Knowledge and Frequency 1 Running head : KNOWLEDGE AND FREQUENCY Prior Knowledge and Exemplar Frequency

New concepts can be learned by statistical associations as well as by relevant existing knowledge. We examined the interaction of these two processes by manipulating exemplar frequency and thematic knowledge, and considering their interaction through computational modeling. Exemplar frequency affects category learning, with high frequency items learned faster than low frequency items, and prior knowledge usually speeds category learning. In an experiment that manipulated both of these factors, we found that the effects of frequency are greatly reduced when stimulus features are linked by thematic prior knowledge, and that frequency effects on single stimulus features are actually reversed in knowledge conditions. We account for these results with the Knowledge Resonance (KRES) model of category learning (Rehder & Murphy, 2003) and conclude that prior knowledge may change representations so that empirical effects such as those caused by frequency manipulations are considerably modulated. Knowledge and Frequency 3 Frequency has long been known as an important property of category structure. Rosch and Mervis (1976) argued that the frequency of properties in a category determines how typical category members are. Those that have properties frequently found in the category are more typical than those possessing less frequent properties, and category members possessing properties frequently found in other categories are less typical than those possessing less frequent properties. Although the overall frequency or familiarity of an object does not itself seem very strongly related to its typicality in natural concepts (Barsalou, 1985; Mervis, Catlin, & Rosch, 1976; Novick, 2003), when item frequency has been experimentally manipulated independently of other variables (such as similarity to category prototypes), it does influence category structure. For example, Nosofsky (1988) showed that repeating one item five times in each block of category learning made the item not only easier to learn but also more typical after learning. Furthermore, the effect spread beyond the frequent item itself, in that similar items in the same category also were rated as more typical. Theories of concepts can explain such frequency effects easily (Barsalou, Huttenlocher, & Lamberts, 1998). If exemplar theories assume that each presentation of a stimulus is a stored instance, then frequent exemplars will have more stored instances, increasing the typicality of items similar to them. Likewise, if prototype theories assume that the category prototype is based on generalizing from instances, then the more an item is repeated, the more influence it will have on that generalization. That is, frequent items will pull the category prototype in their direction. Thus, the effect of frequency seems to be a straightforward example of how category structure influences learning and use of concepts. One might expect basic variables such as frequency to have consistent effects across materials and tasks. However, there are a number of examples in which effects of category Knowledge and Frequency 4 structure are altered when concepts make contact with other knowledge. For example, the learning advantage of conjunctive over disjunctive concepts can be overruled when the disjunctive concept makes contact with prior knowledge (Pazzani, 1991). Wattenmaker, Dewey, T. Murphy, and Medin (1986) examined effects of prior knowledge on learning of linearly separable and nonlinearly separable categories. Linear separability is a structural variable that refers to whether correct categorizations can be made by independently weighting the category’s properties. Wattenmaker et al. showed that linearly separable categories could be made easier or harder to learn than nonlinearly separable categories by varying categories’ content (see also Murphy & Kaplan, 2000). They argued that some conceptual domains encourage summing of evidence, suitable for linearly separable categories, and that other domains encourage configural processing, suitable for nonlinearly separable categories. These content effects are one example of how people’s prior knowledge about a category can affect the processing they perform during learning and thereby influence the category representation. The present research examined whether frequency effects are similarly sensitive to the content of the category being learned. Because frequency is such a basic variable, influencing cognitive processes from learning to lexical access, it is possible that its effects will not be so easily modified by the content of a category. We were particularly interested in this structural variable because it allowed us to investigate possible interactions of structural or formal aspects of a category with the more slippery variable of prior knowledge. We also used this problem of the interaction between knowledge and exemplar frequency to test a model of category learning that attempts to incorporate both structure and knowledge, the Knowledge Resonance (KRES) model (Rehder & Murphy, 2003). Unlike purely formal models of category learning, KRES allows knowledge, represented by links among features and prior Knowledge and Frequency 5 concept nodes, to influence the learning process. We carried out this modeling to try to provide an account of the effects of frequency and knowledge in this task, and more generally, to understand better how prior knowledge affects representations during learning. This work also continues our ongoing validation of the model’s general approach. Earlier KRES modeling work (Harris & Rehder, 2006) compared two model variants on linearly and nonlinearly separable category learning tasks. One model represented prior knowledge by specific nodes that represented already-known categories, which could be associated to the to-be-learned categories. This model could base category responses on the similarity of stimuli to prior concepts. The other variant only allowed prior knowledge to influence the learning of associations by modifying representations of the stimuli. In this second model, knowledge could not directly and independently affect categorization, but instead had to affect responses by modulating the normal category learning and categorization system. The first variant fit Wattenmaker et al.’s data better than the second did. However, this may be because Wattenmaker et al. used categories that corresponded to known concepts (e.g., the personality trait of honesty). The present study will use what we call thematic feature relationships (Murphy & Allopenna, 1994) where knowledge-related features are all consistent with a schema or theme but no known category actually exists. Since people often learn new categories that don’t correspond to already known ones, it is important to study and attempt to model this form of knowledge and its influence on learning. The present experiment, exploring the effects of prior knowledge on category learning with varying exemplar frequency, is a step towards understanding the circumstances under which prior knowledge can affect concept learning, and, when combined with computational modeling, will elucidate the mechanism underlying these effects. For expository purposes, we will postpone Knowledge and Frequency 6 detailed description of our modeling efforts until after the experiment is described, so that we may then discuss the relationships among the data, the model, and the theory in more detail. Experiment: Knowledge and Exemplar Frequency In the experiment, subjects saw descriptions of buildings and had to learn to classify the buildings into two categories. For half of the subjects, most features of the buildings could be linked together by themes like “aerial buildings” and “underwater buildings,” while for the other half of the subjects, the features were unrelated to each other. (Note that aerial and underwater buildings are not familiar concepts for most people, as confirmed by Murphy & Allopenna, 1994, and Spalding & Murphy, 1999.) Table 1 shows the stimulus features. To manipulate frequency, one item of each category was presented six times more often than the other items. Once during learning and twice after learning, subjects classified or rated several types of stimuli (trained items, novel prototype items, and individual features), and the effects of knowledge and stimulus frequency on their responses were examined. Based on the work of Nosofsky (1988) and Barsalou et al. (1998), we expected to find frequency effects when prior knowledge was absent. That is, the frequent exemplar and its features would both be more likely to be categorized into the appropriate category than would less frequent exemplars and their features. The category structure we tested is presented in Table 2. Note that, if one just attends to the different types of exemplars in Table 2, then this structure follows a standard one-away design in which 11111 is the prototype of category A and 00000 is the prototype of category B, and each category member contains one exception feature (a feature characteristic of the other category). However, not all the items in Table 2 were presented an equal number of times. Specifically, 11110 was presented six times more often than the other category A members, and 00001 was presented six times more often than the other category B Knowledge and Frequency 7 members. Note that this manipulation of exemplar token frequency changes which features are in fact associated with which categories. The 0 feature appears more frequently on the fifth dimension in category A members, whereas the 1 feature on that dimension appears more frequently in category B members. To understand this manipulation, imagine that you had a black squirrel living in your back yard. Frequent exposure to this squirrel would not only increase your knowledge of the normal shape, size, and behavior of squirrels but would also incorrectly increase the association between bla