By fitting the dynamical model to the data, we tested the hypothesis that the VOR has a response close to ideal taking into account the time constraints imposed by the sensory inputs and the neural networks performing the computations. The vector computations that we used in the model may not be the representation used in the oculomotor system. Mathematically, the vector representation is only one way to describe the computations involved. Other representations exist such as the quaternion representation which has been studied in the context of the saccadic system ([Tweed and Vilis1987]; see also [Handzel and Flash1996] for a very general representation). Detailed comparisons between the model and recordings from neurons will be require to settle this issue.
Direct comparison between Purkinje cell recordings (L.H. Snyder & W.M. King, unpublished data) and predictions of the model could be used to determine more precisely the different inputs to some Purkinje cells. The model can therefore be an important tool to gain insights difficult to obtain directly with experiments.
The question of how the central nervous system learns the transformations that we described still remains. The cerebellum may be one site of learning for these transformations, and its output may modulate the VOR in real time depending on the context. This view is compatible with the results of Angelaki and Hess (Angelaki95) which indicate that the cerebellum is required to correctly perform an otolith transformation. It is also consistent with adaptation results in the VOR. To test this hypothesis, we have been working on a model of the cerebellum which learns to anticipate sensory inputs and feedbacks, and use these signals to modulate the VOR. The learning in the cerebellum and vestibular nuclei is mediated by the climbing fibers which report a reinforcement signal of the prediction error (Coenen and Sejnowski, in preparation).