Rules and exemplars in categorization: A computational exploration

Rules and Exemplars in Categorization: A Computational Exploration Duncan P. Brumby (Brumby@cs.drexel.edu) Department of Computer Science, Drexel University Philadelphia, PA 19104 USA Ulrike Hahn (HahnU@cardiff.ac.uk) School of Psychology, Cardiff University Cardiff, CF10 3AT UK is therefore adaptive in this task in a way it need not be in general. In response to the critique of the rule description used in Allen and Brooks’ (1991) experiments, Hahn, Prat-Sala and Pothos (2002) sought to test whether exemplar similarity effects would arise in a rule-based task in which category membership was entirely uncorrelated with similarity. Hahn et al. found effects of exemplar similarity on error patterns and reaction times, even under conditions where attending to similarity interfered with performance on the rule application task. At the same time they also found very low error rates, which suggests that the rule was in fact used. Hahn et al.’s findings are of interest because hybrid rule- plus-exemplar models of categorization would generally predict that (1) categorization errors should be associated with exemplar similarity effects and (2) any reduction in error rates should be associated with diminished similarity effects. That people’s categorization judgments juxtapose rule application with instance-similarity, while maintaining very low error rates seems at odds with the basic predictions that can be derived from these models of categorization. In this paper, we first describe the data from two experiments (Hahn et al., 2002; Hahn et al., submitted) that investigate the effect of similarity on the application of a simple, perfectively predictive rule. These data suggest that combining rule application with instance-similarity occurs even under conditions where paying attention to instance similarity is harmful to performance. A reimplementation of Anderson and Betz’s (2001) ACT-R model follows, along with a computational exploration of the parameter space of the model, in order to find the best-fitting model for the first data set. Based on these best-fitting parameter values, a comparison between the performance predictions of the model and the second data set is presented. Abstract Studies have found that human categorization judgments are affected by exemplar similarity, even when a simple, perfectly predictive rule is provided and paying attention to instance similarity is harmful to performance. These data provide an interesting challenge for recent hybrid rule-plus-exemplar models of category learning. We report the results of a modeling effort with a pre-existing hybrid model developed in the ACT-R cognitive architecture. A search of the model’s parameter space revealed that increasing use of an exemplar route improved the fit of the model to the data, because it resulted in faster categorization judgments for high-similarity items compared to low-similarity items. However, use of the exemplar route carried no adaptive value for the model because it necessarily lead to more categorization errors than simply basing judgments on the categorization rule alone. The fact that people’s categorization judgments juxtapose rule application with instance-similarity while maintaining very low error rates presents a non-trivial problem for current hybrid models of category learning. Keywords: categorization; rules; computational modeling; ACT-R exemplars; similarity; Introduction Over the last two decades, categorization research has seen a steady rise in interest in hybrid accounts; particularly rule-plus- exemplar accounts that assume human categorization judgments are formed through some mix of exemplar- and rule-based processes (e.g., Erickson & Kruschke, 1998; Palmeri, 1997; for a different hybrid approach, see Ashby et al, 1998). This interest, for which there is good theoretical reason (e.g., Hahn & Chater, 1998), has fueled experimental tests as well as a range of computational models of varying scope and specificity. Allen and Brooks (1991) provided a seminal experimental demonstration of the joint effects of rules and exemplars in categorization. Participants in the study were given a simple rule to classify both old and novel items. Even though the rule was perfectively predictive there was evidence for systematic effects of exemplar similarity on categorization. Allen and Brooks’ results are somewhat less surprising when one takes into account the specific nature of the rule used in the study. Specifically, the rule described an m-of-n concept (“an object is a digger if it has at least 3 of the following 5 features…”). This type of rule description is functionally equivalent to a prototype-plus-similarity threshold account. Consequently, for Allen and Brooks’ materials similarity is correlated with the rule’s applicability. Attending to similarity Empirical Data Hahn et al. (2002), in an experiment which we will refer to as Experiment 1, constructed a set of items governed by a simple, perfectly predictive rule that specified three necessary and sufficient features for category membership (e.g., “is an A if it has an upside-down triangle at the sides, a cross in the centre, and a curly line at the top”). Participants were told this rule at the beginning of the experiment, and were then given a series of positive exemplars as illustration. At test, participants were given 96 novel items, distributed over four blocks. Participants did not receive feedback regarding the accuracy of their categorization judgments. Half of the test items complied with