cerebellar cortex. We have used neural field equations to investigate the mechanisms of learning in the hierarchical neural network. The numerical resolution of these equations reveals two important properties: (i) The hierarchical structure of this network has the expected effect on learning because the flow of information at the neuronal level is controlled by the heterosynaptic effect through the synaptic density-connectivity function, i.e. the action potential field variable is controlled by the synaptic efficacy field variable at different points of the neuron. (ii) The geometry of the system involves different velocities of propagation along different fibers, i.e. different delays between cells, and thus has a stabilizing effect on the dynamics, allowing the Purkinje output to reach a given value. The field model proposed should be useful in the study of the spatial properties of hierarchical biological systems.