On the dynamics of generalization.

Stimulus generalization is the tendency, after experience with a given stimulus, to react in the same way to other, similar stimuli. Shepard (1987) has proposed a universal law forstimulus generalization that deals with relations in a "psychological space," established through multidimensional curve-fitting techniques (MDS). These methods can discover the smallest number of dimensions such that the judged similarity (difference) relations between pairs ofstimuli conform to an approximately invariant declining monotonic function of the distance between them. For example. given stimuli A, B. and C with judged difference relations AB = I . BC = I, and AC = 2, the .'% psychological space has just a single dimension because the differences among the three stimuli are the same as those among three equidistant points alonga line. An invariant similarity function is the reciprocal, given that similarity = lldifference. Shepard (1 987) marshaled both empirical evidence and functional (optimality) arguments in support ofan exponential generalization function. However, published comments on his paper noted that the Gaussian function is at least as common an experimental finding as the exponential. Shepard (1988a. 1988b) and Ennis (1988a. 1988b) have both proposed process theories to reconcile the Gaussian and exponential data. ShepardS suggestion is based on an earlier paper (Shepard, 1958) in which he introduced the concept ofdrg7iu~ion:"According to that model. on the removal of an external stimulus. the memory trace of the stimulus spontaneously undergoes a continuing process not only of simple weakening or decay but also of outward diffusion in psychological space" (1988. p. 415). Diffusion. of course, yields the Gaussian response-probability distribution. which will be increasingly broad as the time of testingais delayed after stimulus presentation. In this early model, the exponential function is derived by integration across pnviods Gaussian traces: "under regularly repeated pmenta-