Caricatures and Prototypes 1 Conceptual Interrelatedness and Caricatures Isolated and Interrelated Concepts

Concepts are interrelated to the extent that the characterization of one concept is influenced by another concept, and isolated to the extent that the characterization of one concept is independent of other concepts. The relative categorization accuracy of the prototype and caricature of a concept can be used as a measure of concept interrelatedness. The prototype is the central tendency of a concept, whereas a caricature deviates from the concept’s central tendency in the direction opposite to the central tendency of other acquired concepts. The prototype is predicted to be relatively well categorized when a concept is relatively independent of other concepts, but the caricature is predicted to be relatively well categorized when a concept is highly related to other concepts. Support for these predictions comes from manipulations of the labels given to simultaneously acquired concepts (Experiment 1) and the order of categories during learning (Experiment 2). Caricatures and Prototypes 3 Conceptual Interrelatedness and Caricatures Concepts seem to be simultaneously connected to each other and to the external world. On the one hand, concepts seem to gain their meaning by the role that they play within a network of concepts (Collins & Quillian, 1969; Field, 1977). The notion of a “conceptual web” by which concepts all mutually define one another has been highly influential in all of the major fields that comprise cognitive science, including linguistics (Saussure, 1915/1959), computer science (Lenat & Feigenbaum, 1991), psychology (Landauer & Dumais, 1997), and philosophy (Block, 1999). However, there is also dissatisfaction in some quarters with the circularity of this conceptual web account. Researchers have argued that concepts must be grounded in the external world rather than merely related to each other (Harnad, 1990). The British empiricists argued that our conceptual ideas originate in recombinations of sensory impressions (Hume, 1740/1973). More recently, Barsalou (1999; Goldstone & Barsalou, 1998; Solomon & Barsalou, 2001) has argued that concepts are not amodal, completely abstracted symbols, but rather are intrinsically perceptually based. In an attempt to reconcile arguments for a conceptual web and externally grounded concepts, Goldstone (1996) described a continuum between purely isolated and purely interrelated concepts, arguing that a concept is interrelated to the extent that its characterization is influenced by other concepts. Goldstone’s empirical basis for the continuum was the convergence of a set of experimental manipulations and measures of conceptual interrelatedness. A set of manipulations was designed to influence the degree of interrelatedness between simultaneously acquired concepts, and the influence of these manipulations was gauged by a set of measures of interrelatedness. These experiments gave support to the hypothesis that fairly minimal experimental manipulations were capable of changing how influential one concept was on another concept’s representation and processing. The goal of the current experiments is to further test the claim for a continuum between isolated and interrelated concepts, using rich and naturalistic stimuli, and new manipulations and measures of interrelatedness. Caricatures and Prototypes 4 Isolated and Interrelated Concepts In evaluating the claim for a continuum between isolated and interrelated concepts, it is helpful to consider theories at the two poles of the continuum. We will consider representative models of isolated and interrelated concepts, leaving a fuller description to Goldstone (1996). Conceptual interrelatedness is a component of many linguistic treatments of concepts. Ferdinand de Saussure (1915/1959) argued that all concepts are completely “negatively defined,” that is, defined solely in terms of other concepts. He contended that “language is a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others” (p. 114) and that “concepts are purely differential and defined not in terms of their positive content but negatively by their relations with other terms in the system” (p. 117). This notion has evolved into the modern treatment of semantic networks (Collins & Quillian, 1969; Quillian, 1967). In these networks, concepts are represented by nodes in a network, and gain their functionality by their links to other concept nodes. Often times, these links are labeled, in which case different links refer to different kinds of relations between nodes. Dog would be connected to Animal by an Is-a link, to Bone by an Eats link, and to Paw by a Has-a link. Lenat and Feigenbaum have argued (1991) that interconceptual linkages are sufficient for establishing conceptual meanings even without any external grounding of the concepts. A computational approach to word meaning that has received considerable recent attention has been to base word meanings solely on the patterns of co-occurrence between a large number of words in an extremely large text corpus (Burgess, Livesay, & Lund, 1998; Burgess & Lund, 2000; Landauer & Dumais, 1997). Mathematical techniques are used to create vector encodings of words that efficiently capture their co-occurrences. If two words, such as “cocoon” and “butterfly” frequently co-occur in an encyclopedia or enter into similar patterns of cooccurrence with other words, then their vector representations will be highly similar. The meaning of a word, its vector in a high dimensional space, is completely based on the contextual similarity of the word to other words. Finally, researchers have argued that concepts are frequently characterized by their associative relations to other concepts. Barr and Caplan (1987) provide evidence, by having subjects list features associated with words, that many concepts are characterized by what they call “extrinsic features,” features that are “represented as the relationship between two or more entities” (p. 398). Caricatures and Prototypes 5 From the theories above, one might conclude that concepts cannot stand alone, and there could not be such a thing as a system with only one concept (Stich, 1983). However, if one looks at the field of pattern recognition rather than theories inspired by linguistics, then examples of isolated concepts become apparent. One way to conceive of an isolated concept is as a feature detector. A feature detector can become active when an input with a particular perceptual feature is present. Ascending in complexity, a concept can also be represented as a template in a physical or more abstract space (Edelman, 1999). If patterns are categorized by comparing them with stored templates for categories, the representation of the categories do not depend on the other categories. A category’s representation is simply the image that best matches the members of the category. It is possible to have a feature detector or template for a concept without having any other concepts in the system. Categorizing an object may require comparing the relative degrees of match of the object to the representations for the candidate categories (Nosofsky, 1986), but if the categories themselves are represented by templates or feature detectors, then each can exist independently of the other categories. A comparison of these representative examples of interrelated and isolated concepts suggests a useful heuristic for assessing degree of interrelatedness. A Concept X is dependent on Concept Y to the extent that Concept X cannot exist without Concept Y. If the concept Vermicelli is represented as “thinner pasta than spaghetti” then no system could possess Vermicelli without also possessing Spaghetti. However, if the concept Vermicelli is represented by “a long pasta with a typical diameter of 6 mm” then possession of the concept does not depend upon possession of Spaghetti. Partial degrees of dependency owe to the multi-faceted nature of conceptual representations. A person’s concept of Vermicelli may incorporate both characterizations given above, and the relative importance of these characterizations determines how much Vermicelli’s representation is affected by the presence or absence of a Spaghetti concept. Prototypes and Caricatures Consider the example of two categories shown in Figure 1. Categories A and B each have 6 members, and each member has a unique combination of values on Dimensions 1 and 2. We will define the prototype of a category as the central tendency of the category along each of dimensions (Posner & Keele, 1968; Reed, 1972). The prototype of Category A has a Dimension 1 value of 2, while Category B’s Caricatures and Prototypes 6 prototype has a value of 4. In the experiments that follow, we use uniform distributions of dimension values in constructing categories, and consequently our description of a category prototype remains the same if we define central tendency as the average or median. -----------------------------INSERT FIGURE 1 ABOUT HERE ------------------------------We will define a caricature of a category as an object that assumes dimension values that depart from the central tendency of the category in the opposite direction of the central tendency of other simultaneously acquired concepts. In Figure 1, “X” represents the prototype of Category B, and “Y” represents a caricature of Category B. Y has a value of 5 on Dimension 1, and this value is a distortion of Category B’s central tendency in the direction opposite of Category A. This definition of caricature captures the intuitive notion of a caricature as an exaggeration. If Category B has a large value on Dimension 1 (relative to Category A), then the caricature of Category B exaggerates this large value, in the same way that a newspaper caricature exaggerates distinctive facial features of a politician. The current experiments investigate the conditions under which the prototype or caricature of a category is more easily categorized. On the one hand, one might predict better categorization for the prototype because it is, by definition, the item that is most similar to the members of its category (Posner & Keele, 1968; Rosch, 1975). On the other hand, one might predict better categorization accuracy for the caricature because it emphasizes a distinctive value for a category. In fact, there have been several experiments that have found a categorization advantage for caricatures relative to prototypes (Goldstone, 1996; Nosofsky, 1991; Palmeri & Nosofsky, 2001; Rhodes, Brennan, & Carey, 1987). Our current goal is not to argue that caricatures or prototypes are better categorized, but to identify experimental factors that modulate the benefit of one over the other. Specifically, experimental factors that promote relatively isolated concepts should tend to promote an advantage for prototypes over caricatures. In the absence of interconceptual influences, the representation that best exemplifies a concept will be its central tendency. If we try to represent Category B and do not know anything about Category A, then our best representation of Category B will be the point marked “X” in Figure 1. However, if a concept is characterized relative to other simultaneously acquired concepts, then characterizations of the form “Concept B members have relatively large Dimension 1 values compared to Concept A” will be formed. Caricatures and Prototypes 7 Caricatures fit these relational descriptions better than do prototypes. Nosofsky (1991) argued that classification of an object into a category depends on both its absolute similarity to members of the category, and its relative similarity to members of all of the candidate categories. The current experiments explore factors that affect the relative importance of these absolute and relative determinants of categorization. We instantiate caricatures and prototypes by face stimuli that are formed using automatic morphing software developed by Steyvers (1999). An example of caricaturization using this software is shown in Figure 2. A prototypical bald head was generated by combining together 62 bald heads taken from Kayser (1997). To create this prototype without the blurred quality typical of superimposed face photographs (Busey, 1998; Galton, 1878), 127 defining points were found for each of the 62 heads, and the average location for each point was assigned to the average face. The gray scale values of corresponding pixels across the 62 heads were blended to create the gray scale values for the average face. The caricature (shown on the right in Figure 2) of a particular face (shown in the middle of Figure 2) was generated by taking each of the 127 defining points on the face, and distorting them by 20% away from the defining points on the average face. According to the framework of interrelated and isolated concepts, a representation of the actual face in Figure 2 that is relatively isolated from other face representations would tend to resemble the actual face itself. Conversely, if the actual face is represented relative to other faces, then its internal representation would tend to more resemble the caricature. -----------------------------INSERT FIGURE 2 ABOUT HERE ------------------------------Manipulations of Conceptual Interrelatedness The relative ease of categorizing prototypes and caricatures will be used as the measure of concept interrelatedness. The other main task is to develop experimental manipulations that are predicted to affect the interrelatedness of concepts. There already exists a literature suggesting such manipulations. Goldstone (1996) found that interrelated categories were promoted when 1) participants were encouraged to look for features that discriminated between the learned categories, 2), categories were alternated frequently, 3) participants were practiced categorizers, and 4) stimuli were relatively undistorted versions of the categories’ prototypes. In contrast, isolated categories were promoted when 1) participants were encouraged to form images of the categories, 2) categories were alternated rarely, 3) participants were Caricatures and Prototypes 8 relatively unpracticed, and 4) stimuli were highly distorted versions of the categories’ prototypes. Niedenthal and Beike (1997) explored whether people’s self-concepts were relatively independent of other people, or relationally defined. They found that self-concepts were relatively interrelated when participants were asked to consider their distinctive attributes, and when participants were younger siblings comparing themselves to older siblings rather than vice versa. McKenzie (1998, 1999) has explored the conditions under which finding out information about one hypothesis affects mutually exclusive alternative hypotheses. Even in situations where participants are told that a patient has one and only one of two candidate diseases, evidence that increases participants’ confidence that the patient has one disease does not always decrease confidence that the patient has the other disease. Presenting the two diseases concurrently rather than successively makes the diagnoses of the diseases more (negatively) dependent on one another, as does mentioning both diseases when participants make confidence judgments about each disease. The current research explores two experimental manipulations that might be expected to affect concept interrelatedness. Experiment 1 manipulates the labels given to categories being acquired. One category is given a positive label (Club A) and the other category is given a negation label (Not Club A). Although this manipulation was used by Goldstone (1996), it has never been used with the caricature versus prototype measure of interrelatedness, and never used with naturalistic stimuli. Experiment 2 manipulates the order of learning categories, testing the hypothesis that the first learned category will be relatively isolated, while the second category tends to be characterized relative to the first category. Experiment 1 Numerous studies have shown that the labels given to categories of objects influence the characterization of those categories (Harnad, 1987; Malt et al., 1999; Waxman, 1990; Wisniewski & Medin, 1994). One example that is particularly related to concept interrelatedness is the mutual exclusivity hypothesis (Markman, 1990; Waxman, Chambers, Yntema, & Gelman, 1989). Children adopting this hypothesis determine the referent of a noun by assuming that nouns are mutually exclusive, and consequently, if a new term is applied to one of two objects and one object already has a name, children will tend to assume that the term refers to the other object. Similar to Saussure’s (1915/1959) notion of competition between concepts, the mutual exclusivity hypothesis assumes that as one concept gains control Caricatures and Prototypes 9 of a conceptual region, its competitor concepts lose control of the region. This is the same competition that is predicted to make interrelated concepts increasingly characterized by their caricatures rather than prototypes. In both cases, a category is displaced away from another category. Labeling may make pairs of concepts asymmetrically dependent on one another. One concept can be labeled “Category A” while another concept is labeled “not Category A.” In this case, the concept labeled “Not Category A” is predicted to be more influenced by “Category A” than vice versa (Clark, 1990). The concept that has a label that refers to another concept is predicted to be highly influenced by the referenced concept. Even though the category structures are symmetric, and the labels are randomly assigned to two categories, the “Not Category A” concept is predicted to be characterized more in terms of a caricature than the “Category A” concept. More precisely, there should be a tendency to associate the “Not Category A” concept with a stimulus that is more of a caricature than the stimulus associated with the “Category A” concept. There may be a bias to associate both categories with caricatures rather than prototypes (Goldstone, 1996; Palmeri & Nosofsky, 2001; Rhodes, Brennan, & Carey, 1987), but the extent of caricaturization is predicted to be greater for the “Not Category A” concept. The basis for this prediction comes from a combination of two assumptions: 1) the more dependent Concept A is on a mutually exclusive Concept B, the more Concept A’s characterization will be caricatured away from Concept B, and 2) explicitly labeling Concept A as not being Concept B makes Concept A dependent on Concept B. Method Participants. Sixty-two undergraduate students from Indiana University served as participants in order to fulfill a course requirement. The students were split evenly into the two labeling conditions. Materials. The stimuli were faces that were generated by morphing between photographs of two bald heads selected from Kayser (1997). Previous research has suggested that morphs generated from the two selected faces did not introduce conspicuous non-linearities between physical and psychological scalings (Goldstone & Steyvers, 2001). The morph sequence of 10 faces used is shown in Figure 3. Each of the morphs was automatically generated using a morphing technique described by Steyvers (1999). Applying this technique, the main contours in the face images were delineated by 127 control lines. These control lines served to align the features of the four faces. In the warping phase of this morphing algorithm, correspondences were calculated between the pixels of all the images to be morphed. Then, in the crossdissolving phase, the gray scale values of corresponding pixels were blended to create the gray scale values Caricatures and Prototypes 10 of the resulting morph image. The faces on the left and right ends of Figure 3 are actual faces, and the 8 intermediate faces are blends of the two actual faces, with the proportion of the left face shifting from 10% to 90% along the series in equal 10% increments. -----------------------------INSERT FIGURE 3 ABOUT HERE ------------------------------The prototype for a category was defined as the center face within the category’s set of five faces. This is the face that is the most similar, on average, to the other faces within its category. The caricature of a category is defined as the face that is least like the faces from the other category. The face between the caricature and the prototype is also a systematically caricatured face relative to the prototype, but to a lesser extent. Each face was displayed in grayscale with 256 possible brightness values per pixel (one pixel = .034 cm), and measured 14.48 cm tall by 11.68 cm wide. Each face was photographed against a dark background and displayed on a white Apple Imac computer screen. The average viewing distance was 46 cm. Procedure. On each trial, participants saw a face and categorized it by pressing either “Y” or “N” on the keyboard, with feedback on each trial from the computer indicating with a check or an “X” whether or not the participant was correct, and also indicating the correct category assignment for the face. Participants were instructed: "You will see faces appear on the screen. Half of them belong to certain club, while the remaining half do not. If you think that a face belongs to the club, press the ‘Y’ key for ‘Yes.’ If you think that it does not belong to the club, press the ‘N’ key for ‘NO.’” The dividing line between club members and nonclub members is shown by the vertical line in Figure 3. For half of the participants, those in Group 1, the first five faces were club members, and the last five faces were not club members. For Group 2, the first five faces were not club members, and the last five faces were club members. The experiment consisted of 60 repetitions of the 10 faces shown in Figure 3, for a total of 600 trials. The order of the 600 trials was randomized. The placement of a face’s center was also randomized within a 6 X 6 cm square in the center of the screen. Each trial began with a face appearing on the screen. The face remained on the screen until the participant pressed the “Y” or “N” key. Immediately after pressing one of the keys, feedback was given to the participant, and after 1.5 seconds, the screen was erased. Written Caricatures and Prototypes 11 feedback was in the form of “Yes, this face is a club member,” “No, this face is not a club member,” “Yes, this face is not a club member,” or “No, this face is a club member.” The blank interval between trials was 1 second. Participants were given breaks every 100 trials. During these breaks, participants were informed of their accuracy and speed during the preceding block. Results The primary data of interest was participants’ accuracy at categorizing particular faces into the two categories. Accuracy averaged over the 600 trials was variable enough that it was a sensitive dependent measure, and was less noisy than response times. However, response times closely mirrored the accuracy data. The categorization accuracies for each face and each group of participants are shown in Figure 4. The data reveal a bias to respond “Club” rather than “Not club.” This is shown by the horizontal offset between the two lines. Overall, participants responded “Club” and “Not club” on 54% and 46% of trials respectively, paired T-test T(61)=6.2, p< .01. Overall, caricatures were categorized more accurately than prototypes, with respective accuracies of 78.3% and 72.6%, paired T-test T(61)=5.6, p < .01. However, this main effect was modulated by the labeling manipulation. To compare caricature and prototype categorization, Faces 1 and 3 (see Figure 4) from Group 1 and Faces 8 and 10 from Group 2 were categorized together as “standard labeled” faces. Face 1 and 3 from Group 2 and Faces 8 and 10 from Group were categorized together as “negation labeled” faces. For negation labeled faces, caricatures and prototypes were categorized with respective accuracies of 78.6% and 68.6%. For standard labeled faces, these respective accuracies are much more similar, at 78.0% and 76.6%. These four comparisons represent a significant face type by labeling interaction, F(1, 61) = 8.2, p<.01. The faces between the caricature and the prototype (Faces 2 and 9) produced intermediate results to the caricature and prototype for both labeling conditions. Exploratory analyses revealed a second interaction involving caricatures and prototypes, involving practice. The 600 trials given to participants were broken down into two equal groups, early (Trials 1-300) and late (Trials 301-600). Unsurprisingly, accuracy was lower for early than late trials, with respective accuracies of 70.7% and 80.3%. However, the main effect of block was modulated by the type of face. For early trials, caricatures and prototypes were categorized with respective accuracies of 72.0% and 69.4%, and for late trials, these percentages increased to 84.6% and 76%. These percentages reveal a significant Practice X Face type interaction, F(1,61)=7.4, p<.01. This interaction indicates that the categorization Caricatures and Prototypes 12 advantage for caricatures over prototypes increases with practice. This is consistent with earlier results (Goldstone, 1996) and is predicted by the hypothesis that in a categorization task where two categories are frequently alternated, the categories will become increasingly interrelated. As categories become more interrelated, the degree of caricaturization of the category representations is expected to increase. -----------------------------INSERT FIGURE 4 ABOUT HERE ------------------------------Discussion Category labeling influences the relative advantage of caricatures over prototypes even when the structure of the categories remains constant. A category that is labeled as a negation of a standard category tends to be represented as a caricature, systematically distorted away from the standard category. This is revealed by the significantly greater categorization accuracy for the negation category’s caricature than prototype. The standard category itself shows approximately equal categorization accuracies for prototypes and caricatures. This set of results is predicted by the distinction between interrelated and isolated concepts. One way of making Concept A dependent on Concept B is simply by making A’s label depend on B. This produces asymmetrically dependent concepts because A will depend upon B more than B depends upon A. The expected result of this is that A’s representation will be caricatured away from B’s representation, and that the degree of this caricaturization should be greater than the caricature of B away from A. Experiment 2 Experiment 1 created asymmetrically dependent concepts through asymmetric category labeling relations. A second way of creating asymmetric concepts is by presenting the categories sequentially. The first presented category should develop a relatively isolated category representation because there is no other category to serve as a standard of comparison. In contrast, the second presented category can be compared to the earlier category, and thus this second category should be more dependent on the first category than vice versa. Empirical evidence for asymmetrical dependencies between sequentially learned categories comes from Kruschke (1996). He found that the second learned category from a pair of Caricatures and Prototypes 13 categories tends to be characterized in terms of features that are diagnostic for distinguishing the second category from the first category. The first learned category does not show this bias to as large an extent. If the features that are particularly diagnostic for distinguishing a second category from a first category are emphasized in the second category’s representation, then one would also expect a larger caricature-over-prototype advantage for the second than the first category. A caricature is defined as a stimulus that emphasizes features of a category that distinguish it from other learned categories. Accordingly, we predict that the asymmetric dependency of the second category on the first category should cause the second category to be represented in a more caricatured form than the first category. Method Participants. Sixty-six undergraduate students from Indiana University served as participants in order to fulfill a course requirement. The students were split evenly into the two category order conditions. Procedures. The stimuli were identical to those used in Experiment 1. Participants were told that they would eventually be asked to categorize faces into one of two groups. They were told that they would first see examples from one group, then examples from a second group, and then finally would be asked to categorize faces that they had seen before into one of these two groups. Consistent with these instructions, the experiment was broken down into three phases. During the first phase, half of the participants were presented with the left five faces from Figure 3, and the other half were presented with the right five faces. Each of the five faces was presented a total of 15 times, and the presentation order was randomized. On each trial, the face remained on the screen for three seconds with a label “Category A” below it, followed by blank screen for 1 second. On the second phase of the experiment, the faces not shown during the first phase were presented to participants with the label “Category B” below them, using the same procedures as the first phase. During the categorization phase of the experiment, participants were shown the 10 faces from Figure 3 a total of 15 times each, in a random order. Participants were instructed to decide whether each face belonged to Category A or B. Participants indicated their categorizations by pressing either the “A” or “B” key. Participants did not receive feedback during the categorization phase. Results The primary data of interest was participants’ accuracy at categorizing particular faces into the two categories averaged over 150 trials. The categorization accuracies for each face and each group of Caricatures and Prototypes 14 participants are shown in Figure 5. The data reveal a small bias to categorize a face into the second, most recently seen category (Category B). Overall, participants responded Category A and B on 48.7% and 51.3% of trials respectively, paired T-test T(65)=2.1, p< .05. Unlike Experiment 1, there was no main effect such that caricatures were categorized more accurately than prototypes. Overall, extreme caricatures (Faces 1 and 10) and prototypes (Faces 3 and 8) were categorized with accuracies of 70.1% and 69.1%, paired T-test T(65)=1.3, p >0.1. However, there was an interaction between face type and category order. To compare caricature and prototype categorization, Faces 1 and 3 (see Figure 4) for the group that received Faces 1-5 first and Faces 8 and 10 from the group that received Faces 6-10 first were categorized together as “First Category” faces. Face 1 and 3 from the group that received Faces 6-10 first and Faces 8 and 10 from the group that received Faces 1-5 first were categorized together as “Second Category” faces. For faces from the first, early category, caricatures and prototypes were categorized with respective accuracies of 67.1% and 70.0%. For faces from the second, later category, these respective accuracies reverse their rank order, with accuracies of 73.3% and 68.1%. These four comparisons represent a significant face type by order interaction, F(1, 65) = 9.1, p<.01. The faces between the caricature and the prototype (Faces 2 and 9) produced intermediate results to the caricature and prototype for both labeling conditions. -----------------------------INSERT FIGURE 5 ABOUT HERE ------------------------------Discussion According to the results from Experiment 2, whether a caricature or prototype advantage is found during categorization depends on whether the category is the first or second in a pair of sequentially presented categories. For the first presented category, the prototype is better categorized than the caricature. The opposite effect is found for the second category. This is consistent with the hypothesis that the second category is more likely to be characterized relative to the first category than vice versa. Isolated categories are expected to be represented in terms of their prototypes, whereas a category that depends on a second, mutually exclusive category, is expected to be represented in terms of a caricature that is systematically distorted away from the second category. Caricatures and Prototypes 15 In Experiment 1, a general advantage for caricatures over prototypes was found, whereas in Experiment 2, there was no significant main effect of face type. Given procedural differences between the experiments, this is naturally accounted for by the framework of isolated and interrelated concepts. In Experiment 1, items taken from the two categories were randomly intermixed, whereas in Experiment 2, the two categories were presented separately. Categories are predicted to be more interrelated when they are presented simultaneously because there is more opportunity for interactions between developing category representations. This prediction is supported by previous evidence that when simultaneously acquired categories are alternated frequently the category representations are more interrelated than when categories are alternated rarely (Goldstone, 1996). Dividing categories into completely separate blocks, as was done in Experiment 2, can be interpreted as an extreme way of alternating categories rarely. In Experiment 1, there was a bias to respond with the standard-labeled rather than negation-labeled category, and the negation-labeled category was more caricatured than the standard-labeled category. In Experiment 2, there was a bias to respond with the second learned category label rather than the first category, but the second category was more caricatured than the first. Accordingly, across the two experiments, response bias is dissociable from caricaturization. This is useful because it shows that the amount of caricaturization of a category is not simply a function of how often it is given as a response to a stimulus. General Discussion The effects of the two manipulations of Experiments 1 and 2 are well integrated by the proposal that concepts differ in how interrelated they are. In particular, two concepts may be asymmetrically dependent on one another, such that Concept A depends more on Concept B than vice versa. With this perspective, manipulations that might not otherwise be seen as similar are seen as cohering together. Labeling a category “Not Category A” or presenting examples of the category after Category A exemplars are two ways of making the category highly dependent on Category A. Given this dependence and the mutual exclusivity between the categories (items belong to one and only one of the categories), the representation of the category is expected to be caricatured away from the prototype of Category A. Category A, by contrast, is expected to be more independent in these experimental conditions, and its representation is expected to be more prototypical, less caricatured. Caricatures and Prototypes 16 Caricaturization and the Perception of Others The current results are novel in that the experimental manipulations of category interrelatedness have not been tested with rich, naturalistic stimuli. Goldstone (1996) predicted that category presentation order should affect concept interrelatedness, but this notion has not been directly tested until now. However, there are several results in social psychology that are related to the current demonstration. The basis for this link is that an individual is likely to think of himor her-self in a relatively isolated, independent manner, and to think of others in relation to themselves (Niedenthal & Beike, 1997). This principle can also be applied to the group level with the consequence that a person is likely to think of their own group in a relatively isolated manner, and to think of other groups in relation to their own group (Linville & Jones, 1980). Combined with the current framework, this suggests that a person should perceive other people and other groups as more caricatured than they really are, but that they should perceive themselves and their own group in a more veridical fashion. Consistent with this hypothesis, Linville and Jones (1980) found that members of an other group are more likely to be appraised in an extreme manner than members of one’s own group. For example, white participants judged a black applicant more favorably than a white applicant when the both applicants had relatively strong credentials, but judged the black applicant more negatively when both applicants had weak credentials. A mechanism that may underlie this effect is that distinctive attributes of a relatively unfamiliar or rare group have an exaggerated effect on people’s judgments (McConnell, Sherman, & Hamilton, 1994). Caricatures are exactly the kind of representation that exaggerates features of one group relative to another group. The relatively unfamiliar out-group is particularly prone to being represented in a caricatured manner. Social cognition researchers have also found a general bias by which people accentuate the differences between categories (Corneille & Judd, 1999; Krueger & Rothbart, 1990). As with McConnel et al. (1994), the mechanism for this contrast effect appears to be that properties that are particularly diagnostic for distinguishing between categories have their importance exaggerated. The current results extend these findings by showing that these exaggerations can be asymmetric. An independent concept is less susceptible to exaggeration than a relationally defined concept. Under the assumption that white participants living in white majority environment view the category Whites as relatively isolated and view blacks in terms of their differences from whites, the prediction is that these participants would tend to Caricatures and Prototypes 17 represent Whites by the prototype of white people, but Blacks by a caricature distorted away from the prototype for black people in the direction opposite of white people. Although this kind of asymmetry has not been directly tested to our knowledge, greater exaggeration of group differences have been found for individuals from minority rather than majority groups (see Hewstone, Rubin, & Willis, 2002 for a review). Models of Isolated and Interrelated Concepts Existing models of categorization differ in their predictions of the relative accuracy for categorizing prototypes and caricatures. Decision boundary models of categorization (Ashby & Maddox, 1993) predict that categorizations become easier as stimuli move away from the boundaries between categories. A natural consequence of these models is that caricatures should be easier to categorize than prototypes in a two-category situation because caricatures are designed to be displaced away from the boundary between the categories. Exemplar models represent categories in terms of the members belonging to each category, and categorize new items by measuring their summed similarity to the existing members of the candidate categories (Medin &Schaffer;, 1978). In one influential exemplar model, GCM (Nosofsky, 1986, 1991), the likelihood of correctly categorizing a caricature and prototype of a category depends on whether similarity is assumed to be based on an exponential or Gaussian function of stimulus distance. Under an exponential relation between subjective similarity and distance and assuming only one single-dimension item in each of two categories, caricatures and prototypes are predicted to be exactly equally well categorized. Under a Gaussian relation, categorization accuracy increases monotonically as the extremity of caricature increases. Thus, neither of these functions allows GCM to predict either a categorization advantage for a prototype relative to a caricature, or greatest categorization accuracy for an intermediate degree of caricaturization. By contrast, other models have predicted that intermediate stimuli between prototypes and extreme caricatures will be most accurately categorized. These models are useful in accommodating the “peak shift” phenomenon, according to which the maximal response is given to a stimulus that is displaced away from a reinforced stimulus by a specific amount in the direction opposite of an unreinforced stimulus (McLaren, Bennett, Guttman-Nahir, & Kim, 1995; Spence, 1936). The current data challenge any model of categorization that predicts a constant advantage of caricatures over prototypes or vice versa. We found that whether a caricature-over-prototype advantage was found depends on whether the concepts involved were relatively independent or interrelated. This kind Caricatures and Prototypes 18 of interaction is accommodated by Goldstone’s (1996) RECON model. This connectionist model is a twolayer recurrent network. One layer of units represents the input dimensions, and one layer of units represents the learned categories. All units in RECON are connected to each other by weighted links. Unlike standard feed-forward networks, RECON has recurrent connections between category units. These connections provide a mechanism for categories to influence each other. By varying a single parameter, the degree of influence of category units on each other, varying degrees of concept interrelatedness are obtained. Simulations have shown that as the magnitude of category-to-category weights increase, the categorization advantage of caricatures over prototypes increases. Strong lateral inhibition between categories leads to the categories emphasizing distinctive features that uniquely characterize just one category. RECON can also accommodate asymmetrically interrelated categories by removing the constraint that the weight from Category A to Category B must equal the weight from B to A. If the weight from A to B is greater than the weight from B to A, then the representation of Category B will be caricatured (away from A) relative to Category A’s representation. In this manner, the current experiments can be accommodated by RECON, under the assumption that labeling B so as to refer to A, or presenting B after A, will make the weight from Category A to Category B greater than from B to A. More generally, the current results are also consistent with models that assume that the representation of a concept is based not only on its connections to the external, perceptual world (Barsalou, 1999; Goldstone & Barsalou, 1998), but also on its connections to other concepts (Goldstone & Rogosky, in press). Concepts do not typically act like independent detectors polling the world. Concepts are also influenced by the simultaneous presence of other concepts. Understanding the interaction between external and internal determinants of conceptual meaning is an important, but difficult, project. 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