Distributed parallel processing in the vertical vestibulo-ocular reflex: Learning networks compared to tensor theory

The vestibulo-ocular reflex (VOR) is capable of producing compensatory eye movements in three dimensions. It utilizes the head rotational velocity signals from the semicircular canals to control the contractions of the extraocular muscles. Since canal and muscle coordinate frames are not orthogonal and differ from one another, a sensorimotor transformation must be produced by the VOR neural network. Tensor theory has been used to construct a linear transformation that can model the three-dimensional behavior of the VOR. But tensor theory does not take the distributed, redundant nature of the VOR neural network into account. It suggests that the neurons subserving the VOR, such as vestibular nucleus neurons, should have specific sensitivity-vectors. Actual data, however, are not in accord. Data from the cat show that the sensitivity-vectors of vestibular nucleus neurons, rather than aligning with any specific vectors, are dispersed widely. As an alternative to tensor theory, we modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm. Units in mature networks had divergent sensitivity-vectors which resembled those of actual vestibular nucleus neurons in the cat. This similarity suggests that the VOR sensorimotor transformation may be represented redundantly rather than uniquely. The results demonstrate how vestibular nucleus neurons can encode the VOR sensorimotor transformation in a distributed manner.