Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We compare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.

Recent physiological experiments have shown that the responses of many neurons in V1 and V3a are modulated by the direction of gaze . We have developed a neural network model of the hierarchy of maps in visual cortex to explore the hypothesis that visual features are encoded in egocentric (spatio-topic) coordinates at early stages of visual processing. Most psychophysical studies that have attempted to examine this question have concluded that features are represented in retinal coordinates, but the interpretation of these experiments does not preclude the type of retinospatiotopic representation that is embodied in our model. The model also explains why electrical stimulation experiments in visual cortex cannot distinguish between retinal and retinospatiotopic coordinates in the early stages of visual processing. Psychophysical predictions are made for testing the existence of retinospatiotopic representations.