Generalization and Analysis of the Lisberger-Sejnowski VOR Model
Ning Qian, Neural Computation, 1995, 7:735-752.
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Abstract
\citeasnoun{Lisberger92} recently proposed a
computational model for motor learning in the vestibular-ocular reflex
(VOR) system. They showed that the steady state gain of the system
can be modified by changing the ratio of the two time constants along
the feedforward and the feedback projections to the Purkinje cell unit
in their model VOR network. Here we generalize their model by
including two additional time constant variables and two synaptic
weight variables, which were set to fixed values in their original
model. We derive the stability conditions of the generalized system
and thoroughly analyze its steady state and transient behavior. It is
found that the generalized system can display a continuum of behavior
with the Lisberger-Sejnowski model and a static model proposed by
\citeasnoun{Miles80a} as special cases. Moreover, although
mathematically the Lisberger-Sejnowski model requires two precise
relationships among its parameters, the model is robust against small
perturbations from the physiological point of view. Additional
considerations on the gain of smooth pursuit eye movement, which is
believed to share the positive feedback loop with the VOR network,
suggest that the VOR network should operate in the parameter range
favoring the behavior studied by Lisberger and Sejnowski. Under this
condition, the steady state gain of the VOR is found to depend on all
four time constants in the network. The time constant of the Purkinje
cell unit should be relatively small in order to achieve effective VOR
learning through the modifications of the other time constants. Our
analysis provides a thorough characterization of the system and could
thus be useful for guiding further physiological tests of the model.
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