Prototypes in the Mist: The Early Epochs of Category Learning

Transcription

1 Journal of Expermental Psychology: Learnng, Memory, and Cognton 1998, Vol. 24, No. 6, Copyrght 1998 by the Amercan Psychologcal Assocaton, Inc /98/S3.00 Prototypes n the Mst: The Early Epochs of Category Learnng J. Davd Smth and John Paul Mnda State Unversty of New York at Buffalo Recent deas about category learnng have favored exemplar processes over prototype processes. However, research has focused on small, poorly dfferentated categores and on task-fnal performances both may hghlght exemplar strateges. Thus, we evaluated partcpants' categorzaton strateges and standard categorzaton models at successve stages n the learnng of smaller, less dfferentated categores and larger, more dfferentated categores. In the former case, the exemplar model domnated even early n learnng. In the latter case, the prototype model had a strong early advantage that gave way slowly. Alternatve models, and even the behavor of ndvdual parameters wthn models, suggest a psychologcal transton from prototype-based to exemplar-based processng durng category learnng and show that dfferent category structures produce dfferent trajectores of learnng through the larger space of strateges. Categorzng objects nto psychologcal equvalence classes s a basc cogntve task. Descrptons of categorzaton long favored a generalzed prototype prncple (Homa, Rhoads, & ChambUss, 1979; Homa, Sterlng, & Trepel, 1981; Mervs & Rosen, 1981; Posner & Keele, 1968, 1970; Rosch, 1973, 1975; Rosch & Mervs, 1975). Humans were supposed to average ther exemplar experence to derve the category's prototype, compare new tems to t, and accept the tems as category members f smlar enough. More recently, though, some have argued that prototypes are an nsuffcent organzng prncple for categores (Murphy & Medn, 1985). Formal treatments have shown that prototype models sometmes poorly descrbe humans' performance (Medn & Schaffer, 1978; Nosofsky, 1987, 1992). Emprcal studes have challenged the predcton of prototype theores that humans should fnd lnearly separable categores especally learnable (Medn & Schwanenflugel, 1981). As a result, prototype-based descrptons of categorzaton performance have been treated crtcally or margnalzed (McKnley & Nosofsky, 1995,1996; Nosofsky, 1991, 1992; Shn & Nosofsky, 1992), and the lterature has come to favor nstead a generalzed exemplar prncple n categorzaton. Ths possblty, that humans store specfc exemplars and use these encapsulated epsodes as comparatve standards by whch to categorze new nstances, s an mportant clam about cognton. The more general the clam, the more mportant. Yet exstng exploratons of ths exemplar prncple have not mapped completely the doman of categorzaton, wth ts lmtless space of dfferent category structures, exemplar pool szes, observer populatons, performance J. Davd Smth, Department of Psychology and Center for Cogntve Scence, State Unversty of New York at Buffalo; John Paul Mnda, Department of Psychology, State Unversty of New York at Buffalo. Correspondence concernng ths artcle should be addressed to J. Davd Smth, Department of Psychology, Park Hall, State Unversty of New York at Buffalo, Buffalo, New York Electronc mal may be sent to psysmth@acsu.buffalo.edu. condtons, and performance levels. Research must stll specfy the approprate extenson of the exemplar prncple by evaluatng, for example, whether dfferent categorzaton processes apply durng dfferent epochs of learnng or for dfferent category structures. Ths artcle jons others n explorng these two questons (Homa & Chamblss, 1975; Homa, Dunbar, & Nohre, 1991; Homa et al., 1981; Nosofsky, Gluck, Palmer, McKnley, & Glauther, 1994; Nosofsky, Palmer, & McKnley, 1994). Ths exploraton s mportant because n both regards the lterature may have unntentonally exaggerated the generalty of exemplar processes n categorzaton. Regardng dfferent epochs of learnng, partcpants often receve extensve tranng before modelng occurs, wth tranng endng when they acheve a crteron of consecutve correct responses or acheve above-chance performance on all the tranng stmul (Medn & Schwanenflugel, 1981; Medn&Smth, 1981; Nosofsky, 1986). Then, the prototypebased and exemplar-based descrptons of performance are compared. Ths research strategy provdes a statc snapshot of task-fnal, mature performance. However, at ths stage of learnng, strong exemplar traces may have arsen, makng the exemplar model especally approprate. Therefore, ths approach cannot show humans' frst prncples n categorzaton or the early stages of ther category learnng. These wll have been paved over by long tranng wth a restrcted set of exemplars, and they wll be nvsble n a statc, end-ofperformance snapshot To see them, you need somethng more lke a vdeo, a vdeo that explores successve stages of learnng (see Estes, 1986a, p. 501). We provde such a vdeo here. In ths regard, our research s alled to other studes that have evaluated performance n dfferent stages of category learnng (Ann & Medn, 1992; Estes, 1986b; Homa et al., 1991; Medn, Wattenmaker, & Hampson, 1987; Nosofsky, Kruschke, & McKnley, 1992; Nosofsky, Palmer, & McKnley, 1994; Regehr & Brooks, 1995). However, whereas some of ths research (Ahn & Medn, 1992; Medn et al., 1987; Regehr & Brooks, 1995) has adopted a dstnctve sortng paradgm, here we adopt a typcal categorzaton paradgm. 1411

2 1412 SMITH AND MINDA Whereas prevous research (Ahn & Medn, 1992; Medn et al., 1987; Nosofsky, Palmer, & McKnley, 1994; Regehr & Brooks, 1995) has focused on rule-based descrptons, here we focus on the value of prototype-based descrptons for descrbng category learnng. Moreover, prevous research has suggested that partcpants' progresson of strateges mght be general across dfferent category structures (.e., wth poorer or better category dfferentaton, wth smaller or larger exemplar pools see, e.g., Nosofsky, Gluck, et al., 1994; Nosofsky, Palmer, & McKnley, 1994). Here we analyze the doman of category structures more fnely and examne the dea (Homa et al., 1981; Reed, 1978; Smth, Murray, & Mnda, 1997) that dfferent category structures foster dfferent trajectores of learnng. Fnally, prevous research has tred to show the general superorty of one class of model over another (Estes, Campbell, Hatsopoulos, & Hurwtz, 1989; Nosofsky, 1992; Nosofsky, Gluck, et al., 1994; Nosofsky et al., 1992). Ths emphass on global ft msses the possbltes that we focus on here that at dfferent ponts n learnng, partcpants occupy dfferent postons n the larger space of categorzaton strateges and that some of these dfferences have theoretcal mplcatons. Regardng dfferent category structures, those typcally used have favored exemplar-based processes because they have featured small exemplar pools (about four tems per category) and poorly dfferentated categores (Medn, Dewey, & Murphy, 1983; Medn & Schaffer, 1978; Medn & Schwanenflugel, 1981; Medn & Smth, 1981; Nosofsky, 1986, 1989, 1991; Nosofsky, Gluck, et al., 1994; Nosofsky, Palmer, & McKnley, 1994). Medn and Schwanenflugel (1981, p. 365) understood that ths knd of category structure can engender a unque task psychology and specalzed strateges. It can even turn a seemng categorzaton task nto an dentfcaton task n whch partcpants assocatvely pahwhole exemplars and ther category labels but have no sense of coherent categores n dong so. Ths may happen because exemplar memorzaton s easer and more obvous when few exemplars repeat frequently (Homa & Chamblss, 1975; Homa, Cross, Cornell, Goldman, & Shwartz, 1973; Homa et al., 1979, 1981). Ths may happen because less dfferentated categores weaken the urge to form prototype-based clusters of exemplars. By ether account, exemplar-based strateges should domnate for sparse and dffcult category structures, and the lterature confrms that they do. However, ths approach cannot show the categorzaton strateges humans favor when they face larger, better dfferentated categores. We evaluate these strateges here. In ths regard, our research s alled to that of Smth et at (1997). They analyzed performance when partcpants learned both smaller, less dfferentated categores and larger, more dfferentated categores. The former categores produced performance profles that were ft profoundly better by an exemplar-based model than by a prototype-based model. The latter categores produced many performance profles that the standard exemplar model faled n systematc ways to capture and that the prototype model ft better. Accordngly, we consder partcpants* categorzaton strateges, and the potental of dfferent categorzaton models for capturng these strateges, for both knds of category structures. In ths artcle, we descrbe four category-learnng experments that examne the path that partcpants trace through the larger space of categorzaton strateges as they learn, and we consder how dfferent formal models descrbe ths trajectory. Early n learnng, partcpants show strateges that standard exemplar models accommodate poorly but that smple prototype-based descrptons of categorzaton accommodate well. Late n learnng, exemplar-based models and exemplar-based descrptons of categorzaton come nto ther own. These results llumnate humans' early approaches to category learnng and the changng character of performance durng learnng. They also suggest that the progresson of strateges durng category learnng s strongly affected by dfferent category structures. From a formal perspectve, ths trajectory through strategy space durng category learnng s sometmes so pronounced that both the domnant prototype and exemplar models fal to capture t completely. From a psychologcal perspectve, ths trajectory can be smply and productvely hypotheszed to reflect a progresson from a strong relance on prototypes to a strong relance on exemplar memorzaton. Both perspectves encourage models and theores of categorzaton that ncorporate prototype-based and exemplarbased representatons and processes. Both perspectves encourage the dea that prototypes and exemplars have changng roles and nfluences durng the dfferent stages of category learnng and durng the learnng of dfferent category structures. Experment 1 Experment 1 explored the possblty that partcpants' early nformaton-processng strateges may be ft better by assumng prototype-based categorzaton than by assumng exemplar-based categorzaton. To ths end, partcpants' performance at dfferent stages of category learnng was modeled usng the basc and most promnent prototype and exemplar models. We predcted that the basc exemplar model would ft performance better late n learnng, as t has n many prevous studes. We wondered whether the basc prototype model would ft performance better early n learnng. Experment 1 ncluded both lnearly separable (LS) and not lnearly separable (NLS) category structures because there s contnung nterest n both. (LS categores are those that can be parttoned by a lnear dscrmnant functon, and for whch one can smply sum up the evdence offered separately by each feature of an tem and use that sum to correctly decde category membershp.) Two methodologcal aspects of Experment 1 arranged a balanced comparson between models. Frst, Smth et al. (1997) found that prototype models and exemplar models ft best equal numbers of performance profles when better stocked, better structured categores were used. Therefore, Experment 1 adopted these category structures and asked whether dfferent models have a selectve advantage durng dfferent epochs of learnng. Second, Smth et al. found that aggregatng data over partcpants before modelng placed the prototype model at an nherent dsadvantage, camouflagng ts good ft to the performances of many ndvdual

3 CATEGORY LEARNING 1413 partcpants. Therefore, Experment 1 featured the modelng of ndvdual performance profles. Method Partcpants. Thrty-two students partcpated to fulfll a course requrement. Stmul and category structures. The present category structures were made possble by usng sx-dmensonal stmul. The stmul were pronounceable sx-letter nonsense words (CVCVCV). Many artcles have been devoted to stmulus materals lke these, makng ths a well-understood class of ll-defned category n the lterature, and one that has allowed the replcaton of categorzaton phenomena found wth other stmul (Jacoby & Brooks, 1984; Smth & Shapro, 1989; Smth, Tracy, & Murray, 1993; Smth et al., 1997;Whttlesea, 1987; Whttlesea, Brooks, &Westcott, 1994). By focusng on these stmulus materals n Experments 1-3, we made the crtcal varatons of category structure and exemplar-set sze wthn one stmulus doman so that our comparsons were as nterpretable as possble. By usng more pctoral materals n Experment 4, we generalzed the prncpal results. Stmulus generaton began wth the creaton of four prototype pars (kaftdo-nvety, gafuz-wysero, banuly-kepro, lotnagerupy). The frst and second members of each par were desgnated as Stmulus and Stmulus , respectvely. These prototypes were created randomly but wth several constrants to ensure the pronounceablty of all stmul, the orthographc approprateness of all stmul, the dentcal syllabfcaton of all stmul, and the roughly equal use of all vowels. For example, q (whch needs two vowels), c (whose pronuncaton depends on the followng vowel), and a fnal e (that can change syllabfcaton) were dsallowed. Each prototype par contaned sx dfferent vowels and sx dfferent consonants. Appendx A shows the LS and NLS category structures and sample stmulus sets. Each LS category contaned one prototype, two stmul wth fve features n common wth the prototype, and four stmul wth four typcal features. There were no excepton tems. The LS smlarty relatons were thus farly homogeneous, wth all tems sharng a majorty of features wth ther prototype and clustered around t n sx-dmensonal stmulus space. A prototype strategy, usng an addtve rule that summed across ndependent attrbutes, could allow perfect categorzaton f used perfectly. Each NLS category contaned one prototype, fve stmul wth fve features n common wth the prototype, and one stmulus wth fve features n common wth the opposng prototype. The smlarty relatons n the NLS categores were heterogeneous because they contaned a group of smlar tems tghtly clustered around the prototype and one outler stmulus. The clusters of smlar nstances, combned wth the excepton tems, balanced overall wthn- and between-category smlarty at the level of the LS categores. Even so, the NLS category structure defeats any categorzaton strategy that depends on an addtve combnaton of featural evdence. For one thng, such a strategy produces categorzaton errors for Stmul A7 and B7, whch have more features n common wth the opposng prototype. For another thng, the NLS stmulus set contans complementary stmulus pars wthn each category (.e., Stmul A5 and A7; Stmul B5 and B7) that have no features n common at all. These stmulus pars rule out successful categorzaton usng any lnear dscrmnant functon. That s, any weghtng of the ndependent cues that allows the successful classfcaton of A7 (e.g., a very heavy weghtng on the ffth feature) ensures the msclassfcaton of A5. These general category structures were predetermned to allow the generaton of well-matched LS and NLS stmulus sets. Followng these assgnments, hundreds of stmulus sets were computer generated and screened for LS and NLS structures that matched n several ways. The two category structures fnally chosen had dentcal exemplar-exemplar smlarty, both wthn category (3.88 features) and between categores (2.12 features), and had dentcal exemplar-prototype smlarty, both wthn category (4.57 features) and between categores (1.43 features). Thus, the two category structures had dentcal structural ratos (1.83, usng the exemplarexemplar smlartes). These smlarty calculatons were done addtve I y and assumed equal salence for all features. In addton, LS and NLS categores were matched n the overall nformatveness of all attrbutes. For the LS and NLS categores, Category A and Category B stmul took the typcal value 5, S, 5,6, 6, and 5 tmes, respectvely, for Attrbutes 1 through 6. There were no crteral attrbutes avalable n ether stmulus set, and any sngle-letter strategy should have been dentcally salent and vable n both of them. LS and NLS stmulus sets were constructed usng each of the four prototype pars. Procedure Partcpants were tested ndvdually, havng been randomly assgned to a category structure and to a prototype par. Words were presented on a computer termnal n blocks of 14 trals; each block was a random permutaton of all 14 stmul. Each partcpant receved hs or her own unque stmulus order. Partcpants responded usng the / and the 2 keys on the keypad. Correct responses were rewarded by a bref whoopng sound generated by the computer; errors earned a 1-s low buzzng sound. A runnng total of partcpants' correct responses was dsplayed at the top of the screen. Trals contnued n an unbroken fashon untl 392 trals (28 blocks) had been presented. Partcpants had unlmted tme to vew each stmulus before respondng. The stmulus remaned vsble after wrong choces durng the 1-s error sgnal. Enterng the experment, partcpants were told that they would see nonsense-word stmul that could be classfed as Group 1 (Category A) words or Group 2 (Category B) words. They were further told to look carefully at each word and decde f t belongs to Group 1 or Group 2. Type a " 1" on the keypad f you thnk t s a Group 1 word and a "2" f you thnk t s a Group 2 word. If you choose correctly, you wll hear a "whoop" sound. If you choose ncorrectly, you wll hear a low buzzng sound. At frst, the task wll seem qute dffcult, but wth tme and practce, you should be able to answer correctly. Formal Modelng Procedures The basc exemplar model. In evaluatng the exemplar model, we focus on the context model orgnated by Medn (1975 see also Medn et al., 1983; Medn & Schaffer, 1978; Medn & Smth, 1981) and generalzed by Nosofsky (1984, 1986; McKnley & Nosofsky, 1995). Palmer and Nosofsky (1995) referred to ths model as the standard context model. In the exemplar model, the to-be-classfed tem n the present tasks would be compared wth the seven Category A exemplars (ncludng tself f t s a Category A tem) and wth the seven Category B exemplars (ncludng tself f t s a Category B tem), yeldng the overall smlarty of the tem to Category A members and Category B members. Dvdng overall Category A smlarty by the sum of overall A and B smlarty would essentally yeld the probablty of a Category A response. The smlarty between the to-be-categorzed tem and any exemplar was calculated n three steps as follows. Frst, the values

4 1414 SMITH AND MINDA (1 or 0) of the tem and the exemplar were compared along all sx dmensons. (Ths smplfyng step let us proceed wthout psychologcally scalng the entre sx-dmensonal stmulus space.) Matchng features made a contrbuton of 0.0 to the overall psychologcal dstance between the stmul; msmatchng features contrbuted to overall psychologcal dstance n accordance wth the attentonal weght that dmenson carred. In the present model, each dmensonal weght was between 0.0 and 1.0, and the sx weghts were constraned to sum to 1.0. Second, ths raw psychologcal dstance between tem and exemplar was scaled wth a senstvty parameter that could vary from 0.0 to Larger senstvty values essentally magnfy psychologcal space, ncreasng the dfferentaton among stmul, ncreasng overall performance, and ncreasng the value the exemplar model places on exact dentty between the tem and an exemplar. Formally, then, the scaled psychologcal dstance (d) between the to-be-classfed tem (0 and exemplar (f) s gven by w k\ x k where x k and x Jk are the values of the tem and exemplar on dmenson k, w k s the attentonal weght granted dmenson k> and c s the senstvty parameter. The use of the exponent 1 n ths equaton ncorporated the plausble dea that the psychologcal space underlyng the present stmul was organzed accordng to a cty-block smlarty metrc (Nosofsky, 1987, p. 89). Thrd, the smlarty (T y) between the tem and exemplar was calculated by takng T^- = e d]j, wth dy beng the scaled psychologcal dstance between the stmul. The use of the exponent 1 n ths equaton ncorporated the plausble dea that smlarty n the present case was an exponental-decay functon of psychologcal dstance (Nosofsky, 1987, p. 89; Shepard, 1987). These three steps were repeated for calculatng the psychologcal smlarty between a to-be-categorzed tem and each A and B exemplar. Then, summng across the Category A exemplars (jec A ) and Category B exemplars (/EC B ), we calculated the total smlarty the tem had to Category A members and Category B members. In the standard exemplar model, these quanttes would yeld drectly the probablty (P) of a Category A response (R A ) for stmulus (S,) by takng x jk Za ^ y "*" Xw ^ j Repeatng ths process for each of the 14 tems, one would derve the performance profle predcted by the model. However, for reasons to be descrbed, an addtonal guessng-rate parameter was added to the exemplar model as follows. It was assumed that some proporton of the tme (G) partcpants smply guessed Category A or B haphazardly. It was assumed that the rest of the tme partcpants used exemplar-based categorzaton n the way already descrbed. Wth the guessng parameter added, the context model had eght parameters sx dmensonal weghts constraned to sum to 1.0, a senstvty parameter, and a guessng-rate parameter. We count parameters conceptually n ths artcle (.e., eght here). However, the constrant on the sum of the dmensonal weghts means that the number of free parameters n the varous models s one less (.e., seven here). Tofnd the best-fttng parameter settngs of the exemplar model, we seeded the space wth a sngle parameter confguraton and calculated predcted categorzaton probabltes for the 14 stmul accordng to that confguraton. The measure of ft was the sum of the squared devatons between the 14 predcted probabltes and the 14 observed categorzaton probabltes of some partcpant's performance. Ths measure was mnmzed durng an analyss by usng a fne-graned hll-clmbng algorthm that constantly altered slghtly the provsonal best-fttng parameter settngs and chose the new settngs f they produced a better ft (.e., a smaller sum of squared devatons between predcted and observed performance). In ths way, the algorthm moved toward the best-fttng confguraton. To ensure that local mnma were not a serous problem n the present parameter spaces, ths analyss was repeated by seedng the space wth four more qute dfferent confguratons of the exemplar model and hll clmbng from there. The varance among the fve fts tended to be very small, ndcatng that the mnma found were close to global ones. The basc prototype model. To evaluate the prototype model, we supposed that each to-be-categorzed tem would be compared wth the category prototype along the sx ndependent dmensons, usng addtve smlarty calculatons. We assumed addtve smlarty n order to follow most closely the nfluental research of Medn and hs colleagues (Medn & Schaffer, 1978; Medn & Smth, 1981) and to evaluate a smple and ntutve prototype model. Msmatchng features on a dmenson contrbuted 0.0 smlarty; matchng features contrbuted the amount of ther dmenson's weght. The sx attentonal weghts were agan constraned to sum to 1.0. So, for example, f an observer allocated attenton homogeneously (. 166 to each dmenson), and a stmulus shared fve or four features n common wth the prototype, the judged smlarty would be.83 or.67, respectvely. If a stmulus dffered from the prototype n only one sharply attended feature (e.g., a.300 attentonal weght), ts judged smlarty would be.70. In the smplest case, the tem's smlarty to the prototype could be taken to be the probablty of a correct categorzaton and ts complement to be the probablty of an error. An addtonal guessng-rate parameter was also added to the prototype model. Ths parameter s especally useful for modelng partcpants' haltng performance durng the early epochs of category learnng. Wthout t, for example, the prototype (wth perfect self-smlarty) would be predcted to be categorzed perfectly. Thus, t was assumed that some proporton of the tme (G) partcpants smply guessed Category A or B haphazardly, whle usng prototype-based smlarty as already descrbed the rest of the tme (see also Medn & Smth, 1981). So, for example, f a stmulus shared fve or four features wth the prototype, and a homogeneously attendng observer had a guessng proporton of.20, the performances predcted by the prototype model were, respectvely, [(.20/2) + [(1 -.20) X (5 X.166)]] =.76 and ((.20/2) + [(1 -.20) X (4 X.166)]} =.63. The equvalent guessngrate parameter for the exemplar model has already been descrbed. To analyze the behavor of the prototype model wth seven parameters and fnd ts best-fttng confguraton, we seeded the space wth a sngle parameter confguraton and calculated ts predcted categorzaton probabltes for He 14 stmul. Agan we hll clmbed toward the best-fttng confguraton by mnmzng the sum of the squared devatons between the predcted probabltes and some observed performance. Agan the space was seeded wth four addtonal parameter settngs. The small varance among the fve best fts ndcated that the mnma found were close to global ones. The basc prototype and exemplar models just descrbed have been extremely nfluental n the categorzaton lterature. In fact, the basc exemplar model has domnated the lterature (Lamberts, 1994,1995; Medn et al., 1983; Medn & Schaffer, 1978; Medn & Smth, 1981; Nosofsky, 1984,1985,1986,1987,1988,1989,1992; Nosofsky, Clark, & Shn, 1989; Nosofsky et al., 1992; Palmer &

5 Nosofsky, 1995; Shn & Nosofsky, 1992; Smth et al., 1997). The two models typfy the large famly of models n whch exemplars are categorzed more accurately n accordance wth ther perceptual smlarty to the underlyng category representaton or representatons. They equvalently ncorporate ths perceptual smlarty nto the Shepard-Luce choce rule that has long served cogntve psychology. They nstantate wth transparency the dfferent commtments of processng usng prototypes or stored exemplars, allowng these commtments to be evaluated farly aganst humans' performances. Ther domnance, ther typcalty, ther equvalent choce rales and ther transparent representatonal assumptons explan ther favored status and ther use here. We consder varants on both models n the secton on Addtonal Modelng Perspectves. Results To analyze performance at dfferent stages of learnng, we dvded the 392 trals (28 blocks of 14 stmul) nto seven 56-tral segments. Ths analytc strategy balanced two competng goals. Aggregatng more data creates more stable estmates of performance. Aggregatng less data solates purer performance strateges nstead of averagng successve strateges. The 56-tral segment s our compromse between more and less. Smth et al. (1997) demonstrated that fttng models to data aggregated over partcpants averaged away ndvdual dfferences n performance. Accordngly, each partcpant's performance for each tral segment was modeled ndvdually, usng both the seven-parameter prototype model and the eght-parameter exemplar model. The resultng bestfttng confguratons specfed guessng and senstvty parameters and sx attentonal weghts for the sx stmulus features. They also allowed us to assess the degree of ft between predcted and observed performance. Where desred, the 16 outcomes from the modelng could be averaged for the group. Performance over tral segments. The accuracy data were analyzed usng a two-way analyss of varance (ANOVA) wth NLS-LS as a between-subjects varable and tral segment as a wthn-subject varable. Ths analyss confrmed that sgnfcant learnng occurred across tral segments, F(6,180) = 32.83, p <.05, MSE = By the end of learnng, the proportons correct were.81 and.84 for the NLS and LS category structures, respectvely. Guessng and senstvty parameters over tral segments. Modelng suggested that partcpants' strateges changed n ntutve ways through tme. Guessng, as assessed by the prototype model, steadly declned. When the prototype model was ft to performance on the NLS and LS categores, the correlaton of the guessng parameter wth tral segment was, r.86, p <.05, and r =.87, p <.05, respectvely. Guessng-rate parameters were lower for the exemplar model overall and were often near zero. The exemplar model's senstvty parameter steadly ncreased over tral segments. When the exemplar model was ft to performance on the NLS and LS categores, the correlaton of senstvty wth tral segment was, r =.97, p <.05, and r.93, p <.05, respectvely. Hgh values of the senstvty parameter for the last tral segment (9.3 and 9.2 for the NLS and LS condtons, respectvely) suggest CATEGORY LEARNING 1415 that the exemplars became dstnctve and well-ndvduated for partcpants and that some processes lke exemplar self-retreval ncreasngly supported categorzaton as learnng progressed. The ft of models over tral segments. A key ssue n ths experment was whether the basc prototype and exemplar models were each selectvely advantaged at dfferent ponts n learnng. Fgure 1 shows the fts of the two models (averaged across partcpants) for each tral segment. An early advantage for the prototype model seemed to wane or reverse as tranng contnued. To assess the sgnfcance of ths pattern, the fts were entered nto a two-way ANOVA wth type of model (prototype or exemplar) and tral segment (1 to 7) as wthn-subject varables. The nteracton between type of model and tral segment was sgnfcant, both for NLS categores, F(6, 90) , p <.05, MSE = 0.017, and for LS categores, F(6, 90) , p <.05, ^ A. Experment 1: NLS U-j, B. Experment 1: LS o \ '. V () 100 " " * * / Tral Tral ^ ^ Prototype * Exemplar 400 Prototype '< Exemplar 400 Fgure 1. A: The average ft of the prototype and exemplar models at each 56-tral segment to the performance of partcpants learnng not lnearly separable (NLS) categores n Experment 1. B: The average fts for partcpants learnng lnearly separable (LS) categores.

6 1416 SMITH AND MINDA To specfy the character of ths nteracton, the ANOVA was repeated, ncludng only the data from the frst three tral segments (12 blocks or 168 trals) or the last three tral segments. The prototype model's early advantage over the exemplar model was sgnfcant, wth average best fts over 48 observatons (16 partcpants at three tral segments) of 0.49 (SD =.250) and 0.54 (SD =.250), respectvely, F(l, 15) = 10.76, p <.05, MSE = 0.006, for the NLS categores, and wth average best fts of 0.46 (SD =.292) and0.54(sd =.261),respectvely,F(l, 15) = 5.99,p<.05, MSE = 0.025, for the LS categores. 1 Moreover, these ft advantages were as large as many of those that have favored exemplar models n past research. For example, Nosofsky (1992) strongly crtczed prototype models by summarzng 13 studes n whch the exemplar model had a average ft advantage over the addtve prototype model. Here the prototype model exactly turned the tables, wth a ft advantage across the two category structures. The fts for the prototype and exemplar models were statstcally equvalent late n tranng, wth average best fts over 48 observatons (16 partcpants at 3 tral segments) of 0.52 (SD =.283) and 0.41 (SD =.250) for the NLS categores, F(h 15) = 3.00, ns, MSE = 0.084, and average best fts of 0.38 (SD =.200) and 0.33 (SD =.243) for the LS categores, F(l, 15) = 1.51, ns, MSE = In Tral Segments 5,6, and 7, respectvely, 17 of 32,16 of 32, and 10 of 32 performance profles (ncludng both LS and NLS tasks) were ft better by the prototype model. Ths balanced pattern of best fts replcates exactly the results of Smth et al. (1997), who also modeled performance over Trals 225 to 392 (Tral Segments 5, 6, and 7 here), and who also found that half the profles were ft better by the prototype model. However, ths balance contrasts sharply wth the results from many prevous studes (Medn & Schaffer, 1978; Medn & Smth, 1981; Nosofsky, 1987,1992). Statstcally, the equvalence of the models late n the NLS condton occurred because some partcpants (but not others) passed through a transton that produced excellent fts by the exemplar model but poor fts by the prototype model. These ndvdual dfferences severely nflated the value of the relevant error term by a factor of 14 (.e., and for late and early performance, respectvely). Even so, the NLS result approached sgnfcance, rasng the possblty that extendng tranng would brng the basc exemplar model nto favor. Conceptually, the equvalence between the basc prototype and exemplar models s probably lnked to Experment l's category structures (see also Smth et al., 1997). Typcally studes have used three- or four-dmensonal stmul wth about four exemplars per category and wth structural ratos of about 1.3. But here the stmulus dmensonalty was of a hgher order (sx dmensons), the categores were better dfferentated from one another (structural ratos of about 1.8), and the exemplar pools were larger (seven per category). Any of these factors could have slowed the emergence of strongly dfferentated exemplar traces n Experment 1, or could have set asde the perceved need for those traces, allowng alternatve categorzaton strateges to be more nfluental. For example, Homa et al. (1981) supported the specfc clam that larger exemplar pools foster the emergence of prototype-based categorzaton strateges. 2 One sees that the levels of ft obtaned by the prototype and exemplar models are hgher than typcally reported (e.g., Nosofsky, 1992). The reason les n our modelng of four-block epochs of performance to gan temporal resoluton. Ths modelng strategy means that every observed 1 One mght wonder whether the letters combne nto ntegral patterns that would be modeled better by a Eucldean smlarty metrc, and whether assumng a Gaussan smlarty-decay functon mght let the exemplar model accommodate the present data more comfortably. Accordngly, we modeled each partcpant's data at each tral segment usng all four alternatve versons of the context model that are featured n the lterature (cty-block metrc wth exponental decay, cty-block metrc wth Gaussan decay, Eucldean metrc wth exponental decay, Eucldean merk wth Gaussan decay; Ashby & Perrn, 1988; Maddox & Ashby, 1993; Nosofsky, 1985, 1989). All versons of the exemplar model produced successons of average fts just lke those already shown. All were dsadvantaged early on relatve to the smple, addtve prototype model wth only seven parameters. Note that to the extent one evaluates dfferent Mnkowsk metrcs and decay functons tryng to reduce the exemplar model's dsadvantage, one starts to grant the exemplar model more parameters, makng t complex, unweldy, and dong t a dsservce. It would be helpful f the stuaton were clarfed regardng these alternatve versons of the model that may have outlved ther usefulness. 2 We also explored the possblty that rule-based processng, not prototype-based processng, caused the prototype model's advantage. To do so, we frst found for each partcpant at each tral segment the one-dmensonal rule (among sx) that ft the data best. The rule model was a prototype model, shorn of ts guessng parameter (partcpants usng such a smple rule have no need to guess), wth all attenton placed on one dmenson. Ths model confguraton predcts the rule-use pattern of 100% or 0% Category A responses, respectvely, as the focal dmenson takes on the typcal Category A or Category B value. Complete attenton to all sx sngle dmensons was modeled, and the smallest ft was assumed to represent the one-dmensonal focus closest to partcpants' actual attentonal allocaton. The fts acheved by assumng the best one-dmensonal rule averaged 1.70 and 1.37 for the NLS and LS category structures, respectvely. We also found for each partcpant at each tral segment the best-fttng two-dmensonal rule. The two-dmensonal rule model assumes that partcpants evenly dvded ther attenton between some combnaton of two dmensons. Ths model confguraton predcts ether 100% or 0% Category A responses, respectvely, as the two focal dmensons both take on the typcal Category A or Category B values. If the two features dsagreed on category membershp, partcpants were predcted to guess gven ths conflct and to make the Category A response 50% of the tme. All 15 two-dmensonal rules were evaluated n ths way, and the best-fttng combnaton was assumed to represent the twodmensonal attentonal allocaton closest to that of the partcpants. The fts acheved by assumng the best two-dmensonal rule averaged 1.14 and 0.88 for the NLS and LS category structures, respectvely. The fts for both one-dmensonal and two-dmensonal rules were massvely worse than the average fts of 0.50 and 0.43 acheved by the prototype model for the NLS and LS category structures. Rule use dd not adequately descrbe performance.

7 CATEGORY LEARNING 1417 categorzaton proporton must be ether.00,.25,.50,.75, or 1.00, even f the partcpant's categorzaton probabltes n some longer run would fall between these steps. Both models must ft more poorly than usual these steplke data, because commttng to explan performance on one.25 step makes t more dffcult to smultaneously explan performance that sts on 13 other.25 steps. Another way to put ths s that some of each performance s error (.e., a.87 deal proporton expresses tself as ether 1.00 or.75, and nether s exactly rght). To llustrate the effect on ft of modelng 56-tral segments, we turned to a smulaton that ncluded 500 smulated exemplar-based categorzers and 500 smulated prototypebased categorzers. Each smulated categorzer was made obedent to a randomly selected confguraton of ts respectve model, wth a partcular set of attentonal weghts and partcular levels of guessng and senstvty as applcable. Each categorzer then performed 56 trals (four blocks) n Experment l*s NLS task, wth chance dsturbng the categorzaton probabltes around the long-run values each confguraton of the model would produce. That s, f the model predcted 80% Category A responses n the long run, the smulated categorzer had an 80% chance of makng that Category A response on each tral, but also a 20% chance of makng a B response. The performance for the tral segment was the average of the four ndependent events assocated wth each stmulus. Havng run each categorzer for 56 trals, we then ft the prototype and exemplar models to each of the 1,000 performances. Prototype-based categorzers were ft better by the prototype model than by the exemplar model (average fts of 0.49 [SD =.217] and 0.56 [SD =.236], respectvely). Exemplarbased categorzers were ft worse by the prototype model than by the exemplar model (average fts of 0.51 [SD =.263] and 0.40 [SD =.236], respectvely). Three ponts follow from ths smulaton. Frst, these fts on known exemplar-based and prototype-based performances are exactly at the level we observed, confrmng that our fts are where they should be for modelng wth temporal precson. Second, despte the granness of performance, modelng easly resolves whether the smulated performances were prototype or exemplar based. Thrd, and most mportant, the advantage for the prototype model we observed n Experment 1 's early performance (.05 for the NLS category structure,.08 for the LS category structure, and.065 on average) s the same as that found for smulated categorzers that are all perfectly prototype based (0.07). Thus, our observed ft advantages early n performance are as large as they could possbly be n prncple, and they are consstent wth the possblty that partcpants' early performances were produced purely n accordance wth a smple prototype-based strategy. The frequent falures of the basc exemplar model, both early n learnng and later n learnng, llustrate a lmtaton on that model to whch we return. They also urge a broader exploraton of dfferent category structures and the dfferent categorzaton strateges they encourage. However, these frequent falures would be expected f partcpants were transtonng at dfferent tmes toward categorzaton strateges that were more based n the encodng of specfc exemplars and that favored an exemplar-based descrpton of categorzaton performance. Ths rases the possblty, addressed n Experment 2, that extendng tranng would produce an advantage for the exemplar model. Experment 2 When Experment 1 ended at Tral Segment 7, t seemed that an advantage mght be emergng for the exemplar model. We may have stopped flmng our vdeo too soon. By extendng tranng, one mght let ths advantage express tself fully. Accordngly, Experment 2 replcated Experment 1 but gave partcpants 10 tral segments (560 trals) nstead of 7 tral segments (392 trals). Once agan we predcted an early advantage for the prototype model, but now we predcted that the often-reported advantage for the exemplar model would assert tself n the end. Method Partcpants. Thrty-two students partcpated to fulfll a course requrement. Stmul and category structures. The stmul, prototype pars, and category structures were the same as those of Experment 1. Procedure. The procedure was lke Experment 1 's except that partcpants receved 40 blocks of the 14 stmul. Results Performance over tral segments. We dvded the 560 trals nto ten 56-tral segments. Accuracy data were analyzed usng a two-way ANOVA wth NLS-LS as a betweensubjects varable and tral segment as a wthn-subject varable. Ths analyss confrmed that sgnfcant learnng occurred, F(9, 270) = 46.72, p <.05, MSE = The task-fnal proportons correct were.86 and.89 for the NLS and LS category structures, respectvely. Guessng and senstvty parameters over tral segments. Both the prototype and exemplar models were ft to the data for each 56-tral segment for each partcpant. Once agan the value of the guessng parameter declned over tme. When the prototype model was ft to performance on the NLS and LS category structures, the correlatons of the guessng parameter wth tral segment were.78 and.60, respectvely. Guessng-rate parameters were lower for the exemplar model overall and soon fell to nearly zero. The exemplar model's senstvty parameter steadly ncreased over tral segments. When the exemplar model was ft to performance on the NLS and LS category structures, the correlatons of ths parameter wth tral segment were.86 and.73, respectvely. The task-fnal senstvtes were and for the NLS and LS category structures, respectvely. Ths magnfcaton of psychologcal space s agan consstent wth partcpants' comng to hold strongly ndvduated exemplar traces. The ft of models over tral segments. Once agan we asked whether the two models were each selectvely advantaged at dfferent ponts of learnng. Fgure 2 shows, for the

8 1418 SMITH AND MDSfDA A. Experment 2: NLS \ V--"-. ^ I B. Experment 2: LS , I I Tral / \ Tral ^ Prototype. Exemplar ^^_- Prototype ' ' Exemplar Fgure 2. A: The average ft of the prototype and exemplar models at each 56-tral segment to the performance of partcpants learnng not lnearly separable (NLS) categores n Experment 2. B: The averageftsfor partcpants learnng lnearly separable (LS) categores. NLS and LS category structures, the average fts of the two models for each tral segment. Here there seems to have been an early advantage for the prototype model only for the NLS category structure, and there seems to have been a late advantage for the exemplar model for both category structures. To evaluate these patterns, the fts were entered nto a two-way ANOVA wth type of model and tral segment as wthn-subject varables. There was a man effect for model for the LS category structure only. The average fts were 0.39 and 0.28 for the prototype and exemplar models, respectvely, F(U 15) = 5.48, p <.05, MSE = The nteracton between type of model and tral segment was sgnfcant for NLS categores, F(9, 135) = 7.83, p <.05, MSE = 0.041, and for LS categores, F(9, 135) = 6.90, p <.05, MSE^ To nterpret ths nteracton, we repeated these ANOVAs, ncludng frst the data from the frst three tral segments and then the data from the last three tral segments. The prototype model's early advantage over the exemplar model was sgnfcant only for the NLS category structure (average best fts of 0.47 and 0.56, respectvely), F(l, 15) = 10.98, p <.05, MSE = The exemplar model's late advantage was sgnfcant for both category structures. For the NLS category structure, the average best fts for the prototype and exemplar models were 0.65 and 0.30, respectvely, F(l, 15) = 9.40,p <.05, MSE = For the LS category structure, the average best fts for the prototype and exemplar models were 0.43 and 0.20, respectvely, F(l, 15) = 10.83, p <.05, MSE = The character of early performance. Fgures 3A and 3B show snapshots that compare observed and predcted performance for both models at Tral Segment 3 (Trals ) of Experment 2 T s NLS condton. To make these fgures, the 16 observed performances were averaged nto the observed composte profle shown. Then each partcpant's performance durng Tral Segment 3 was modeled ndvdually, and the 16 best-fttng predcted profles were averaged nto the predcted composte profle shown. In ths way, f each partcpant's predcted profle matched well hs or her observed profle, the observed and predcted compostes would match well. If not, the two compostes would dverge approprately. Fgures 3A and 3B make plan that only the prototype model grants the prototype tems (Stmul 1 and 8) ther observed performance advantage whle smultaneously allowng poor performance on excepton tems (Stmul 7 and 14). The basc exemplar model fts less well because t persstently underpredcts and overpredcts performance on the prototypes and exceptons, respectvely. It homogenzes performance too much. The NLS category structure dagnoses ths falure clearly because t offers partcpants both prototypes and exceptons. The NLS condton of Experment 1 produced the same falure by the basc exemplar model, and Experment Ts LS condton produced ths falure too. 3 3 LS categores reveal the exemplar model's dffcultes less clearly than do NLS categores, because they lack the exceptons that are so dagnostc. Ths may be why only one of the two LS condtons strongly dfferentated the two models early n performance. Even gven the exemplar model's falure n the LS condton of Experment 1, t s more dffcult to show the character of that falure than n the NLS case. The problem s that even f some partcpants regard some LS stmul as exceptonal and perform poorly on them, other partcpants wll regard other stmul as exceptonal. The averaged profles of observed and predcted performances wll wash out these dfferences and reveal no localzed, nterpretable falure of the exemplar model. To preserve partcpants' ndvdual senses of prototypes and exceptons n the LS category structure, one can rank order performances wthn subjects and then examne how each model deals wth partcpants' own partcular worst, medum, and best category exemplars. Ths analyss lets one create consensus prototypes and exceptons for the LS category structure, too, by lettng each partcpant defne hs or her own through hs or her performance. Illustratng ths technque wth Experment l's LS condton, we ranked the observed performances from the thrd tral segment wthn subjects and then averaged wthn ranks across subjects. The prototype model does reach lower and hgher than the basc exemplar model does to predct partcpants' worst and best performances. The sgnfcance of ths pattern was confrmed wth a two-way ANOVA on

9 CATEGORY LEARNING 1419 A. Early NLS Performance: Prototype Model Early NLS Performance: Exemplar Model I I I I I t I I I I Stmulus \ Stmulus C. Late NLS Performance: Prototype Model D. Late NLS Performance: Exemplar Model o co t o Q.1-1 r Stmulus u o O o ' Ip HJ0.8- $0.7- O o.b a Stmulus Fgure 3. A: The ft of the prototype model to the early performance of partcpants learnng Experment 2's not lnearly separable (NLS) categores. The sold lne represents the average observed proporton correct, and the dotted lne represents the average predctons of the prototype model. B: The ft of the exemplar model to the same observed performance. C: The ft of the prototype model to the late performance of partcpants learnng Experment 2's NLS categores. D: The ft of the exemplar model to the same performance. The character of late performance. Fgures 3C and 3D show performance snapshots that compare the models 1 performances durng Tral Segment 10 of Experment 2's NLS condton (Trals ). The exemplar model fts these performances well. The prototype model cannot. the predcton errors of the two models that s, wth the quantty (observed mnus predcted performance) as a dependent measure. Model and stmulus rank were wthn-subject varables n ths analyss. There was a sgnfcant nteracton, F(13, 195) = 4.89, p <.05, MSE = 0.003, showng that the exemplar model makes larger negatve predcton errors for lower performance, but larger postve predcton errors for hgher performance. To ground ths analyss further, we conducted the dentcal analyss usng Experment 1's NLS condton and found agan a sgnfcant nteracton, F(13, 195) = 7.77, p <.05, MSE = The only dfference between the LS and NLS analyses s that the lower NLS ranks are consensually occuped by the true exceptons, whereas the lower LS ranks represent partcpants 1 self-defned exceptons. Experment 2's LS condton produced the same falure by the prototype model. The problem for the prototype model late n learnng s that t stll must predct that partcpants classfy the stmul n strct obedence to the typcalty gradents n the task. But partcpants were smply better on the exceptons n the NLS condton and better on all tems generally than the basc prototype model can predct. The results from the later tral segments add a new fact to those establshed by Smth et al. (1997). Smth et al. (and the present Experment 1) found that about equal numbers of performance profles were ft better by the basc prototype and exemplar models for the blocks spannng Trals Clearly, though, the basc exemplar model holds a more domnant poston when one models performance later n learnng (.e., Trals ). Ths supports the dea that processng based n specfc exemplars comes on more strongly as learnng progresses and the tranng exemplars become hghly famlar.

10 1420 SMITH AND MINDA The trajectory of category learnng. Three other vews of the data make clear the trajectory that partcpants traced through the larger performance space as they learned. Frst, Fgure 4A shows, for Experment 2's NLS condton, the performance varance among 14 stmul for the composte observed profle for each tral segment. Early n learnng (.e., Trals 1-224) there s a sharp ncrease n the heterogenety of observed performance as the task comes nto focus for partcpants. The fgure also shows the performance varance among stmul for the composte predcted profles of both models at each tral segment. The prototype model predcts correctly the large varance of partcpants' early observed performances, and ths helps the model comfortably ft that early data pattern. At ths pont, the basc exemplar model fals serously by predctng only half of the varance that observed performances show. Then, over the next sx tral segments, the observed performance varance drops as partcpants come to perform better on all tems. As ths reducton occurs, the two models exchange ft advantages (Fgure 2A) and the exemplar model comes nto ts own. Second, Fgures 4B and 4C show the relaton between prototype-tem and excepton-tem performance over the 10 tral segments n Experment 2's NLS condton. Early on there s a profound mprovement n performance on the prototypes wthout any mprovement on the excepton tems. Indeed, through the early tral segments, the excepton tems essentally are msdassfed as effcently as the normal category members are classfed. Ths stage of learnng lasts for more than 200 trals the whole length of many category experments. Through ths msclassfcaton, partcpants turn the NLS categores nto good LS ones, gnorng over 16 presentatons of each excepton tem the correctve feedback and the possbltes for exemplar memorzaton. It s clear from ths reallocaton of the exceptons that partcpants ntally make a strong lnear separablty assumpton about the categores they are learnng. The partcpants' learnng trajectory s overlan on the entre constellaton of performances that are producble by the basc prototype model (Fgure 4B) or the exemplar model (Fgure 4C). The early tranng epochs brng the average performance of the entre sample nto a regon of performance space that no confguraton of the basc exemplar model can occupy, even granted an addtonal free parameter, but where prototype-based descrptons of performance capture performance well. Ths s a stronger result than that of Smth et al. (1997), who found that half of ther partcpants occuped ths regon of performance space. One sees that the basc exemplar model's falure s qualtatve at ths stage of learnng; there smply s no confguraton of the model that predcts what the partcpants average early on. The exemplar model can predct excepton performance as low as that shown by partcpants early on, but then t underpredcts ther prototype performance by an average of 19%. The exemplar model can predct prototype performance as hgh as that shown by partcpants early on, but then t overpredcts ther excepton performance by an average of 44%. The problem s that the exemplar model cannot accomplsh these two goals smultaneously. The prototype model accommodates ths pattern easly. Nonethe ! B c Tral I 0.8-I I 0.6- E So.4- c o Q o X UJ o Prototype Item Performance 1-, 0.8- I 0.6-0) Q. E c o ' g o & Prototype Item Performance Prototype Model Observed ~ Exemplar Model Fgure 4. A: The performance varance among 14 stmul for the composte observed and composte predcted performance profles at each tral segment (Experment 2, not lnearly separable [NLS] category structure). B: Average prototype-tem and excepton-tem performance by tral segment for partcpants learnng Experment 2's NLS categores. The 10 tral segments are numbered from 1 to 0. Also shown s the constellaton of prototype-excepton performances that the seven-parameter addtve prototype model can produce. The behavor of the model was found by samplng 3,000 randomly selected confguratons of parameter settngs. C: The same observed performances together wth the prototypeexcepton performances of 3,000 randomly selected confguratons of the eght-parameter exemplar model.

11 : : 1 ' 1 E ; - - CATEGORY LEARNING 1421 A. Prototype Model Q. less, by Tral Segment 6, partcpants enter a regon of performance space that no confguraton of the prototype model can occupy. They transcend ther ntal lnear separablty assumpton, usng some auxlary strateges to master the excepton tems. It s possble that partcpants memorze the offendng members or begn to rely on famlar exemplar traces n some other way. It s possble that partcpants begn to code multple stmulus features more confgurally or correlatonally. Exemplar storage and confgural representatons are two key features of the exemplar model. The character of later performance replcates many publshed successes of the basc exemplar model. Thrd, many aspects of performance show the same transton from early performances that dsfavor the basc exemplar model toward mature performances that favor t. Fgures 5A and 5B show the two models' general expecta u 1M ,- ";;S.-N. ^ ^ ^ - ^ ' " / * aexennplar Model I 06 " 0.4- Q " ' " " Guessng Parameter a Senstvty Parameter E E v A 1 ' - ' Prototype Varance x 14 Normal Excepton Advantage Normal Excepton Varance x 14 "1 Advantage 16 Fgure 5. A: The average predctons of the addtve prototype model at dfferent levels of guessng (fve dotted lnes) for fve aspects of performance (performance on prototypes, normal tems, excepton tems, the prototype advantage over normal tems, and 14 multpled by the varance among the 14 predcted categorzaton probabltes [ths precursor of the varance s scaled better for ncluson on the graph]). Also shown are the actual performance characterstcs (P, N, E, A, and V) observed n Tral Segment 3 of Experment 2's not lnearly separable (NLS) condton. B: The average predctons of the basc exemplar model at dfferent levels of senstvty for the same fve aspects of performance. Also shown are the actual performance characterstcs (P, N, E, A, and V) observed n Tral Segment 10 of Experment 2's NLS condton. tons regardng prototype performance, normal-tem performance, excepton-tem performance, prototype advantage over normal tems, and the sum of the squared devatons of the 14 categorzaton probabltes around ther mean (ths precursor of the varance s scaled better for ncluson on the graph). To draw the prototype model's behavoral space, we chose 500 randomly selected confguratons of the basc prototype model at each value of guessng from 0.00 to 1.00 n.05 steps and found the average performance characterstcs at each level of guessng. To draw the exemplar model's behavoral space, we chose 500 randomly selected confguratons of de basc exemplar model at each value of senstvty from 1 to 15 and found the average performance characterstcs at each level of senstvty. Overlan on Fgure 5 A are the actual performance characterstcs (ndcated by captal letters) that partcpants showed durng Tral Segment 3 of Experment 2's NLS condton. A least-squares procedure allowed us to mnmze the fvedmensonal error and place the data n ther best-fttng spot on ths graph. The mnmum error dstance was It s nstructve to magne sldng these performance characterstcs across the behavoral space of the exemplar model shown n Fgure 5B. No place along that Jt-axs offers remotely the rght performance characterstcs. The mnmum error dstance (at a senstvty level of 4.0) was , whch s 15.1 tmes as large as that found for the addtve prototype model. Thus, partcpants' early performance characterstcs have precsely a prototype-model confguraton. The basc exemplar model cannot produce anythng lke these performance characterstcs. Once agan, though, turnabout s far play (Fgure 5B). The performance characterstcs at Tral Segment 10 ft somewhat comfortably (mnmum error dstance of at a senstvty of 15) on the exemplar model's behavoral space. They ft nowhere n the behavoral space of the prototype model (mnmum error dstance of at a guessng value of.40, whch s 8.9 tmes the exemplar model's error dstance). The stamp of exemplar-based processng may be on these late performances. These three perspectves all show that the trajectory of category learnng through the larger space of categorzaton strateges s so pronounced that both the basc prototype and exemplar models fal to provde a complete descrpton of all stages of learnng. The prototype model fals later on; the exemplar model fals early on. Ths leads us n the Addtonal Modelng Perspectves secton to consder alternatve models that may better capture the whole progresson of learnng and may llumnate the changng strateges partcpants choose at dfferent stages. Frst, though, we demonstrate that dfferent category structures can deflect the progresson of learnng nto very dfferent regons of performance space. Experment 3 Experments 1 and 2 demonstrated that a prototype-based descrpton made a strong showng over the frst 200 learnng trals for larger, better dfferentated categores. In three out of four cases, t ft partcpants' early performance

12 1422 SMITH AND MINDA profles better than the basc exemplar model dd. In one case, t ft partcpants' performance profles as well as the basc exemplar model dd. Later n learnng, especally n the later tral segments of Experment 2, the exemplar model assumed the domnant poston. To provde a contrast to Experments 1 and 2, Experment 3 consdered smaller, less dfferentated categores. One dea behnd the present research s that these categores wll encourage exemplarbased strateges to emerge sooner and take hold more strongly. Thus, we hypotheszed that humans learnng these categores mght not perform early on n accordance wth a prototype-based descrpton. In fact, we hypotheszed that these categores would produce no prototype-model advantage anywhere. Method Partcpants. Thrty-two students partcpated to fulfll a course requrement. Stmul and category structures. The NLS and LS category structures were those used by Medn and Schwanenflugel (1981, Experment 2). The NLS Category A members were 0001,0100, , and ; the Category B exemplars were ,1 01 0, l.andol 1 l.thels Category A members were 101 0,01 10, , and ; the Category B exemplars were ,1 01 1, 110 1, and These exemplars share on average only about 2.6 features wth ther prototypes (Category A) and 1111 (Category B), and ndvdual features are poorly predctve (65%) of category membershp. Both characterstcs reflect the reduced category dfferentaton n these category structures (structural ratos of about 1.2) compared wth those n Experments 1 and 2 (structural ratos of about 1.8). The stmul were derved from the four prototype pars (bunokypa, dak sego, mufa-vosy, leta-gru). The frst member of each par was the stmulus ; the second was the stmulus These prototypes were created subject to the constrants descrbed n Experment 1. Procedure. The procedure was lke Experment 2's except that here the 560 trals comprsed 70 blocks of the eght stmul. Results Performance over tral segments. We agan dvded the 560 trals nto ten 56-tral segments, each now contanng seven blocks of the eght stmul. Accuracy data were analyzed usng a two-way ANOVA wth NLS-LS as a between-subjects varable and tral segment as a wthnsubject varable. Sgnfcant learnng occurred across tral blocks, F(9, 270) = 38.26, p <.05, MSE = The task-fnal proportons correct were.82 and.93 for the NLS and LS category structures, respectvely. Guessng and senstvty parameters over tral segments. Both the prototype and exemplar models were ft to the data just as n Experments 1 and 2. Once agan the guessng parameter always declned strongly over tral segments. The estmated guessng rates were substantally hgher n Experment 3 than n Experments 1 or 2, consstent wth these categores' poor dfferentaton and dffculty. The exemplar model's senstvty parameter once agan ncreased strongly over tral segments, up to and for the NLS and LS category structures, respectvely. The ft of models over tral segments. The fts of the two models for each category structure and each tral segment are shown n Fgures 6A and 6B. Once agan the fts by partcpant and tral segment were entered nto a two-way ANOVA wth type of model and tral segment as wthnsubject varables. Here we observed a man effect for type of model for the NLS category structure, F(l f 15) = 21.79,p <.05, MSE = 0.472, and for the LS category structure, F{1, 15) = 29.32, p <.05, MSE = The nteracton between type of model and tral segment was also sgnfcant both for NLS categores, F(9, 135) = 10.56, p <.05, MSE = 0.045, and forls categores, F(9,135) = 18.03,p <.05, MSE = Early n tranng (Tral Segments 1-3), the prototype model had no advantage for ether category structure. Late n tranng (Tral Segments 8-10), the exemplar model had the clear advantage. For the NLS category structure, the average best fts for the prototype and exemplar models were 0.73 and 0.13, respectvely, F(l, 15) = 32.84, p <,05, MSE = For the LS category structure, the average best fts for A. Experment 3: NLS C 1 1G0 B. Experment 3: LS ' " ' () ^ l 300 Tral *.. / / l Tral s t. Exemplar ^^_^ Prototype "" - Exemplar Fgure 6. A: The average ft of the prototype and exemplar models at each 56-tral segment to the performance of partcpants learnng not lnearly separable (NLS) categores n Experment 3. B: The average fts for partcpants learnng lnearly separable (LS) categores.

13 CATEGORY LEARNING 1423 the prototype and exemplar models were 0.69 and 0.12, respectvely, F(l, 15) = 57.34,p <.05, MSE = Moreover, t s clear that partcpants n Experment 3 moved very dfferently through performance space than dd those n Experment 2. For example, Fgures 7 A and 7B show for each tral segment the average prototype-tem performance and excepton-tem performance by partcpants n Experment 3's NLS condton. Ths trajectory s once agan overlan on the entre constellaton of perfor- A. 0) 1" u c re E DL 0.4 c o "" ) u 2 o B Prototype Item Performance ' o c re 0.8- I 0.6- E c o "". 0.2 a> o x UJ o I I I I I Prototype Item Performance Fgure 7. A: Average prototype-tem and excepton-tem performance by tral segment for partcpants gven not lnearly separable categores n Experment 3, together wth the prototype-excepton performances of 3,000 randomly selected confguratons of the fve-parameter addtve prototype model. B: The same observed performances, together wth the prototype-excepton performances, of 3,000 randomly selected confguratons of the sxparameter exemplar model. mances that are producble by the basc prototype model (Fgure 7A) or exemplar model (Fgure 7B). Early prototype performance was never so hgh as n Experment 2; early excepton performance was never so low. Partcpants always stayed wthn a regon of performance space that the exemplar model can accommodate. They quckly entered a regon of performance space that the prototype model cannot accommodate. Ther movement up the majot dagonal of performance space s consstent wth the gradual strengthenng of all exemplar traces through tme and tranng epochs. There s none of the backward-l trajectory (Fgure 4B) that suggests an early commtment to somethng lke a prototype strategy. Somethng about Experment 3's category structure caused partcpants never to enter ths corner of performance space. The result of all these dfferences s that the prototype model not only never had any advantage n Experment 3 t never had a chance. All n all, the results show clearly that the small, poorly dfferentated categores of Experment 3 gave the exemplarbased descrpton of categorzaton a strong advantage over the prototype-based descrpton, far more so than dd the category structures used n Experments 1 and 2. Of course, many successes of the basc exemplar model have featured small and poorly dfferentated categores lke those n Experment 3 (Medn, Altom, & Murphy, 1984; Medn et al., 1983; Medn & Schaffer, 1978; Medn & SchwanenfAugel, 1981; Medn & Smth, 1981; Nosofsky, Gluck, et al., 1994; Nosofsky et al., 1992; Nosofsky, Palmer, & McKnley, 1994; Palmer & Nosofsky, 1995). Thus, Experment 3's results confrm all that work. What s the nformaton-processng bass for these successes? The four-dmensonal categores of Experment 3 featured smaller exemplar pools, more stmulus repettons, weaker prototypes, and more easly assmlable exceptons. Any of these factors could have dscouraged the use of prototypes whle encouragng exemplar strateges and remndng partcpants of them (see also Homa et al., 1981). The sx-dmensonal category structures of Experments 1 and 2 featured larger exemplar pools, fewer stmulus repettons, stronger (more useful) prototypes, and stranger (more dsconcertng) exceptons. Any of these factors could have camouflaged and undermned exemplar strateges whle encouragng and renforcng prototype-based strateges. These dfferences lead us to stress the mportance of research programs mat explore both general knds of categores. The relance on three or four stmulus dmensons has hampered ths exploraton by constranng the avalable exemplar pools and levels of category dfferentaton. It s evdent (compare Fgures 4B and 7A) that these constrants profoundly alter the course of category learnng. Experment 4 The mportance of these ssues led us to replcate and extend our results wth dfferent stmulus materals. Therefore, n Experment 4 partcpants learned NLS categores wth the category structures from Experments 2 and 3, but wth lne drawngs of bug-lke creatures, not nonsense-word stmul. Once agan we predcted that the smple prototype

14 1424 SMITH AND MINDA model would have the ft advantage early n learnng over the basc exemplar model when partcpants learned the large, well-dfferentated categores. In contrast, we predcted that the prototype model would be profoundly dsadvantaged over the whole course of learnng when partcpants learned the small, poorly dfferentated categores. Method Partcpants. Thrty-two students partcpated n ths experment to fulfll a course requrement. Stmul The stmul were lne-drawn bug-lke creatures, shown n profle facng left (Appendx B). These bugs were analogous to the Brunswck faces that have been used extensvely n categorzaton research (Medn & Smth, 1981; Nosofsky, 1991; Reed, 1972; Smth et al., 1993). Dfferent creatures could be created by dfferent combnatons of the bnary-valued attrbutes that defned the stmulus space. Other studes have featured smlar stmul such as drawngs of starfsh (Ann & Medn, 1994), rocket shps (Palmer & Nosofsky, 1995), or magnary creatures (Brooks, 1978; Malt, 1989). The four bnary features used to construct the four-dmensonal bugs were as follows: short or long body (a 1.5-cm X 1.0-cm oval or a 2.4-cm X 1.0-cm oval), round or oval head (a 0.8-cm dameter crcle or a 0.7-cm x 1.4-cm oval), red open eye or green halfclosed eye (a 0.4-cm crcle wth a 0.2-cm central red dot or a 0.4-cm crcle wth a green-colored top half), and short or long legs (0.6 cm or 1.0 cm). The sx-dmensonal bugs also were dstngushed by havng a curved forward antenna or a straght back antenna (a 1.0-cm forward curve wth a purple 0.2-cm termnal dot or a back-angled 0.7-cm straght lne wth an orange 0.2-cm termnal dot), and by havng gray-trangle feet (0.4 cm across the bottom and 0.2 cm hgh) or blue-semcrcle feet (0.4 cm across the bottom and 0.3 cm hgh). Plot experments. Smlarty-scalng experments were conducted to ensure that thefeaturesof the bugs had approxmately equal salence. Partcpants rated pars of bugs for how alke or dfferent they were. If the average dfference between bugs was about the same for all sngle-feature dfferences, t would suggest that perceptual salence was approxmately balanced across the stmulus dmensons. Ten partcpants rated pars of four-dmensonal bugs on a scale of 1 to 5 for how alke (1) or dfferent (5) they were. Trals were presented n 20 blocks of random permutatons of eght trals. There were three possble tral types: bugs that were the same (two trals n each block), bugs that were dfferent on one feature (four trals n each block one for each feature contrast), bugs that were dfferent on two features (two trals n each block). For the trals contanng two-feature dfferences, the choce of the contrastng features was made randomly. The zero-dfference and twodfference trals served only to anchor partcpants' sngledfference judgments, and they were not analyzed further. The average dfference ratng was then calculated for each sngle-feature dfference for each partcpant. Average ratngs for the four dmensons ranged from 3.37 to These ratngs were entered nto an ANOVA wth feature as the sngle varable. There was no sgnfcant dfference n salence over the four dmensons, F(3, 36) = 1.98, ns, MSE = 0.396, suggestng that all of the features had about the same perceptual mpact. Thrteen partcpants rated pars of sx-dmensonal bugs on the same 1-5 scale of ncreasng dfference. Trals were presented n 20 blocks of random permutatons of 10 trals. There were three possble tral types: bugs that were the same (2 trals n each block), bugs that were dfferent on one feature (6 trals n each block 1 for each feature contrast), bugs that were dfferent on two features (2 trals n each block). The average dfference ratng was then calculated for each sngle-feature dfference for each partcpant. Average ratngs for the sx-dmensonal bugs ranged from 2.96 to These ratngs were entered nto an ANOVA wth features as the sngle varable. There was no sgnfcant dfference n salence over the sx dmensons, F(5, 72) = 2.25, ns, MSE = 0.504, suggestng agan that all of the features had about the same perceptual mpact. Four-dmensonal category structure. The four-dmensonal NLS categores had the logcal structure used n Experment 3. The logcal Category A prototype was made to correspond to a randomly chosen polarty confguraton of the bnary stmulus features (.e., 0 referred to a short or a long body for dfferent partcpants, to short or long legs for dfferent partcpants, etc.). The Category A stmul were then generated from that prototype. The logcal Category B prototype 1111 was always made to correspond to the featural combnaton that was the opposte of the Category A prototype, and the Category B stmul were then generated from ths Category B prototype. Four random polarty confguratons were bult for the experment, and a random quarter of the sample receved each confguraton. Sx-dmensonal category structure. The sx-dmensonal NLS categores had the logcal structure used n Experment 2. The logcal Category A prototype was made to correspond to a randomly chosen polarty confguraton of the bnary stmulus features (.e., 0 referred to a round or oval head for dfferent partcpants, to a straght-back or curved-forward antenna for dfferent partcpants, etc.). The Category A stmul were then generated from that prototype. The logcal Category B prototype always corresponded to the featural combnaton that was the opposte of the Category A prototype, and the Category B stmul were then generated from ths Category B prototype. Four random polarty confguratons were bult for the experment, and a random quarter of the sample receved each. Procedure. Partcpants were frst assgned randomly to one of the two category structures (four dmensonal or sx dmensonal) and to one of the four feature-polarty confguratons. Sxteen partcpants were assgned to learn each category structure. The bug stmul were presented n blocks of 8 trals (four dmensonal) or 14 trals (sx dmensonal), wth each block contanng a random permutaton of all the stmul n the experment. As n Experments 2 and 3, partcpants receved a total of 560 trals (70 blocks for the four-dmensonal categores, 40 blocks for the sx-dmensonal categores). Trals contnued n an unbroken fashon untl the 560 trals had been presented. Partcpants were tested ndvdually. Each partcpant was seated at the computer and read the followng nstructons on the screen: In ths experment, you wll see a seres of lne drawngs of bugs whch can be classfed ether as "Group 1" bugs or as "Group 2" bugs. Your job s to look carefully at each bug and decde f t belongs to Group 1 or Group 2. Type a "1" on the keyboard f you thnk t s a Group 1 bug and a "2" f you thnk t s a Group 2 bug. If you choose correctly, you wll hear a "whoop" sound. If you choose ncorrectly, you wll hear a low buzzng sound. At frst, the task wll seem qute dffcult, but wth tme and practce, you should be able to answer correctly. The stmul were presented on a 11.5-n. (29.5 cm) dagonal computer screen on a whte background. Each tral conssted of a drawng of the bug, whch appeared slghtly to the left of center. Slghtly to the rght of center, the large numerals / and 2 appeared on the screen to remnd partcpants how to respond. Partcpants had unlmted tme to vew each stmulus before respondng. A correct response was followed by a bref, computer-generated

15 CATEGORY LEARNING 1425 whoopng sound; an error was followed by a 1-s low buzzng sound. The stmulus remaned vsble after wrong choces durng the 1-s error sgnal. A. Experment 4: Sx Dmensons Results Performance over tral segments. We agan dvded the 560 trals nto ten 56-tral segments contanng four or seven blocks of the 14 or 8 stmul for the sx- and fourdmensonal categores, respectvely. In both cases, the accuracy data were analyzed wth a one-way ANOVA wth tral segment as a wthn-subject varable. In both cases, sgnfcant learnng occurred across tral blocks: F(9,135) = 4.88, p <.05, MSE = 0.003, for the sx-dmensonal categores; F(9, 135) = 38.14, p <.05, MSE = 0.006, for the four-dmensonal categores. The task-fnal proportons correct were.84 and.91 for the sx-dmensonal and four-dmensonal categores, respectvely. Guessng and senstvty parameters over tral segments. Both the prototype and exemplar models were ft to the data just as n Experments 1-3. Once agan the guessng parameter declned strongly over tral segments. Once agan the estmated guessng rates were substantally hgher n the four-dmensonal condton than n the sx-dmensonal condton, replcatng the contrast between Experments 3 and 2. The exemplar model's senstvty parameter once agan ncreased strongly over tral segments. The task-fnal senstvtes were 7.65 and for the sx- and fourdmensonal categores, respectvely. The ft of models over tral segments. The fts of the two models through tme for the sx-dmensonal categores are shown n Fgure 8A. The fts were entered nto a two-way ANOVA wth type of model and tral segment as wthnsubject varables. As n Experments 1 and 2, there was a sgnfcant nteracton between type of model and tral segment, F(9,135) = 3.83,/? <.05, MSE = To specfy the character of ths nteracton, the ANOVA was repeated, ncludng only the data from the frst three tral segments (12 blocks or 168 trals) or the last three tral segments. The prototype model's early advantage over the exemplar model was sgnfcant, wth average best fts over 48 observatons (16 partcpants at three tral segments) of 0.32 (SD =.240) and 037 (SD =.220), respectvely, F(l, 15) = 10.92, p <.05, MSE = The exemplar model's late advantage approached sgnfcance, wth average best fts for the prototype and exemplar models of 0.43 and 0.30, respectvely, F(l, 15) = 3.93, p -.07, MSE = The exemplar model faled to show a sgnfcant advantage late n Experment 4 for the same reason t faled to show one late n Experment 1. Partcpants were transtonng at dfferent rates toward strateges that favored the exemplar model, and these strategy dfferences multpled the relevant error term here by a factor of 20. These strategy transtons are the focus of the present research. In all respects, the results from the sx-dmensonal categores replcated those of Experments I and 2 (compare Fgures 1A and 2A). Indeed, t appears that the transton to performance strateges that favor exemplar-based descrptons occurred even more gradually wth the pctoral stmul B. Experment 4: Four Dmensons Prototype Exemplar Fgure 8. A: The average ft of the prototype and exemplar models at each 56-tral segment to the performance of partcpants learnng sx-dmensonal categores n Experment 4. B: The average fts for partcpants learnng four-dmensonal categores. than wth the nonsense-word stmul. Here the standard exemplar model could not even gan a sgnfcant ft advantage after 560 trals. The fts of the two models through tme for the fourdmensonal categores are shown n Fgure 8B. The fts were entered nto a two-way ANOVA wth type of model and tral segment as wthn-subject varables. As n Experment 3, we observed a man effect of model, wth the exemplar model fttng far better overall than dd the prototype model (average fts of.14 and.60, respectvely), F(9, 135) = 10.56, p <.05, MSE The nteracton between type of model and tral segment was also sgnfcant, F(9, 135) = 20.29, p <.05, MSE = 0.031, ndcatng that the ft advantage for the exemplar model grew stronger over the course of the experment. In all respects, the results from the four-dmensonal categores replcated Experment 3 (compare Fgure 6A). Thus, Experment 4 generalzed all the results of Experments 1-3 from the doman of nonsense-word stmul to a more pctoral stmulus doman. The very dfferent trajecto- 600

16 1426 SMITH AND MINDA res by whch partcpants learn dfferent category structures (ncludng trajectores that favor prototype-based descrptons for large, well-dfferentated categores) may be a general phenomenon deservng more research attenton. Summary of Experments 1-4 In Experment 3, partcpants learned small, less dfferentated categores. The prototype model was never at an advantage and quckly became serously dsadvantaged. Experment 4 confrmed ths result wth dfferent stmulus materals. Both experments suggest that exemplar processes domnate for the category structures typcally used and for the mature performances typcally modeled. In Experments 1 and 2, partcpants learned larger, more dfferentated categores. The prototype model ft early performance better for both the NLS and LS category structures n Experment 1 and for the NLS category structure n Experment 2. Experment 4 confrmed ths result wth dfferent stmulus materals. Ths result llumnates the early stages of category learnng and shows the effect of larger, better dfferentated categores on learners. Yet there also seemed to be a transton n performance as learnng progressed. The basc exemplar model fnally ganed ascendance n Experment 2, for both NLS and LS category structures, though more slowly than when partcpants learned the small, poorly dfferentated categores of Experments 3 and 4. The exemplar model nearly ganed ascendance for Experment 4's large, well-dfferentated categores. A measure responsve to ths pont of ascendance could help assay the relatve promnence of exemplar strateges n dfferent categorzng populatons facng dfferent category structures. The prototype model's early advantage s related to the heterogenety of performance across stmul. The prototype model performs well when prototype-tem performance and excepton-tem performance dverge strongly n an NLS category structure. Ths dvergence correctly reflects the prototypes' perfect self-smlarty and the exceptons' dssmlarty to the prototype of ther category. In contrast, the basc exemplar model fts poorly heterogeneous performance profles. The exemplar model's late advantage n Experments 2, 3, and 4 s related to partcpants' homogeneously good performance across stmul of dfferng levels of typcalty. Of course ths pattern s consstent wth performance based n the retreval of hghly famlar patterns. Accordngly, the exemplar model predcts ths performance pattern; the prototype model cannot. Addtonal Modelng Perspectves The falure of both models clearly emphaszes the trajectory that partcpants trace through the larger space of categorzaton strateges as they learn. Nether model bends flexbly enough to retrace ths trajectory. Therefore, we now consder addtonal models that may better capture the whole progresson of learnng and that may llumnate further the changng strateges of partcpants durng learnng. Prototypes Combned Wth Exemplar Memorzaton: A Mxture Model Frst, we examne a smple mxture of prototypes and exemplar memorzaton. The mxture model adopted here receved some early attenton (Medn et al, 1983; Medn & Smth, 1981), though t was not used to descrbe the course of category learnng or to trace an ncreasng relance on exemplar processes. The mxture model assumes that partcpants base ther classfcaton decsons ether on the smple, addtve smlarty of a gven stmulus to the prototype (n whch case they obey typcalty gradents very strctly), or on random guesses (n whch case they place stmul nto Categores A or B haphazardly), or on the recognton of memorzed specfc exemplars (n whch case they defntely classfy the tem correctly). The key aspect of fttng data wth the mxture model s to estmate the balance among these three processes that best accounts for any partcpant's performance profle. Note that the exemplar process assumed by the mxture model s smple memorzaton that s, ndvdual exemplars are stored, self-retreved, and self-boosted toward correct categorzaton. Ths process s qute dfferent from the context model's exemplar process n whch many tranng exemplars enter the computatons that produce a classfcaton decson. In fact, the context model's exemplarto-exemplar comparson processes have seemed mplausble to some (see dscussons n Palmer & Nosofsky, 1995, p. 548; Nosofsky & Palmer, 1997, p. 292), makng t valuable to see whether a smpler exemplar process suffces also. The mxture model evaluated here contaned a guessng parameter that functoned as t dd for the other models. It contaned an exemplar-memorzaton parameter that could gve all exemplars a performance boost to reflect the successful categorzatons that would result from relyng on specfc, memorzed exemplar traces. It contaned a prototypeprocessng parameter that ncorporated addtve smlarty to the prototype nto the categorzaton decson (exactly lke the prototype model already descrbed). These three parameters were constraned to sum to 1.0, and the fttng process found the best-fttng mxture of these three alternatve processng strateges. The mxture model also contaned four or sx dmensonal weght parameters (for the four- and sx-dmensonal tasks, respectvely) that were constraned to sum to 1.0, just as n the other models. Accordngly, the mxture model, just lke the context model, had fve or seven free parameters, wth two free parameters for the alternatve processng strateges, and three or fve free parameters for the attentonal weghts. The mxture model was ft to the data from Experment 2's NLS condton for each partcpant for each tral segment, usng the seedng and hll-clmbng procedures already descrbed. It re-creates the early advantage of the prototype model over the basc exemplar model (because the specfc exemplar parameter can be estmated near zero), and t re-creates the late advantage of the exemplar model over the prototype model (because t can also emulate a strong relance on memorzed exemplars; see Fgure 9A). Thus, the mxture model captures performance well throughout learn-

17 CATEGORY LEARNING 1427 B. Experment 2: NLS 1-1 S0.8- m 0.6 H Prototype Prototype Use C. Experment 3: NLS.So.em JO.BH! Tral \ \ / Guessng Exemplr.-' Memorzaton Prototype Ute Guessng 1! I I I Tral Fgure 9. A: The average ft of the prototype, exemplar, and mxture models at each 56-tral segment to the performance of partcpants learnng not lnearly separable (NLS) categores n Experment 2. B: Medan parameter estmates across 16 partcpants of the mxture model fttng these performances. C: Medan parameter estmates across 16 partcpants of the mxture model fttng the performances at each tral segment of partcpants learnng NLS categores n Experment 3. ng. It bends more flexbly through strategy space by supposng that two dfferent processes are promnent durng dfferent stages of learnng. Fgure 9B shows the medan estmates of guessng, prototype use, and exemplar memorzaton across 16 partcpants when the model tracks these parameter values across the 10 tral segments of Experment 2's NLS condton. The mxture model's descrpton has guessng tal off early on, yeldng to prototype use as the domnant process through 400 trals of the experment. Gradually, though, estmates of exemplar memorzaton ncrease, consstent wth an ncreased relance on hghly famlar traces. Ths ncrease begns just where the prototype model falters (Fgure 9A) and contnues untl exemplar memorzaton fnally becomes the domnant categorzaton process as estmated by the mxture model. Fgure 9C shows the same parameter estmates through tme for Experment 3's NLS condton wth small, poorly dfferentated categores. Ths trajectory through parameter space s profoundly dfferent. Hgher rates of guessng reflect the slowness wth whch these categores come nto focus for partcpants. Hgher termnal relances on exemplar memorzaton eventuate. Most strkngly, the use of prototypes s never the domnant categorzaton process under the descrpton of the mxture model. We beleve ths mxture perspectve has many nterpretatve strengths. Frst, t makes plan that the trajectory through performance space durng category learnng s as profound as a transton from strong relance on prototypes to strong relance on exemplar memorzaton. Second, the mxture model ponts to a face-vald tme of guessng durng whch the task crystallzes for partcpants. Thrd, the model solates a tme n learnng when a smple prototype model fts the data well, wth no guessng and no exemplar process at all (Fgure 9B). To our knowledge, ths extended stage of learnng has not been ponted out before, and we beleve t may be an mportant stage n the learnng of many categores. Fourth, the mxture model allows one to consder the possblty that the balance between category representatons shfts durng learnng. Nether prototype nor exemplar models allow ths possblty they are too sngle-mnded. Ffth, the mxture model demonstrates the suffcency here of a very smple exemplar process (memorzaton). One may not always need the context model's exemplar-to-exemplar comparsons that have garnered crtcsm (see dscussons n Nosofsky & Palmer, 1997, p. 292; Palmer & Nosofsky, 1995, p. 548). Sxth, the mxture model makes plan the dfferent learnng trajectores produced by dfferent category structures (Fgures 9B and 9C) and lets one consder why dfferent category structures so strongly deflect partcpants nto dfferent regons of performance space. Seventh, the mxture perspectve can even help one understand and nterpret the parameters of the context model tself. For example, over the last sx tral segments of Experment 2's NLS condton, the correlaton between the ncreasng value of the senstvty parameter (n the basc exemplar model) and the ncreasng value of the exemplar memorzaton parameter (n the mxture model) was r{94) =.84, p <.05. Ths close relatonshp between senstvty and memorzaton recommends the consderaton of smpler exemplar prncples n category research. By the mxture model's descrpton, somethng lke prototype use precedes somethng lke exemplar memorzaton n the learnng of the sx-dmensonal categores, whereas exemplar memorzaton domnates for the four-

18 1428 SMITH AND MINDA dmensonal categores. Ths dfference s consonant wth the suggeston of Homa et al. (1981) that prototype- and exemplar-based generalzaton processes, respectvely, fgure more strongly n the learnng of larger and smaller categores. Even so, t s useful to consder why ths sequence (prototypes to exemplars) s the one the mxture model fnds (asde from the obvous fact that partcpants' early and late performance profles dctate ths sequence). Our vew s that partcpants can quckly start to grasp the task's regulartes. After only a few trals, they can start to see whch features nform well and whch should be dscounted. In contrast, before specfc exemplars can gude categorzaton, partcpants must store those exemplars as separate, ndvduated traces traces of the sort that mght serve the related processes of dentfcaton, recognton, and so forth. Then, they must develop categorzaton cues that are grounded n that separateness and ndvduaton. In our vew, these capactes wll develop slowly, especally when the categores are large, when the exemplars use the same sx bnary trats repettvely, when the exemplars are hghly confuseable wth each other, when the partcpants are told to categorze the stmul (not dentfy or memorze them), and when partcpants do not even know that the same stmul wll repeat. Remember also that every exemplar can renforce prototype-level nformaton, whereas n effect partcpants receve only 1/8 or 1/14 as much specfc-exemplar tranng. For all these reasons, t may be common and natural for regulartes (.e., prototype-level nformaton) to mpress themselves on partcpants earler than unquenesses (.e., exemplar-level nformaton). Reed (1978) renforced ths dea. He found that category learnng proceeded far faster than dd tem learnng. He argued that early n learnng (up to about Tral 200), there s not enough "wthn-categores dscrmnaton of patterns to use a classfcaton rule that requres comparng the dstance of a test pattern to the ndvdual exemplars" (p. 617). He argued that partcpants may not even bother to store the ndvduated exemplars requred by an exemplar model because they have no ncentve to under categorzaton nstructons. He concluded that performance durng the early and mddle stages of category learnng was nconsstent wth exemplar processes but consstent wth prototype abstracton. For the small, poorly dfferentated categores used here, our vew s that exemplar-based categorzaton processes can emerge early and strongly, possbly even turnng the categorzaton task nto an dentfcaton or tem-learnng task. Medn and Schwanenflugel (1981, p. 365) expressed ths fear. Homa's work (e.g., Homa et al., 1981) also clearly rases ths possblty. McKnley and Nosofsky (1995, p. 129) also worred about ths possblty. In fact, t s surprsng, gven ths clear concern, that so much research has focused on category structures that favor a pror the exemplar prncple. Recommendng research on a range of category structures, Reed (1978, p. 619) sad As the number of patterns wthn a category ncreases, prototype abstracton should mprove (Homa et al., 1973), but exemplar learnng should decrease. As the varablty of patterns wthn a category s reduced, prototype abstracton should mprove (Peterson, Meagher, Chat, & Glle, 1973), but exemplar learnng should decrease. These factors of category sze and wthn-category coherence are two key factors dstngushng the sx- and fourdmensonal categores used n all four experments here. Therefore, the fndng that the two category structures produce very dfferent trajectores of learnng s just what Reed mght have antcpated. In the next two sectons of ths artcle, we consder a complementary modelng approach that may also accommodate successfully the progresson of performance profles produced durng learnng. To ntroduce ths approach, we frst explan why the exemplar model's processng assumptons are the orgnal source of ts falure to accommodate early performance. Then, we consder a recent profound modfcaton of the exemplar model that fares better but remans problematc. Why the Standard Exemplar Model Fals to Descrbe Early Performance The source of the standard exemplar model's falure and of the prototype model's success les n the heterogenety of early performance whether ndexed by the large prototype advantages, the dsmal excepton-tem performance, or any other assay of performance. Two aspects of the exemplar process assumed by the exemplar model ensure that t wll fal to accommodate these knds of performance profles. Frst, the exemplar model allows exemplar self-retreval. All the tems experenced repeatedly n tranng prototypes and exceptons ncluded can rely on these self-retreval processes, boostng ther performance levels, brngng ther performance levels closer together, and homogenzng the overall performance profle. In contrast, the prototype model fts well the strongly heterogenzed performances partcpants produced early n learnng, because exceptons are more smlar to the prototype of the opposng category (and no exemplar self-retreval counters ths effect), and because the prototype's perfect self-smlarty does boost ts predcted performance. In fact, the prototype model assumes that the better the prototype s performed, the worse the exceptons wll be performed (e.g., across 5,000 random confguratons of the prototype model, the correlaton between those two performance levels was.75). In contrast, the behavor of the standard exemplar model does not express ths relatonshp (across 5,000 random confguratons of that model, the correlaton between these performances was.27). Second, the exemplar model reles on exemplar-toexemplar comparsons n makng category decsons. It s seldom recognzed that specfc, stored exemplar traces are nosy sgnals for gudng categorzaton decsons, because category members are often surprsngly unlke each other. To see ths, consder Stmulus A2 n the LS task shown n Appendx A ( ). That stmulus shares 5,6,4, 3,3, 3, and 5 features n common wth the Category A stmul (ncludng tself) and shares 1, 2, 2, 1,3, 1, and 3 features n common wth the Category B stmul. By a rough calculaton (that the exemplar model carres out fnely), the evdence

19 CATEGORY LEARNING 1429 favorng a Category A response for A2 s 29 Category A features shared dvded by (29 Category A features shared plus 13 Category B features shared), or about 69%. It s ths low because, by storng the specfc exemplars, one stores the chaff (the atypcal features that ndvduate the exemplars) along wth the wheat (the typcal features that defne the prototype). As a result, n the comparsons to the exemplars, the evdence base favorng a Category A decson s systematcally undercut because, when the exemplars are retreved, all those featural dsagreements are retreved also and they reduce the surety of a Category A response. Any plausble processng account wll realze ths reducton, whether partcpants attend to some dmensons and not others, retreve some exemplars and not others, or even f they process all dmensons of all exemplars. The opposte effect wll occur for excepton tems wth many atypcal features. The atypcaty sgnal wll be muted on comparson to the exemplars. If strong evdence weakens and weak evdence strengthens, the result wll tend to be the homogenzed performance profles that the exemplar model shows n our studes and n others, too. In contrast, f partcpants smply compare the stmulus wth the Category A and Category B prototypes, they wll fnd that the evdence favorng a Category A response s roughly 5 Category A features shared dvded by (5 Category A features shared plus 1 Category B feature shared), or about 83%. The evdence base favorng the Category A response s stronger than n the case of exemplar storage. Ths occurs because the prototypes contan only the wheat, not the chaff. As a result, n the comparsons to the prototype, the evdence base favorng a Category A decson s not undercut by any featural dsagreements that the other exemplars had wth the prototype. Any plausble processng account wll realze ths strengthenng of the evdence base. Once agan, excepton tems wll receve the opposte effect (moderate dssmlarty to the exemplars wll mply strong dssmlarty to the prototype). If postve evdence and negatve evdence both grow more extreme, the result wll tend to be the heterogeneous performance profles that the prototype model shows, and that partcpants showed early n performance. Fgures 10A and 10B llustrate these contrastng tendences of the two models by showng the composte behavor of 20,000 random confguratons of the prototype and exemplar models, respectvely, gven the NLS stmulus set of Experments 1,2, and 4. Prototype-based processng produces terrble excepton-tem performance (Stmul 7 and 14), large prototype advantages (Stmul 1 and 8), and sprawlng performance profles overall. Its performance profles look lke those that partcpants produced early n Experment 2 (Fgure 3A). Exemplar-based processng produces much hgher exceptontem performance, mnmal prototype advantages, and cramped performance profles overall. Ths statement s not judgmental n many cases these operatng characterstcs wll be just the ones needed to ft performance. For example, the exemplar model's profles look exactly lke those that partcpants produced late n Experment 2 (Fgure 3D). In fact, notce that these cramped knds of performance profles wll emerge just when one models the aggregate \ I I I r 1 I I Stmulus B. Exemplar Model o 0 o on o 0.4- a. g a n Stmulus Fgure 10. A: The composte performance profle of 20,000 randomly selected confguratons of the prototype model on the sx-dmensonal not lnearly separable (NLS) categores. B: The composte performance profle of 20,000 randomly selected confguratons of the standard exemplar model on the sx-dmensonal NLS categores. performance for a group (and people's dosyncraces cancel out), when one models task-fnal performance (wth hgh performance on all stmul), or when one models performance on small, poorly dfferentated categores (and performance on all exemplars mproves homogeneously n parallel). That s, the standard exemplar model has had ts bggest successes at just the tmes when methodology guaranteed performance profles that the model was nherently most comfortable wth. Ths happy confluence of method and model s a possble reason why exemplar models were so successful early on and became so domnant. It s a possble reason to reman cautous about them now.

20 1430 SMITH AND MINDA On the other hand, t s a possblty, not prevously consdered, that heterogeneous performance profles lke those shown n Fgures 10A and 3A may ndcate that partcpants are referrng to untary representatons (.e., prototypes) n the servce of categorzaton, not to the nosy sgnals sent by specfc, stored exemplars. Gamma Other research has suggested that exemplar processng, as orgnally conceved by exemplar theorsts and nstantated n 20 years of exemplar models, may be nsuffcent to explan what ndvdual partcpants are dong (Ashby & Gott, 1988; Maddox & Ashby, 1993). Therefore, researchers have occasonally modfed the context model profoundly by addng on the gamma parameter (Maddox & Ashby, 1993; McKnley & Nosofsky, 1995, 1996). Gamma ntervenes by allowng every quantty n the choce rule to be rased to whatever power best recovers partcpants' actual performance profles. That s, whereas the choce rule that long served category models was Exemplar Model Predcton Gamma=3.0 Fgure 11. The relatonshp between the prototype and gamma models. The ponts represent the medan Category A response predcton of the prototype model at each level of Category A response predcton of the exemplar model for the sx-dmensonal not lnearly separable (NLS) category structure (see text for detals). The lne shows the Category A response predcton of the gamma model (7 = 3) at each level of Category A response predcton of the exemplar model for the sx-dmensonal NLS category structure. the augmented verson s JtCA I A y The need for gamma to supplement exemplar processng has strong resonances wth the utlty of prototype models demonstrated here and n Smth et al. (1997). For example, Smth et al. showed that good prototype-model fts reman hdden whle one models group performance. The requrement for gamma also remaned hdden whle researchers modeled group performance (Maddox & Ashby, 1993). In contrast, the present results show the usefulness of prototype models for modelng ndvdual profles. Ths s when gamma s necessary and why gamma was nvented. Moreover, we have shown that prototype descrptons are useful because they naturally produce more heterogeneous performance profles (Fgure 10A) than those of the standard exemplar model (Fgure 10B). Gamma produces heterogenety too. It systematcally undoes the homogenzng effect of exemplar-exemplar comparsons and restores the heterogenety that partcpants actually show, by rasng the choce rule to the 1.8th power, the 4.6th power, or the 9.7th power. In fact, one can show that gamma has representatonal entanglements wth prototypy that reman to be explored. We dscussed earler how prototypes provde clearer sgnals than exemplars for gudng categorzaton. The scatter plot n Fgure 11 gves precse mathematcal shape to ths dea. To make ths scatter plot, we chose randomly 1,000 attentonal confguratons. For each, we found the Category A response proportons predcted by the addtve prototype model and the standard exemplar model for the 14 stmul of the sx-dmensonal NLS category structure. The scatter plot shows the medan Category A response predcton of the prototype model at each level of Category A response predcton of the exemplar model. That s, f a stmulus would prompt the exemplar model to predct that there would be about 40% or 60% Category A responses, the stronger, clearer classfcatory sgnal from the prototype would predct about 20% or 80% Category A responses, respectvely. Overlan on these ponts s the Category A response predcton of the gamma model (7 = 3) at each level of Category A response predcton of the exemplar model. Ths lne shows how gamma-based categorzaton ntrnscally relates to exemplar-based categorzaton. The gamma lne explans 97.9% of the varance n the relatonshp between prototype-based and exemplar-based smlarty. Thus, gamma can arrange a precse mathematcal converson from a pattern of respondng consstent wth exemplar processng to one consstent wth prototype processng. Gven ths fact, a varety of crtera, lke smplcty and the ntutve framng of psychologcal questons, encourage a sgnfcant role for prototype-based descrptons of data lke those from the early tral segments that show clearly every expected feature of prototype processng (Fgure 5A). On the other sde, advocates of the gamma parameter as an adjunct to exemplar processng must note carefully that n many cases gamma has exactly the effect on categorzaton profles that s created by processes that have been the hstorcal and theoretcal antthess of exemplar processng. Gamma must be used and nterpreted wth cauton, for

21 CATEGORY LEARNING 1431 gamma can be a prototype n exemplar clothng (for a related dscusson, see Ashby & Maddox, 1993). The relaton of gamma to prototypy was especally clear for partcpants' early performances that the exemplar model faled to accommodate (Fgure 12A). In such cases, a large value of gamma let the gamma model use more parameters to emulate the behavor of an addtve prototype model and better ft the performances durng the early tral epochs (Fgure 12B). In dong so, the gamma model chose just the parameters that allowed t to mtate best the smple prototype model. Fgure 13 shows the results of the careful fttng procedure that confrmed ths. To make the curve for varyng levels of gamma, we took 1,000 random attentonal confguratons, and for each calculated the gamma model's Category A predctons (at 91 levels of gamma from 1 to 10 n steps of.10, wth senstvty always gven a random value between 1 A. Early NLS Performance: Exemplar Model O g Stmulus I I I! I I B. Predcted Performance: Gamma and Prototype Models 0.9- o 0.8- o, - O f 0.4 " 0.3- a K VM Gamma * Prototype I I r r Stmulus Fgure 12. The ft of the exemplar model to the early performance of partcpants learnng Experment 2's not lnearly separable (NLS) categores. B: The composte predcted performance profles of the gamma and prototype models when they ft the early performances of partcpants learnng Experment 2's NLS categores. Q 100- <n 80- Senstvty, - Gamma Parameter Value Fgure 13. The ft (sum of the squared devatons [SSD]) of the gamma model to the smple prototype model for dfferent levels of gamma and senstvty (see text for detals). and 10) and the prototype model's Category A predctons, for each of the 14 stmul n our sx-dmensonal NLS category structure. We then calculated the sum of the squared devatons (SSDs) between the 14,000 prototypebased predctons and the 14,000 gamma-based predctons at each level of gamma. The lne n the fgure plots these SSDs by levels of gamma and shows that the ft functon was mnmzed for gammas near 3. For our real partcpants, the average medan gamma estmated over the frst three tral segments of Experment 2's NLS condton was 3.4, nearly the gamma that lets the context model act most prototype based. By a parallel analyss, we found the levels of senstvty that let the context model mtate best the prototype model. To make the curve for varyng levels of senstvty, we took 1,000 random attentonal confguratons, and for each calculated the gamma model's Category A predctons (at 101 levels of senstvty from 0.0 to 10.0 n steps of.10, wth gamma always gven a random value between 1 and 10) and the prototype model's Category A predctons, for each of the 14 stmul n our sx-dmensonal NLS category structure. We then calculated the SSDs between the 14,000 prototype-based predctons and the 14,000 predctons of the gamma model at each senstvty. The lne plots these SSDs by levels of senstvty and shows that the ft functon was mnmzed for senstvtes near 2. The average medan senstvty for our real partcpants over the early tral segments was 2.0, just the senstvty that lets the context model act most prototype based. Therefore, of the hundreds of trllons of confguratons that the gamma model can take on, t takes on, to ft the early performances, just the terrbly narrow range of confguratons that allows t to mtate exactly a smple prototype model. Now, ths s no concdence because partcpants at ths stage of learnng do occupy a spot n the larger space of categorzaton strateges that s descrbable by a smple prototype model. In a sense, the emprcal story here s mat partcpants do reman for an extended perod n ths sngular place n the huge space of possbltes. One can then descrbe ths place as one where performance s consstent

22 1432 SMITH AND MINDA wth the pure use of addtve prototypes. Or one can descrbe t as the place where gamma equals 3 and senstvty equals 2 (whle wonderng what gamma equals 3 and senstvty equals 2 means, and whle beng helped by knowng that gamma equals 3 and senstvty equals 2 means that performance s consstent wth the pure use of addtve prototypes). We beleve the prototype descrpton s smply more llumnatng than the gamma descrpton. For example, only the prototype descrpton makes plan the sngularty of ths place n the larger space of categorzaton strateges and encourages approprately sharp research attenton to t. Only the prototype descrpton encourages one to ask what knds of (exemplar?) processes partcpants add to the mx to move out of ths place as learnng matures. Only the prototype descrpton emphaszes approprately the dramatc trajectory that partcpants trace through the larger space of categorzaton strateges. The trajectory they trace s as profound as that from performance based n smple prototypes (early n learnng) to performance based n memorzed exemplars (late n learnng). Our vew s that learnng trajectores of ths knd deserve sharper research attenton too, because they may reveal partcpants' early default strateges as they enter category tasks, the sngular postons n the larger performance space they sometmes occupy, the successon of strateges that they adopt through learnng, and the dfferent successons of strateges fostered by dfferent category structures. Our vew s that gamma does not hghlght any of these ssues as well as do the prototype or mxture perspectves. General Dscusson Humans' Ultmate Capactes and Natural Predspostons Regardng Categorzaton Whatever parameterzaton of the formal modelng space one chooses, our results are about the trajectory through the large space of categorzaton strateges that partcpants trace durng the learnng of many categores. Early on, partcpants' performance profles are consstent wth processng based n prototypes. They show large prototype effects, strctly obey ntutve typcalty gradents, show dsmal excepton-tem performance, and heterogeneous performance profles overall. Moreover, ther strong reassgnment of the excepton tems shows that they ntally make a strong lnear separablty assumpton about category structure they naturally assume, despte extensve evdence and feedback to the contrary over 200 trals, that the exemplars cluster n smlarty space near or around the prototypes. Later on, all aspects of performance are consstent wth a gradual transton to strateges that feature some knd of exemplar processng gven hghly famlar tranng exemplars. Many parameterzatons of the formal space of categorzaton strateges would descrbe later performance n ths way, though t remans an open queston whether those exemplar processes are to be understood as pure exemplar memorzaton (as n the mxture model) or as exemplar-to-exemplar comparson processes (as n the context model). In any case, the demonstraton of ths trajectory of learnng jons results from others (Nosofsky, Gluck, et al ; Nosofsky, Palmer, & McKnley, 1994; Smth et al., 1997) to assert the mportance of organzng prncples n early category learnng that may not be exemplar based and that are very dfferent from those at the end of extensve category tranng. Therefore, we beleve that t s useful to dstngush two research questons regardng human categorzaton that the lterature has not dstngushed suffcently. Frst, there s the queston of humans' ultmate categorzaton capactes, at the end of extended tranng, when they have developed an asymptotc strategy for copng wth dffcult category structures. Illustratng research on ths queston, McKnley and Nosofsky (1995) gave partcpants 4,000 trals (the amount of tranng our partcpants would have had f we had traned them every day for a week) on category tasks that were so dffcult that asymptotc performances were stll only 81% and 68% n two experments. Then they modeled the last 300 trals to assess ultmate performance. Ths research tradton rases mportant ssues. Can humans master exceptons? Can they learn NLS categores completely? Can they defend nonlnear decson boundares? These ssues have been promnent for 20 years (McKnley & Nosofsky, 1995; Medn & Schaffer, 1978; Medn & Schwanenflugel, 1981; Nosofsky, 1987). Experments lke those by McKnley and Nosofsky have shown that humans can do all these thngs and have shown that exemplar models descrbe these performances best. However, these experments cannot reveal humans' natural default assumptons about category tasks or ther natural default strateges when enterng category tasks. Instead, these experments bear on humans* ultmate capactes n categorzaton and on the knds of category structures they can eventually transcend and learn. Consequently, there remans the second queston about humans' natural, ntal default strateges and ther assumptons on enterng a category task. Do humans naturally assume LS categores and lnear decson boundares? Do they sometmes begn wth strateges that are captured especally well by prototype-based algorthms? Do they systematcally redefne exceptons nto the opposng category n an expresson of these assumptons and strateges? The present data suggest that humans do these thngs too early n category learnng, and ths may, too, be why prototype models descrbe these performances best Ths queston s about humans' defaults and predspostons. We hope that more research wll examne them. Convergng Perspectves on Categorzaton Ths examnaton s begnnng. For example, Nosofsky, Palmer, and McKnley (1994) suggested that partcpants learn categores by frst usng a rule to make a straght-edged cut through the stmulus space (see also Ann & Medn, 1992; Medn et al., 1987; Regehr & Brooks, 1995). They suggested that partcpants then nvoke specal learnng algorthms (exemplar memorzaton or confgurally codng featural complexes) to master the problematc exceptons. Nosofsky and hs colleagues (Nosofsky, Gluck, et al., 1994; Nosofsky, Palmer, & McKnley, 1994) have developed these deas by usng the rule-plus-excepton (RULEX) model. RULEX supposes that partcpants ntally seek

23 CATEGORY LEARNING 1433 rules that handle many tems n a task. Then, they encode more holstcally or confgurally the rule's exceptons and remember ther approprate category labels. RULEX successfully predcts varous aspects of partcpants' performance gven three- and four-dmensonal category structures lke those adopted n Experments 3 and 4. RULEX s even able to track through the epochs of learnng the performance levels on prototype and excepton tems, provdng a formal vdeo of performance as we have done here. Nosofsky's partcpants, lke ours n Experments 3 and 4, show strong mprovement on both central and exceptonal category members. Both hs and our partcpants move up the major dagonal of the performance spaces shown n Fgure 7 (see Fgures 6-8 n Nosofsky, Palmer, & McKnley, 1994). In contrast, the data from our sx-dmensonal category task provde a good target for Nosofsky, Palmer, & McKnley's (1994) model to shoot at and could represent an excepton to RULEX. For example, n Experment 2 partcpants mproved dramatcally on prototypes over 224 trals whle showng no mprovement on exceptons. It would be nterestng to know whether the RULEX model can separate so cleanly n tme the early mprovement on prototypes and the later cogntve work that masters exceptons. Here too, larger, well-dfferentated categores could shed a new lght on category learnng. It also may be mportant that our partcpants' early performances seem to be based n somethng closer to prototypes than to rules. However, we note that rule-based and prototype-based performance descrptons have some commonaltes. For example, both descrptons predct the strong reassgnment of excepton tems; both embody a strong lnear separablty assumpton about category structure and predct performance patterns that reflect that assumpton. Generally speakng, then, the deas formalzed n RULEX converge wth our own. RULEX endorses that dfferent epochs of learnng nvolve dfferent categorzaton strateges and varetes of stmulus codng. It endorses that early learnng epochs reveal a strong lnear separablty assumpton. It places exemplar-based processng n later epochs and predcts the exemplar model's advantage there, because t also lnks exemplar processes to the eventual-transcendence strateges that conquer exceptons. Thus, our research shares wth RULEX a perspectve that blends what human adults naturally assume and ultmately can do. Ths knd of perspectve could eventually provde a fuller descrpton of human categorzaton than has been prevalent. Contnutes and Dscontnutes Wth Other Categorzers Moreover, a focus on epochs of learnng, and the dfferent processng strateges that attend them, could also nform the lteratures on developmental change n categorzaton and speces dfferences n categorzaton. For example, young chldren may lack the delberate cogntve set that adults brng to category tasks or the abstracton/rule-use ethc that formal educaton fosters (Kemler Nelson, 1984; Smth, 1989; Smth & Kemler Nelson, 1984; Smth et al., 1993; Smth & Shapro, 1989). Young chldren may also lack the sophstcated metacogntve capactes that let adults montor error sgnals senstvely, target problematc exemplars, and enact secondary exemplar-based strateges to master them (Baker, 1985; Brown, Bransford, Ferrara, & Campone, 1983; Nelson, 1992, 1996). One could explore these age dfferences n category learnng by consderng the plot lne of the 4-year-old's categorzaton vdeo. Ths could show the ntal commtments chldren make to ether prototypes or exemplars and ther ultmate capactes to transcend obstacles and exceptons n category tasks. Ths research would make constructve contact wth exstng developmental research, n whch young chldren's task-fnal categorzaton processes have been varously descrbed as holstcally based n exemplar processes (Kemler Nelson, 1984), holstcally based n prototypes (Kemler Nelson, 1984, 1988, 1989; Smth, 1989; Smth & Kemler Nelson, 1984; Smth & Shapro, 1989), or based n narrow and rule-lke attenton to sngle dmensons (Ward, 1988; Ward & Scott, 1987). Ths research would also lnk current formal approaches and current debates about exemplars and prototypes to earler, elegant research explorng young chldren's progresson of hypothess-testng actvtes durng dscrmnaton learnng (e.g., Kemler, 1978). One could also use the category structures of Experments 1 and 2 to compare the performances of human and nonhuman anmals, to see when humans' unque cogntve capactes come most nto play. The human edge mght be sharpest at the start of the categorzaton vdeo (for the early epochs of learnng), n whch case anmals would produce a weaker ntal advantage for prototype-based descrptons than humans do. Or the human edge mght be sharpest at the end of the vdeo (for the fnal epochs of learnng), n whch case anmals mght stay welded to a prmtve lnear separablty constrant and assumpton for longer than humans. Ether pattern of results would be nterestng, for ether pattern would establsh both contnutes and dscontnutes between human and anmal speces, ether n ther ntal approaches to categorzaton tasks or n ther flexblty at shorng up those approaches gven specal crcumstances. The crucal pont for us s that both patterns of results emphasze the value of grantng a tme depth to analyses of categorzaton and to our formal models of those processes, and emphasze the value of understandng the trajectory of the learnng processes and the strategy transtons mat occur. The movng pcture, and not the frozen stll, may well provde the rcher descrpton of categorzers great and small. References Ahn, W., & Medn, D. L. (1992). A two-stage model of category constructon. Cogntve Scence, 16, Ashby, F. G., & Gott, R. E. (1988). Decson rules n the percepton and categorzaton of multdmensonal stmul. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 14, Ashby, F. G., & Maddox, W. T. (1993). Relatons between prototype, exemplar, and decson bound models of categorzaton. Journal of Mathematcal Psychology, 37, Ashby, F. G., & Perrn, N. A. (1988). Toward a unfed theory of smlarty and recognton. Psychologcal Revew, 95, Baker, L. (1985). How do we know when we don't understand? Standards for evaluatng text comprehenson. In D. L. Forrest-

24 1434 SMITH AND MINDA Pressley, G. E. MacKnnon, & T. G. Waller (Eds.), Metacognton, cognton, and human performance (pp ). New York: Academc Press. Brooks, L. R. (1978). Non-analytc concept formaton and memory for nstances. In E. Rosch & B. B. Lloyd (Eds.), Cognton and categorzaton (pp ). Hlls dale. NJ: Erlbaum. Brown, A. L., Bransford, J. D., Ferrara, R. A., & Campone, J. C. (1983). Learnng, rememberng, and understandng. In J, H. Flavell & E. M. Markman (Eds.), Handbook of chld psychology (Vol. 3, pp ). New York: Wley. Estes, W. K. (1986a). Array models for category learnng. Cogntve Psychology, 18, Estes, W. K. (1986b). Memory storage and retreval processes n category learnng. Journal of Expermental Psychology: General, 112, Estes, W. K., Campbell, J. A., Hatsopoulos, N., & Hurwtz, J. B. (1989). Base-rate effects n category learnng: A comparson of parallel network and memory storage-retreval models. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 75, Homa, D., & Chamblss, D. (1975). The relatve contrbutons of common and dstnctve nformaton on the abstracton from ll-defned categores. Journal of Expermental Psychology: Human Learnng and Memory, 10, Homa, D M Cross, J., Cornell, D., Goldman, D., & Shwartz, S. (1973). Prototype abstracton and classfcaton of new nstances as a functon of number of nstances defnng the prototype. Journal of Expermental Psychology, 101, Homa, D., Dunbar, S., & Nohre, L. (1991). Instance frequency, categorzaton, and the modulatng effect of experence. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 17,444^58. Homa, D., Rhoads, D., & Chamblss, D. (1979). Evoluton of conceptual structure. Journal of Expermental Psychology: Human Learnng and Memory, 5, Homa, D., Sterlng, S., & Trepel, L. (1981). Lmtatons of exemplar-based generalzaton and the abstracton of categorcal nformaton. Journal of Expermental Psychology: Human Learnng and Memory, 7, Jacoby, L. L., & Brooks, L. R. (1984). Nonanalytc cognton: Memory, percepton, and concept formaton. Psychology of Learnng and Motvaton, 18, Kemler, D. G. (1978). Patterns of hypothess testng n chldren's dscrmnatve learnng: A study of the development of problem solvng strateges. Developmental Psychology, 14, Kemler Nelson, D. G. (1984). The effect of ntenton on what concepts are acqured. Journal of Verbal Learnng and Verbal Behavor, 23, Kemler Nelson, D. G. (1988), When category learnng s holstc: A reply to Ward and Scott. Memory & Cognton, 16, Kemler Nelson, D. G. (1989). The nature and occurrence of holstc processng. In B. E. Shepp & S. Ballesteros (Eds.), Object percepton: Structure and processes (pp ). Hllsdale, NJ: Erlbaum. Lamberts, K. (1994). Flexble tunng of smlarty n exemplarbased categorzaton. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 20, Lamberts, K. (1995). Categorzaton under tme pressure. Journal of Expermental Psychology: General, 124, , Maddox, W. T., & Ashby, G. (1993). Comparng decson bound and exemplar models of categorzaton. Percepton and Psychophyscs, 53, Malt, B. C. (1989). An on-lne nvestgaton of prototype and exemplar strateges of classfcaton. Journal of Expermental Psychology: Human Learnng and Memory, 15, McKnley, S. C, & Nosofsky, R. M. (1995). Investgatons of exemplar and decson bound models n large, ll-defned category structures. Journal of Expermental Psychology: Human Percepton and Performance, 21, McKnley, S. C, & Nosofsky, R. M. (1996). Selectve attenton and the formaton of lnear decson boundares. Journal of Expermental Psychology: Human Percepton and Performance, 22, Medn, D. L. (1975). Atheory of context n dscrmnaton learnng. In G. H. Bower (Ed.), The Psychology of Learnng and Motvaton (Vol. 9, pp ). New York: Academc Press. Medn, D. L., Altom, M. W., & Murphy, T. D. (1984). Gven versus nduced category representatons: Use of prototype and exemplar nformaton n classfcaton. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 10, Medn, D. L., Dewey, G. I., & Murphy, T. D. (1983). Relatonshps between tem and category learnng: Evdence that abstracton s not automatc. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 9, Medn, D. L., & Schaffer, M. M. (1978). Context theory of classfcaton learnng. Psychologcal Revew, 85, Medn, D. L., & Schwanenfhgel, P. J. (1981). Lnear separablty n classfcaton learnng. Journal of Expermental Psychology: Human Learnng and Memory, 7, Medn, D. L., & Smth, E. E. (1981). Strateges and classfcaton learnng. Journal of Expermental Psychology: Human Learnng andmemory, 7, Medn, D. L., Wattenmaker, W. D., & Hampson, S. E. (1987). Famly resemblance, conceptual cohesveness, and category constructon. Cogntve Psychology, 19, Mervs, C. B., & Rosch, E. (1981). Categorzaton of natural objects. In M. R. Rosenzweg & L. W. Porter (Eds.), Annual Revew of Psychology, 32, Murphy, G. L., & Medn, D. L. (1985). Role of theores n conceptual coherence. Psychologcal Revew, 92, Nelson, T. O. (Ed.). (1992). Metacognton: Core readngs. Needham Heghts, MA: Allyn & Bacon. Nelson, T. O. (1996). Metacognton and conscousness. Amercan Psychologst, 51, Nosofsky, R. M. (1984). Choce, smlarty, and the context theory of classfcaton. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 10, Nosofsky, R. M. (1985). Overall smlarty and the dentfcaton of separable-dmenson stmul: A choce model analyss. Percepton and Psychophyscs, 38, Nosofsky, R. M. (1986). Attenton, smlarty, and the dentfcatoncategorzaton relatonshp. Journal of Expermental Psychology: General, 115, Nosofsky, R. M. (1987). Attenton and learnng processes n the dentfcaton and categorzaton of ntegral stmul. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 13, Nosofsky, R. M. (1988). Smlarty, frequency and category representatons. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 14, Nosofsky, R. M. (1989). Further tests of an exemplar-smlarty approach to relatng dentfcaton and categorzaton. Percepton and Psychophyscs, 45, Nosofsky, R. M. (1991). Tests of an exemplar model for relatng perceptual classfcaton and recognton memory. Journal of Expermental Psychology: Human Percepton and Performance, 17, Nosofsky, R. M. (1992). Exemplars, prototypes, and smlarty rules. In A. F. Healy, S. M. Kosslyn, & R. M. Shffrn (Eds.), From learnng theory to connectonst theory: Essays n honor of Wllam K. Estes (pp ). Hllsdale, NJ: Erlbaum.

25 CATEGORY LEARNING 1435 Nosofsky, R. M., Clark, S. R, & Shn, H. J. (1989). Rules and exemplars n categorzaton, dentfcaton andrecognton.journal of Expermental Psychology: Learnng, Memory, and Cognton, 15, Nosofsky, R. M, Gluck, M. A., Palmer, T. J., McKnley, S. C, & Glauther, P. (1994). Comparng models of rule-based classfcaton learnng: A replcaton and extenson of Shepard. Hovland and Jenkns (1961). Memory & Cognton, 22, Nosofsky, R. M., Kruschke, J. K., & McKnley, S. C. (1992). Combnng exemplar-based category representatons and connectonst learnng rules. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 18, Nosofsky, R. M, & Palmer, T. J. (1997). An exemplar-based random walk model of speeded classfcaton. Psychologcal Revew, 104, Nosofsky, R. M., Palmer, T. J., & McKnley, S. C. (1994). Rule-plus-excepton model of classfcaton learnng. Psychologcal Revew, 101, Palmer, T. J., & Nosofsky, R. M. (1995). Recognton memory for exceptons to the category rule. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 21, Posner, M. I., & Keele, S. W. (1968). On the geness of abstract deas. Journal of Expermental Psychology, 77, Posner, M. I., & Keele, S. W. (1970). Retenton of abstract deas. Journal of Expermental Psychology, 83, Reed, S. K. (1972). Pattern recognton and categorzaton. Cogntve Psychology, 3, Reed, S. K. (1978). Category vs. tem learnng: Implcatons for categorzaton models. Memory & Cognton, 6, Regehr, G., & Brooks, L. (1995). Category organzaton n free classfcaton: The organzng effect of an array of stmul. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 21, Rosch, E. (1973). On the nternal structure of perceptual and semantc categores. In T. E. Moore (Ed.), Cogntve development and the acquston of language (pp ). New York: Academc Press. Rosch, E. (1975). Cogntve reference ponts. Cogntve Psychology, 7, Rosch, E., & Mervs, C. B. (1975). Famly resemblances: Studes n the nternal structure of categores. Cogntve Psychology, 7, Shepard, R. N. (1987). Toward a unversal law of generalzaton for psychologcal scence. Scence, 237, Shn, H. J., & Nosofsky, R. M. (1992). Smlarty-scalng studes of dot-pattern classfcaton and recognton. Journal of Expermental Psychology: General, 121, Smth, J. D. (1989). Analytc and holstc processes n categorzaton. In B. E. Shepp & S. Ballesteros (Eds.), Object percepton: Structure and processes (pp ). Hllsdale, NJ: Erlbaum. Smth, J. D., & Kemler Nelson, D. G. (1984). Overall smlarty n adults' classfcaton: The chld n all of us. Journal of Expermental Psychology: General, 113, Smth, J. D., Murray, M. J., & Mnda, J. P. (1997). Straght talk about lnear separablty. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 23, Smth, J. D., & Shapro, J. H. (1989). The occurrence of holstc categorzaton. Journal of Memory and Language, 28, Smth, J. D., Tracy, J., & Murray, M. J. (1993). Depresson and category learnng. Journal of Expermental Psychology: General, 122, Ward, T. B. (1988). When s category learnng holstc? A reply to Kemler Nelson. Memory & Cognton, 16, Ward, T B., & Scott, J. (1987). Analytc and holstc modes of learnng famly resemblance concepts. Memory & Cognton, 15, Whttlesea, B. W. A. (1987). Preservaton of specfc experences n the representaton of general knowledge. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 13, Whttlesea, B. W. A., Brooks, L., & Westcott, C. (1994). After the learnng s oven Factors controllng the selectve applcaton of general and partcular knowledge. Journal of Expermental Psychology: Learnng, Memory, and Cognton, 20, Appendx A Category Structures Used n Experments 1 and 2 Structure Category A Stmul Structure Categores lnearly separable b anuly benuly kanuly banlo kanulo bapury bepuly Categores not lnearly separable g afu z wafuz gyfuz gas u z gafur gafuzo wysezo ooo oo Category B Stmul kepro keplo ken ro kapry bepry kapuro benro wysero gysero w asero w y fero wysuro wy ser g afe z (Appendx B follows on next page)