Connectionist modeling of multidimensional generalization

Perceptual-cognitive universals as reflections of the world

“…N. Shepard, , 1991. This distinction has also been found to have a natural basis in the idea of consequential regions (R. N. Shepard, 1987bShepard, , 1991R. N. Shepard & Tenenbaum, 1991).…”

“…N. Shepard, Hovland, & Jenkins, 1961): The learning proceeds more rapidly when the consequential set of objects forms a region in the representational space that is connected rather than disconnected (R. N. Shepard & Kannappan, 1991). The learning also proceeds more rapidly when the consequential set is compact in terms of the Euclidean metric if the dimensions are integral, but more rapidly when the consequential set is based on shared features (or conjunctions of features) if the dimensions are separable (R. N. Shepard & Tenenbaum, 1991). (For related simulations, see Nosofsky, Gluck, Palmeri, McKinley, & Glauthier, in press;Nosofsky, Kruschke, & MeKinley, 1992; and for a similar Bayesian approach in which, however, the underlying hypotheses are taken to be Gaussian distributions rather than the sharply bounded regions posited here, see Anderson, 1991.…”

“…Over a sequence of learning trials in which different objects are found to have or not to have a particular consequence, Bayesian revision of the prior probabilities associated with the various candidate regions yields a convergence to the true consequential region (R. N. Shepard & Kannappan, 1991;R. N. Shepard & Tenenbaum, 1991).…”

Group theory and geometric psychology

“…Moreover, it does so in a way that agrees with results for human categorization (e.g., Nosofsky 1987;Shepard & Chang 1963;Shepard et al 1961): The learning proceeds more rapidly when the consequential set of objects forms a region in the representational space that is connected rather than disconnected (Shepard & Kannappan 1991). The learning also proceeds more rapidly when the consequential set is compact in terms of the Euclidean metric if the dimensions are integral, but more rapidly when the consequential set is based on shared features (or conjunctions of features) if the dimensions are separable (Shepard & Tenenbaum 1991). (For related simulations, see Nosofsky et al 1992; and for a similar Bayesian approach in which, however, the underlying hypotheses are taken to be Gaussian distributions rather than the sharply bounded regions posited here, see Anderson 1991.…”

“…Over a sequence of learning trials in which different objects are found to have or not to have a particular consequence, Bayesian revision of the prior probabilities associated with the various candidate regions yields a convergence to the true consequential region (Shepard & Kannappan 1991;Shepard & Tenenbaum 1991). Moreover, it does so in a way that agrees with results for human categorization (e.g., Nosofsky 1987;Shepard & Chang 1963;Shepard et al 1961): The learning proceeds more rapidly when the consequential set of objects forms a region in the representational space that is connected rather than disconnected (Shepard & Kannappan 1991).…”