Neural representations for sensory-motor control, II: Learning a head-centered visuomotor representation of 3-D target position

-A neural network model is described for how an invariant head-centered representation of 3-D target position can be ataonomously learned by the brain in real time. Once learned, such a target representation may be used to control both eye and limb movements. Tile target representation is derived from the positions of both eyes in the head. and the locations which the target activates on the retinas of both eyes. A Vector Associative Map (VAM) learns the many-to-one transformation from multiple combinations of eye-and-retinal position to invariant 3-D target position. Eye position is derived from outflow movement signals to the t:l'e muscles. Two successive stages o f opponent processing convert these corollary discharges into a head-centered representation that closely approximates the azimuth, elevation, and vergence o f the eyes' gaze position with respect to a cyclopean origin located between the eyes. I.f4M learning combines this cyclopean representation of present gaze position with binocular retinal information about target position into an invariant representation of 3-D target position with respect to the head. VAM learning can use a teaching vector that is externally derived from the positions o f the eyes when they foveate the target. A VAM can also autonomously discover and learn the invariant representation, without an explicit teacher, by generating internal error signals from enviromnental fluctuations in which these invariant properties are implicit. VAM error signals are computed b), Difference Vectors ( DVs) that are zeroed by the VAM learning process. VAMs may be organized into I,'AM Cascades lbr learning and performing both sensory-to-spatial maps and spatial-to-motor maps. These multiple uses clarif|' why D V-type properties art, computed by cells in the parietal, frontal, and motor cortices of many mammals. I,'AMs are modulated by gating signals that express different aspects o f the will-to-act. These signals transform a single invariant representation into movements o f d~fferent speed (GO signal) and size ( GRO signal), and thereby enable I ~ M controllers to match a plamwd action sequence to variable environmental conditions. Keywords--Neural networks, Sensory-motor control, Spatial representation, Learning, Vector associative map, Gaze, Motor plan. 1. SPATIAL R E P R E S E N T A T I O N S FOR T H E N E U R A L C O N T R O L O F FLEXIBLE M O V E M E N T S This paper introduces a neural network model o f how the brain learns spatial representations with which to control sensory-guided and memory-guided eye and Acknowledgements: The authors wish to thank Kelly A. Dumont and Carol Y. Jefferson for their valuable assistance in the preparation of the manuscript. * Supported in part by the National Science Foundation (NSF IRI-87-16960 and NSF IRI-90-24877) and the Otfice of Naval Research (ONR N00014-92-J1309 ). t Supported in part by National Science Foundation (NSF IRI87-16960 and NSF IRI-90-24877 ). Requests for reprints should be sent to Stephen Grossberg, Center for Adaptive Systems, Boston University, 1 I 1 Cummington Street, Room 244, Boston, MA 02215. limb movements. These spatial representations are expressed in both head-centered coordinates and bodycentered coordinates since the eyes move within the head, whereas the head, arms, and legs move with respect to the body. This paper describes a model for learning an invariant head-centered representation of 3-D target position. A model for learning an invariant body-centered representation of 3-D target position will be described elsewhere (Guenther, Bullock, Greve, &