Connectionist Implementation of a Theory of Generalization

Abstract

Empirically, generalization between a training and a test stimulus falls off in close approximation to an exponential decay function of distance between the two stimuli in the "stimulus space" obtained by multidimensional scaling. Math(cid:173) ematically, this result is derivable from the assumption that an individual takes the training stimulus to belong to a "consequential" region that includes that stimulus but is otherwise of unknown location, size, and shape in the stimulus space (Shepard, 1987). As the individual gains additional information about the consequential region-by finding other stimuli to be consequential or nOl-the theory predicts the shape of the generalization function to change toward the function relating actual probability of the consequence to location in the stimulus space. This paper describes a natural connectionist implementation of the theory, and illustrates how implications of the theory for generalization, discrimination, and classification learning can be explored by connectionist simulation.