Sensorimotor systems face complex and frequent discrepancies among spatial modalities, for example, growth, optical distortion, and telemanipulation. Adaptive mechanisms must act continuously to restore perceptual-motor alignments necessary for perception of a coherent world. Experimental manipulations that exposed participants to localized discrepancies showed that adaptation is revealed by the acquisition of a constrained relation between entire modalities rather than associations between individual exemplars within these modalities. The computational problem faced by the human nervous system can thus be conceived as having to induce constrained relations between continuous stimulus and response dimensions from ambiguous or incomplete training sets, that is, performing interpolation and extrapolation. How biological neuronal networks solve this problem is unknown. Here we show that neural processing based on linear collective computation and least-square (LS) error learning in populations of frequency-coded neurons (i.e., whose discharge varies in a monotonic fashion with a parameter) has built-in interpolation and extrapolation capacities. This model can account for the properties of perceptual-motor adaptations in sensorimotor systems.