Many neurons in the posterior-parietal cortex (PPC) have saccadic responses to visual and auditory targets. The responses are modulated by eye position and head position. These findings suggest that PPC integrates multisensory inputs and may provide information about saccadic targets represented in different coordinate frames. In addition to an eye-centered output representation, PPC may also project to brain areas which contain head-centered and body-centered representations of the space. In this report, possible coordinate transformations in PPC were examined by comparing several sets of models of PPC, each having different representations in the output layer: (i) an eye-centered map only; (ii) a head-centered map only; (iii) an eye-centered map and a head-centered map; and (iv) an eye-centered map, a head-centered map, and a body-centered map. These output maps correctly encoded saccades to visual and auditory targets through training. The units in the hidden layers of the models exhibited the following properties: (1) The units had gain fields (GFs) for eye position, and also for head position if the model had a body-centered output representation; (2) As the result of the GF and the nonlinear activation function of the units, the hidden layers often employed “intermediate” coding, e.g., the hidden units coded targets partially in eye-centered coordinates and, partially, in head-centered coordinates; (3) Different types of coordinate transformations in these models were carried out by different relationships between the receptive fields (RFs) and the GFs of the hidden units; and (4) The properties of PPC neurons are in better accordance with the hidden units of the models that had multiple-output representations than the models that had only one single-output representation. In conclusion, the results show that the GF is an effective mechanism for performing coordinate transformations. The models also suggest that neurons with intermediate coding are to be expected in the process of coordinate transformations.

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