Comparisons of prototype- and exemplar-based neural network models of categorization using the GECLE framework

Comparisons of prototype- and exemplar-based neural network models of categorization using the GECLE framework Toshihiko Matsuka (matsuka@psychology.rutgsers.edu) RUMBA, Rutgers University – Newark 101 Warren St., Smith Hall 327, Newark, NJ 07102 USA Abstract GECLE In the present study, GECLE (Matsuka, 2003) was used as a general modeling framework to systematically compare the plausibility of two prominent assumptions about internal representations of neural network (NN) models of human category learning. In particular, exemplar-model friendly Medin and Schaffer’s 5/4 stimulus set (1978) was used for comparing prototype- and exemplar-based NN models. The results indicate that some prototype-based models performed as good as or better than an exemplar-based model in replicating the empirical classification profile. In addition, a phenomenon called A2 advantage (i.e., people tend to categorize the less “prototypical” stimulus A2 more accurately than more “prototypical” stimulus A1) reported in empirical studies (e.g., Medin & Schaffer 1978) was also successfully reproduced by these prototype-based NN models. GECLE (for Generalized Exploratory models of Category LEarning) is a general and flexible exploratory approach for modeling human category learning, that is capable of modeling human category learning with many variants using different model assumptions (Matsuka, 2003). This general modeling framework allows model assumptions to be manipulated separately and independently. For example, one can manipulate assumptions about how stimuli are internally represented (e.g. exemplars vs. prototypes), or about how people selectively pay attention to input feature dimensions (e.g., paying attention to dimensions independently or not). The GECLE model uses the Mahalanobis distances (in the quadratic form) between the internally represented reference points (RP: corresponding to either exemplars or prototypes) and the input stimuli as the measure of similarity between them. Thus, unlike other neural network models of category learning, GECLE does not necessarily assume that attention is allocated independently dimension- by-dimension. Rather, it assumes that humans in some cases might pay attention to correlations among feature dimensions. This allows GECLE to model processes interpretable as dimensionality reduction or mental rotation in the perception and learning of stimuli. Such processes may increase the interpretability of stimuli in categorization tasks. Another motivation for using the Mahalanobis distance is that the capability for paying attention to correlations among feature dimensions may be necessary for classification tasks defined on integral stimuli. In the GECLE framework, the attention parameters (which are the diagonal and off-diagonal elements of the covariance matrices) can be considered as shape and orientation parameters for receptive fields or attention coverage areas of the reference points. It should be noted, however, that one can constrain GECLE to incorporate the “dimensional attention processes” assumption (i.e., attention is allocated independently on a dimension-by-dimension basis) by forcing the off-diagonal entries in the covariance matrices to be equal to zero. Another unique feature of GECLE’s attention mechanism is that it allows each reference point to have uniquely shaped and oriented attention coverage area, which is referred to as “local attention coverage structure” (Matsuka 2003). Again, one can impose a restriction on the model’s attention mechanism by fixing all covariance matrices to be the same, which may be called “global attention coverage structure”. Many NN models of category learning, ALCOVE (Kruschke, 1992) for example, incorporate the global attention coverage structure. Introduction There have been an increasing number of studies debating how stimuli are internally represented in human cognition during the last few decades (e.g., Minda & Smith 2002; Nosofsky & Zaki 2002). Most of these debates have been based on quantitative models of categorization, and only a few have considered representational aspects of adaptive, network, or learning models of categorization. Several studies (Matsuka, 2002; Matsuka, Corter, & Markman, 2003) have compared exemplar-based (EB) and prototype- based (PB) adaptive network models of categorization, but there has been no systematic comparison of specific assumptions in EB and PB modeling. Although these comparative studies provided information on the models’ capabilities for reproducing human-like categorization learning, they did not necessarily provide information that can lead to specific understanding of the nature of human category learning. That is because model-to-model comparisons are not informative for testing the plausibility of each specific assumption, rather such model comparisons are essentially omnibus tests collectively comparing all variations in assumptions at once. In other words, it has been difficult to use the results of these previous comparative studies to understand which specific assumptions are supported by the empirical data. Therefore, it seems desirable to make systematic comparisons between competing model assumptions using a general modeling framework that allows us to manipulate and test one or a limited number of model assumptions at a time. In the present study, a generalized exploratory modeling approach for human category learning is introduced. Then, using this general framework two assumptions about how categories are internally represented, namely prototypes and exemplars, are compared in a systematic fashion.