Connectionist Implementation of a Theory of Generalization
Roger N. Shepard, Sheila J. Kannappan · Neural Information Processing Systems · 1990
Empirically, generalization between a training and a test falls off in close approximation to an exponential decay function of distance between the two stimuli in the stimulus obtained by multidimensional scaling. Mathematically, this result is derivable from the assumption that an individual takes the training to belong to a region that includes that but is otherwise of unknown location, size, and shape in the space (Shepard, 1987). As the individual gains additional information about the consequential region--by finding other stimuli to be consequential or not--the theory predicts the shape of the generalization function to change toward the function relating actual probability of the consequence to location in the 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.