Cortical Maps as Topology-Representing Neural Networks Applied to Motor Control:

Substantial advances have been achieved, since the pioneering work in the 50’s and 60’s by Mountcastle, Hubel, Wiesel and Evarts, amongst others, in understanding the cortex as a continuously adapting system, shaped by competitive and co—operative interactions. However, the greatest part of the effort has been devoted to the investigation of the receptive—field properties of cortical maps, whereas relatively little attention has been devoted to the role of lateral connections and the cortical dynamic processes that are determined by the patterns of recurrent excitation (Amari 1977, Kohonen 1982, Grajski and Merzenich 1990, Reggia et al. 1992, Martinetz and Schulten 1994, Sirosh and Miikkulainen 1997, Sanguineti et al. 1997a, Levitan and Reggia 1999, 2000). In this chapter we explore the hypothesis that lateral connections may actually be used to build topological internal representations and propose that the latter are particularly well suited for the processing of high—dimensional ‘spatial’ variables and for solving complex problems of motor control that involve sensorimotor information. In particular, we apply the methods to the case of speech motor control in which acoustic and articulatory variables are typically high-dimensional, and describe an approach to articulatory speech synthesis that is based on the dynamic interaction of two computational maps.