Instance memorization and category influence: Challenging the evidence for multiple systems in category learning

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Instance memorization and categoryinfluence: Challenging the evidence formultiple systems in category learningMark K. Johansen a , Nathalie Fouquet b , Justin Savage a & David R. Shanksc

a School of Psychology , Cardiff University , Cardiff , UKb College of Human and Health Sciences , Swansea University , Swansea ,UKc Division of Psychology and Language Sciences , University CollegeLondon , London , UKAccepted author version posted online: 01 Oct 2012.Published online: 12Nov 2012.

To cite this article: Mark K. Johansen , Nathalie Fouquet , Justin Savage & David R. Shanks (2013) Instancememorization and category influence: Challenging the evidence for multiple systems in category learning,The Quarterly Journal of Experimental Psychology, 66:6, 1204-1226, DOI: 10.1080/17470218.2012.735679

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Instance memorization and category influence:Challenging the evidence for multiple systems in category

learning

Mark K. Johansen1, Nathalie Fouquet2, Justin Savage1, and David R. Shanks3

1School of Psychology, Cardiff University, Cardiff, UK2College of Human and Health Sciences, Swansea University, Swansea, UK3Division of Psychology and Language Sciences, University College London, London, UK

A class of dual-system theories of categorization assumes a categorization system based on actively formedprototypes in addition to a separate instance memory system. It has been suggested that, because they haveused poorly differentiated category structures (such as the influential “5-4” structure), studies supporting thealternative exemplar theory reveal little about the properties of the categorization system. Dual-system the-ories assume that the instance memory system only influences categorization behaviour via similarity tosingle isolated instances, without generalization across instances. However, we present the results of twoexperiments employing the 5-4 structure to argue against this.Experiment 1 contrasted learning in the stan-dard 5-4 structure with learning in an even more poorly differentiated 5-4 structure. In Experiment 2, par-ticipantsmemorized the 5-4 structure based on a fiveminute simultaneous presentation of all nine categoryinstances. Both experiments revealed category influences as reflected by differences in instance learnabilityand generalization, at variance with the dual-system prediction. These results have implications for theexemplars versus prototypes debate and the nature of human categorization mechanisms.

Keywords: Category learning; Exemplars; Prototypes; Categorization; Representation.

The ability to categorize objects and events and toform conceptual representations of those categoriesis a core cognitive capacity. Research on categoriz-ation in both psychology and neuroscience has beenheavily influenced in recent years by attempts toevaluate various “dichotomy” frameworks such asthe distinctions between implicit/explicit learningand rule-based/similarity-based category learning(Ashby & Maddox, 2005; Seger & Miller, 2010).

Particularly prominent among these distinctions isthat between exemplar versus prototype represen-tation of categories, and debate over this distinctioncontinues to be a core research issue in categoriz-ation and learning. While at least initially exemplarand prototype theories seem conceptually well dif-ferentiated, specifying what the debate is trulyabout has been more difficult, especially in thebroadening context of multisystem models where

Correspondence should be addressed to Mark K. Johansen, Cardiff University, Tower Building, Park Place, Cardiff CF10 3AT,

UK. E-mail: [email protected]

We thank Lewis Bott, Marc Buehner, Stephan Lewandowsky, and several anonymous reviewers for detailed comments and sug-

gestions on an earlier version of this manuscript.

1204 # 2013 The Experimental Psychology Society

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Vol. 66, No. 6, 1204–1226, http://dx.doi.org/10.1080/17470218.2012.735679

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for some the abstraction-based subsystem uses rulesrather than prototypes (e.g., ATRIUM, Erickson& Kruschke, 1998).

Exemplar theory (e.g., Kruschke, 1992; Medin& Schaffer, 1978; Nosofsky, 1984, 1986) assumesthat people represent categories during learningby storing the experienced instances of the cat-egories in memory. This representation can stillreflect some abstraction—for instance, selectiveattention can moderate similarity to make within-category instances more similar than between-category instances (Kruschke, 1992; Nosofsky,1986)—but the representation is relatively uninte-grated and unabstracted in that the individualexemplars are assumed to be separately encoded.The probability of a new instance being classifiedinto a particular category is the sum of its simi-larities to the stored category instances relative tothe corresponding summed similarities for othercategories. So the greater the overall similarity tothe instances of the category, the more likely anew case is to be classified into that category. Inbrief, memory for instances is crucial and the for-mation of new abstractions is, at most, limited inthe context of adaptive categorization.

In contrast, prototype theory (e.g., Blair &Homa, 2001; Homa, Rhoads, & Chambliss,1979; Homa, Sterling, & Trepel, 1981; Posner &Keele, 1968; Smith & Minda, 1998, 2000)assumes that categories are represented duringlearning by an actively integrated average orcentral tendency of the observed instances, the cat-egory prototype. New instances are categorized attest based on their similarity to various categoryprototypes, where the probability of a particular cat-egorization is proportional to the similarity of theinstance to the category prototype relative toother category prototypes. Hence the greater theoverall similarity to a category prototype, themore likely a new case is to be classified into thatcategory. In brief, long-term memory for specificinstances is not required while formation of newabstractions—that is, actively integrated proto-types—is crucial for adaptive categorization.

Importantly, the exemplars versus prototypesdebate is not about whether prototypicality effectsoccur. Virtually everyone now agrees that a

fundamental property of most real world categoriesis that some instances are better, more typical,members than other instances. Moreover, exemplarmodels would not be nearly as successful as theyhave been if they could not provide some accountof such effects (e.g., Nosofsky & Kruschke, 1992;but also see the recent debate about potential pre-diction differences in typicality gradients in thedot-distortion paradigm: Homa, Hout, Milliken,& Milliken, 2011; Smith, 2002, 2005; Zaki &Nosofsky, 2004, 2007). Nor does anyone disputethat participants can remember particular instancesof categories or that these can influence categoriz-ation as demonstrated by the large body of evidencefor exemplar effects, which most notably occur evenin the presence of explicit and perfectly diagnosticrules (e.g., Allen & Brooks, 1991; Hahn, Prat-Sala, Pothos, & Brumby, 2010). In particular, itis worth emphasizing in advance that prototypetheory does not preclude the influence of instancememory on categorization or even categorizationbehaviour based solely on instance memory insome cases, as we describe below. Needless to say,these complicating facts emphasize the importanceof being clear about the key aspects of the debate.

To be useful, categories have to add something;category membership knowledge needs to improveadaptive functionality. Knowing that a particularanimal is in the category “dog” is not very usefulif it does not help predict unseen properties. This“category influence” can take many forms; forinstance, it can influence the learnability of categoryinstances as shown in the experiments reportedbelow. And there are a variety of perspectives inthe literature about what categories do; forexample, the perspective embodied in Anderson’s(1990, 1991) rational model is that categories arefor optimized feature inference whereas the empha-sis in Pothos and Chater’s (2002) simplicity modelis on representing information efficiently. But mostfundamentally, category influence involves inte-gration of information from across the experiencedinstances of the categories in a way that improvesprediction and control. The particular entitynearby is apparently a dog. Dogs tend to be territor-ial and protective as indicated by growling, in whichcase approach is inadvisable, but a wagging tail can

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2013, 66 (6) 1205

INSTANCE MEMORIZATION AND CATEGORY INFLUENCE

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indicate they are friendly and that approach is safe.Not only do exemplar and prototype theories makedifferent predictions about how category inte-gration occurs, but this difference in proposedmechanisms for category influence is the funda-mental difference between them.

The crux of the difference between prototypeand exemplar theories is whether or not categoryinfluence is the result of a separate, abstraction-generating, cognitive system distinct from instancememory (Blair & Homa, 2001, 2003; Nosofsky,2000; Smith & Minda, 2000, 2002). Specifically,does category integration as measured particularlyby prototypicality effects occur in a separatesystem from instance memory via an activeprocess resulting in an abstracted category proto-type? Or is category integration fundamentally apassive process resulting from similarity to the cat-egory instances stored in a single memory system—

possibly moderated by selective attention,forgetting, and interference?

Once prototypicality and exemplar effects incategorization are both acknowledged to occur,distinguishing prototype from exemplar represen-tation can be conceptually, not to mention pragma-tically, quite difficult. However, one usefuldifference between the theories follows from theconceptual distinction between a single systemmediating categorization and instance memory(exemplar theory) versus separate systems for categ-orization and instance memory (prototype theory)and leads to the following crucial question: Doesmore than one category instance influence a givencategorization decision? Or does memory forinstances influence categorization only via a singlenearest exemplar? Both Smith (2005) andNosofsky (2000) have specified this as a key issuewhile arguing from opposite theoretical positions.In particular, Smith (2005, p. 47) specifies thetheoretical distinction in terms of “whether exem-plar generalization in memory and categorizationis broad and collective – extending to manyrelated exemplars stored in memory – or whetherit is focused and singular – extending only tohighly similar (nearly identical) exemplars”.

The view that the true (i.e., abstraction-generat-ing) categorization system is mentally separate from

the instance memory system suggests the predictionthat there should be a lack of generalizationbetween category instances when a new instancethat needs to be categorized queries the instancememory store. Obviously, specific categoryinstances can be memorized, and these instance–category pairings could be stored in an instancememory system quite distinct from the prototypeformed in a separate categorization system. Sothis suggests a conceptually precise way in whichexemplar and prototype theory can be systemati-cally specified and differentiated, especially in thehistorically popular binary featured category struc-tures: On the prototype theory, a response deter-mined by the memory system, as distinct fromthe categorization system, should be the result ofsimilarity to only a single memorized categoryinstance.

As a preview, the purpose of the present researchwas to evaluate this key issue of lack of exemplargeneralization in instance memory as distinctfrom generalization in a putative categorizationsystem. While the exemplars versus prototypesdebate has usually involved contrasting exemplarand prototype model accounts of a given data setand picking a winner, such an approach does notdirectly address the key generalization issue,which is fundamentally about the behaviour ofthe exemplar model. So rather than contrastingexemplar and prototype models (as has been donenumerous times in the past), we have operationallyevaluated exemplar generalization, exemplar “cross-talk”, by unpacking the exemplar model’s behav-iour. To emphasize, our focus is not on whetherthe exemplar model can account for the data wepresent but rather on how it accounts for thosedata. When the exemplar model determines theprobability that a test case belongs in a particularcategory, it calculates the overall similarity of thetest case to the category exemplars (in contrast toexemplars of other categories; the Appendix pre-sents a formalization of this account). So the issueof exemplar generalization/crosstalk reduces tolooking at the exemplar similarity components ofthe overall category similarity, specifically the pro-portion of overall category similarity that is notdue to the single nearest instance as the exemplar

1206 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2013, 66 (6)

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model is at least conceptually compatible with wideor narrow generalization. If test item categoryassignment is determined by similarity to a singlenearest exemplar, then overall category similarityshould be only negligibly greater than the similarityto the single exemplar. On the other hand, if mul-tiple exemplars are contributing to overall categorysimilarity when determining test item categoriz-ation, then this exemplar crosstalk should be appar-ent in terms of more than one exemplarcontributing nontrivially to the overall categorysimilarity. Before discussing the critical problemof how to evaluate instance memory generalizationin isolation from generalization in a categorizationsystem, we need to make clear that the hypothesisof nongeneralizing instance memory is not simplya straw man.

This position is most closely implied by theconclusions of Blair and Homa (2003) but is alsorelated to the narrow exemplar generalizationargued for by Smith (2005) and others:“Researchers have raised the possibility that par-ticipants learning categories based on binary-valued dimensions (BVD) may simply memorizeeach member, rather than generalize acrossmembers (Blair & Homa, 2001; Smith &Minda, 2000)” (Blair & Homa, 2003, p. 1293).If a response is based on more than one instancein the memory system, then this system wouldbe likely to generate prototypicality effects, typi-cality gradients, etc., and the theoretical value ofa separate prototype-based categorization systemwould be much reduced both on the grounds ofparsimony and on the grounds of pragmaticallydifferentiating the theories. In effect, prototypetheory’s separate memory store for instanceswould be generating categorization behaviour ina similar way to exemplar theory’s single system,thus calling into question the conceptual and prac-tical utility of a separate categorization systembased on prototypes.

Additionally, the recent debate about predicteddifferences in typicality gradients for exemplarsversus prototypes in the dot-distortion categorylearning paradigm has done little to reduce the con-ceptual importance of non-generalizing exemplarsto differentiating the theories (Homa et al., 2011;

Smith, 2002, 2005; Zaki & Nosofsky, 2004,2007). In this paradigm, participants make categoryendorsement judgements for prototypes and forlow, medium, and high distortions of a prototype.Smith (2002) argued that exemplar theory necess-arily predicts a flatter typicality gradient aroundthe prototype than prototype theory and that proto-types better account for the observed pattern ofresponding. The intuitive argument for this(Smith, 2002) is to imagine a ring of exemplarswith an untrained prototype at the centre.Consider test items that approach the prototypealong a straight line. As test items get progressivelycloser to the ring of exemplars, there should be asharp rise in category endorsement, but this typical-ity gradient should flatten out for items within theexemplar ring because as the test item is gettingcloser to items on the far side of the ring it isgetting farther from exemplars on the near side ofthe ring. Zaki and Nosofsky (2004) agree thatthis prediction is to some degree correct but arguethat the data in this paradigm are misleading dueto methodological problems, for example testphase stimuli, especially prototypes, being incor-porated into the representation. Zaki andNosofsky (2007) further support this argument byproviding evidence of higher rates of endorsementfor high distortions than for prototypes by simplyincluding many high distortions in the test phase.In response, Homa et al. (2011) argue that the con-clusions of Zaki and Nosofsky (2004, 2007) are inturn based on an artefact deriving from use of thesingle category endorsement paradigm, and thatfalse prototype enhancement effects largely disap-pear in a multi-category paradigm. However,examination of the typicality gradients obtainedby Homa et al. (2011) suggests that they lookrather more like the flat gradients that Smith(2002) ascribes to the exemplar model than thesteep gradients typical of the prototype, and inaddition Homa et al. did not report exemplar andprototype model fits to their results.

As is not uncommon in the exemplar versus pro-totype debate, the arguments are becoming moreand more complex, and there does not (at leastyet) seem to be a clear winner in the dot-distortionparadigm. Nor, in our opinion, is there likely to be



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one in the near future, as some of the key thingsthat make the dot distortion paradigm interesting,such as the complexity and apparent ecologicalplausibility of the stimuli, also make clear assess-ment of the precise similarity relationshipsbetween the instances in individual participants dif-ficult. In addition, the complex nature of thestimuli seems likely to induce highly idiosyncraticrepresentations in different participants in partfrom large differences in selective attention as wellas complex interactions with prior representationsalong the lines of the different patterns people seewhen looking at the stars.

A priori, establishing differences between typi-cality gradients seems likely to correspond to a con-siderably weaker theoretical contrast than to arguefor the presence versus absence of generalizationacross instances. Hence, the present researchfocuses on contrasting exemplar theory with adual-system prototype theory: In addition to speci-fying the behaviour of the separate, prototype-based categorization system, this dual-systemtheory makes a clear prediction for how the instancememory system should behave in a category learn-ing task; namely it computes similarity to only asingle category instance without generalizationacross category instances. This is the positionstrongly espoused by Blair and Homa (2003) andat least partly espoused by Smith (2005). Inaddition, it makes clear, falsifiable predictionsabout whether multiple instances influence categor-ization, as will be detailed below. To evaluate thesepredictions behaviourally, there must be some wayof separately detecting the influence of both ofthese two systems on responding. In particular,there needs to be a way of testing the hypothesizedinstance memory system, preferably uncontami-nated by the prototype-based categorizationsystem, to see if only a single stored instance influ-ences categorization responding without generaliz-ation across instances.

Applying a classic neuropsychological method-ology to a cognitive problem, Blair and Homa(2003; also see Smith, 2005; Smith & Minda,2000, 2002) not only proposed that the proto-type-based categorization system can be effectivelyablated but argued that this is in fact what has

happened in many categorization studies support-ing exemplar theory because they have used ecolo-gically implausible category structures.Specifically, a lot of support for exemplar theoryhas come from studies using two categories com-posed of a small number of poorly differentiatedinstances with features that are only binary-valued across instances (e.g., the 5-4 structurefrom Medin & Schaffer, 1978). In this context,“poorly differentiated” means that the prototypicalfeatures of one category occur quite frequently ininstances of the other category and vice versa.These structures are argued to be ecologicallyinvalid because most real-word categories puta-tively have well-differentiated prototypes gener-ated from many instances composed ofnumerous features and are learned in contrast tofar more than a single other category. So binary-valued category structures with few instances donot represent a reasonable simplification of thevast majority of categories that occur in the realworld, and as such, categorization performanceon these categories tells us little if anythingabout how the mind actually generates adaptivecategory-based behaviour.

From this dual-system perspective, requiringpeople to memorize poorly differentiated cat-egories composed of binary-valued stimulishould have the useful consequence of resultingin a failure of the categorization system to abstractcategory prototypes. This leaves responding to bebased solely on single memorized instancesretrieved from the separate memory system andso allows the influence of that system on respond-ing to be directly evaluated, uncontaminated bythe prototype-based categorization system whichhas been ablated and rendered irrelevant.Effectively, the argument is that the mind doesnot treat this as a categorization task at all andso just deals with it as an instance memorizationtask where some of the instances happen toshare common labels.

Of all these problematic binary-valued categorystructures, arguably the most influential is thewidely employed 5-4 category structure fromMedin and Schaffer (1978). Blair and Homa(2003) proposed that this particular category


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structure, shown in Table 1, column 2, undulyfavours exemplar representation because itencourages instance memorization due to its smallnumber of poorly differentiated instances (see alsoSmith & Minda, 2000, for a similar line of reason-ing). In this category structure there are fiveinstances of category A and four instances of cat-egory B, designated A1–A5 and B1–B4 in Table1, column 2 (top). In addition, there are seven gen-eralization test items, designated T1–T7 in Table1, column 2 (bottom). Each category instance isrepresented in a row of the table and is composedof one of two possible features on each of fourfeature dimensions.

In this context, Blair and Homa (2003) pro-posed a formal measure of a category influence on

category learning that they called “category advan-tage”. They had participants learn the instances ofthe 5-4 category structure as an identification(rather than a categorization) task over a series oftrials with feedback where each of the nineinstances was assigned a unique label. Blair andHoma then compared performance in this identifi-cation learning task with performance in a standardcategory learning task, where participants learnedto assign the instances to two categories. Categoryadvantage is defined as higher accuracy at a givenpoint in learning for the categorization task com-pared to the identification task once differences inguessing are controlled for, which is crucialbecause of the difference in the number ofresponses in the two tasks (two versus nine). So asignificant category advantage at any point in learn-ing was argued to reflect a well-differentiated cat-egory structure having a category influence on thespeed of learning due to generalization betweeninstances. In brief, similarity among categoryinstances influences their individual learnability.On the other hand, the absence of a categoryadvantage was argued to indicate little if any cat-egory influence on learning due to generalizationbetween instances. In that case, categorization be-haviour would simply be due to instance memoriza-tion just as in the identification learning task.

Across several experiments with different stimu-lus sets, Blair and Homa (2003) found no systema-tic category advantage for the 5-4 category structureas measured by accuracy in the categorization taskrelative to the identification task. That is, partici-pants were not able to learn the 5-4 category struc-ture in a categorization task any faster than theywere able to learn to assign the nine instances tonine unique outcomes, each with a different label,in an identification task.

Blair and Homa used this lack of a categoryadvantage to argue that “the widely used and influ-ential 5-4 categories are learned chiefly by memor-ization, with no generalization across categorymembers” (p. 1300). More generally: “If oneassumes that there is little or no relationshipbetween memorization and categorization, thenthe 5-4 category learning task has little to do withcategorization” (p. 1299). It follows that the

Table 1. Standard 5-4 category structure (Medin & Schaffer,

1978), low-differentiation 5-4 structure, and test cases used in

Experiment 1’s standard and low-differentiation conditions

Trial types Standard Low-differentiation

A1 A 1 1 1 2 A 2 2 2 1

A2 A 1 2 1 2 A 1 2 1 2

A3 A 1 2 1 1 A 2 1 1 2

A4 A 1 1 2 1 A 1 1 2 1

A5 A 2 1 1 1 A 2 1 1 1

B1 B 1 1 2 2 B 1 1 2 2

B2 B 2 1 1 2 B 1 2 1 1

B3 B 2 2 2 1 B 1 1 1 2

B4 B 2 2 2 2 B 2 2 2 2

T1 ? 1 2 2 1 ? 1 2 2 1

T2 ? 1 2 2 2 ? 1 2 2 2

T3 ? 1 1 1 1 ? 1 1 1 1

T4 ? 2 2 1 2 ? 2 2 1 2

T5 ? 2 1 2 1 ? 2 1 2 1

T6 ? 2 2 1 1 ? 2 2 1 1

T7 ? 2 1 2 2 ? 2 1 2 2

In the test cases, ? indicates that there was no correct category as

participants never received feedback for these items. The

category instance trial type labels A1–B4 are for reference

purposes only, as are the generalization test trial labels T1–

T7. The two bold instances in each category of the low-

differentiation condition were members of the other

category in the standard category structure in the middle

column. Specifically, A1 and A3 in the low-differentiation

condition are B3 and B2, respectively, in the

standard condition, and B2 and B3 in the low-

differentiation condition are A3 and A1, respectively, in the

standard condition.



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enormous amount of support that exemplar theoryhas received from binary-valued category structuresis called into question. Also, as we have arguedabove, this “generalization across categorymembers” is, indeed, important to systematicallydifferentiate prototype and exemplar theory bothpragmatically and theoretically.

It is worth emphasizing that this is not just aminor methodological dispute over a specific cat-egory structure, however influential that structurehas been. Paradoxically the very attributes of thisstructure that have been argued to be ecologicallyinvalid, maybe even eliminating much of the evi-dence for exemplar theory all at once, make it anideal candidate for evaluating the dual-system pro-totype theory described above: Categorizationresponding in the absence of well-differentiatedprototypes should exhibit no category influencebut rather be based solely on a single memorizedexemplar retrieved from instance memory withno generalization across category members.Experiments 1 and 2 were designed to evaluatethis claim operationally.

EXPERIMENT 1

The purpose of this experiment was to assess cat-egory influences on instance “memorization”(Blair & Homa, 2003) using the poorly differen-tiated 5-4 category structure, shown in Table 1,column 2 (Medin & Schaffer, 1978). However,unlike Blair and Homa, we do not contrast categoryand identification learning because we accept theyhave demonstrated an absence of “category advan-tage” for this category structure (though we recon-sider the interpretation of this evidence in theGeneral Discussion). It is worth noting that if wehave been too quick to accept Blair and Homa’s evi-dence for the absence of a category advantage forthe 5-4 structure, then their argument is immedi-ately invalidated. For instance, identification learn-ing of this structure may simply be harder thanclassification learning and there may be a true cat-egory learning advantage that they did not detect.However, our approach does not call into question

their key empirical starting assumption, and it isalso worth noting that our evaluation of categoryinfluence and crosstalk similarity is relevant evenif this assumption is incorrect.

Rather than comparing categorization withidentification learning, our approach was to con-trast instance memorization in the standard 5-4category structure with instance memorization inan even more poorly differentiated category struc-ture. We generated this low-differentiation cat-egory structure by swapping two of the instancesin the standard category A with two of the instancesin the standard category B, as shown in Table 1,column 3. It is not material that this low-differen-tiation structure is linearly inseparable and accurateperformance cannot be based on prototype rep-resentation: The prototype-based system has beenargued to already be uninvolved in learning thestandard 5-4 structure anyway. The two conditionswere otherwise identical.

A variety of theoretical perspectives provide apractical rationale for thinking that poorly differen-tiated category structures should be harder to learnthan better differentiated ones, including Pothosand Bailey’s (2009) concept of category intuitive-ness (see also Pothos et al., 2011b, and Pothos,Edwards, & Perlman, 2011a). Pothos and Baileyused category intuitiveness framed in the contextof unsupervised categorization and an exemplarmodel to account for testing trial differences fromstandard feedback learning of the 5-4 structure.However, our specification of the low-differen-tiation condition was most closely dictated by thediscussion of the relatively poor differentiation ofthe 5-4 category structure itself, as described inSmith and Minda’s (2000) consideration of 30replications of this category structure. Specifically,they evaluated the 5-4 categories in terms of “struc-tural ratio” as a measure of category differentiation(related to a similar concept from Homa et al.,1979); that is, the ratio of within-category simi-larity (including self-similarity) to between-cat-egory similarity in terms of average numbers offeatures shared between instances. The ratio forthese categories is 2.4/1.6= 1.5, where 1 representsa complete lack of differentiation with identicalinstances in both categories. Hence these instances


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are quite poorly differentiated.1 However, ourswapping the category assignment of two pairs ofinstances from the standard to the low-differen-tiation condition (Table 1) resulted in even poorerdifferentiation, as measured by a structural ratioof 2.2/1.9= 1.2; that is, fewer shared featureswithin the same category and more shared featuresbetween categories. Before moving on to why wewere interested in learnability differences, it isworth emphasizing that, while a variety of theoreti-cal perspectives predict these differences, ourresearch does not presuppose the truth of any ofthese perspectives. Rather our conclusions arebased on the learnability differences we observedas reported below.

The theoretical rationale for this instance swap-ping manipulation was simply that if participantslearn the standard 5-4 category task as an instanceidentification task, with no category influence fromother category members on responding, then itshould not matter how the instances are assignedto categories. The low-differentiation categorystructure should be as easy to learn as the standardone and all the instances in both conditions shouldbe equally easy to learn because the participant issimply learning to assign a label to each uniqueinstance. On the other hand, if there is a categoryinfluence on learning, then the low-differentiation5-4 structure should be even harder to learn thanthe standard 5-4 structure, and differences ininstance learnability should correspond to differ-ences in similarity across instances.

Specifically, the dual-system perspective of pro-totypes plus memory for single instances predictsno category influence for either learning conditionbecause these poorly differentiated structures donot give the prototype-based categorizationsystem anything to work with, leaving respondingto be based solely on memorized single instanceswithout generalization. This implies that test accu-racies on the different training items (A1–B4 in

Table 1) should not be systematically differentfrom each other and the resolution of ambiguitiesin terms of nearest single category exemplars forthe generalization test items, T1–T7, should bearbitrary (e.g., for the standard condition incolumn 2, Table 1, T5 2121 shares an equalnumber of features with A4 1121 and with B32221). Test items should not reflect the influenceof multiple instances or the number of prototypicalfeatures as the prototype-based categorizationsystem should have been effectively ablated.Generalization test items with many featurestypical of the prototype of one category (e.g., T31111 for the standard condition in Table 1)which match many exemplar features of that cat-egory should be no more likely to be categorizedas members of that category than instances withfewer features (e.g., T6 2211 for the standard con-dition in Table 1) because neither matches a train-ing exemplar exactly and both have multipleambiguous matches based on subsets of features.

The single-system exemplar theory, on the otherhand, is consistent with differences in accuracy forthe training items corresponding to a categoryinfluence in terms of differences in similarity tomultiple category instances. That is, categoryinstances that are similar to many other categoryinstances and correspondingly dissimilar toinstances in the other category should be easier tolearn than category instances that are not similarto multiple instances in the same category andthat are rather similar to instances in a contrast cat-egory. Likewise, since categorization and instancememory are assumed to be part of a singlesystem, the influence of multiple instances onresponding is consistent with prototypicalityeffects in the generalization test items: items withmany typical features of a given category shouldtend to have a higher proportion of responses forthat category than items with fewer typical featuresbecause they will tend to be similar to many

1Structural ratio as a measurement does not have a fixed upper bound corresponding to perfect differentiation as, among other

reasons, sharing zero features with instances of a contrast category leaves the ratio undefined to avoid division by 0. But some indication

of a relevant upper bound can be had by making all of the instances of Category A identical to the category prototype, A 1111, and

likewise the B instances to B 2222 except for one B instance that shares a single feature with A, i.e., B2221. In this case the structural

ratio is 3.8/0.3= 12.7, clearly a very long way from the 1.5 for the standard 5-4 structure.



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instances of the category. Lastly, exemplar theory isconsistent with a category influence in terms ofdifferences in learning and generalization test per-formance between the standard and low-differen-tiation conditions based on differences insimilarity relations across instances for the twoconditions.

Method

ParticipantsThere were 40 participants in the standard and 41participants in the low-differentiation conditions,all undergraduate psychology students at CardiffUniversity.

MaterialsThe abstract category structure for the standardcondition in Table 1, column 2 is the 5-4 structurefrom Medin and Schaffer (1978). There are fiveinstances of Category A, four instances ofCategory B (at the top of column 2, Table 1), aswell as seven generalization test items (at thebottom of column 2, Table 1). Each categoryinstance is represented in a row and was composedof features from four binary-valued stimulusdimensions as indicated by 1s and 2s in the table.The low-differentiation condition in Table 1,column 3, was generated from the standard con-dition by swapping the category assignment fortwo pairs of instances: A1 1112 was switchedwith B3 2221 in the standard structure to be A12221 and B3 1112 in the low-differentiation con-dition, and A3 1211 was switched with B2 2112to become A3 2112 and B2 1211. In Table 1, theswitched items are in bold in the low-differen-tiation condition. All other training and testitems were the same in the two conditions.

The stimuli were the alien insects from Johansenand Kruschke (2005). Four binary-valued stimulusdimensions were randomly assigned to the fourabstract category dimensions for each participantin the standard and low-differentiation conditions.These four stimulus dimensions were randomlychosen from a set of five possible dimensions—shape of the head (round or square), orientationof the nose (up or down), length of the tail (short

or long), shape of the antennae (curved or straight),and leg number (eight or four)—and the fifthdimension had a fixed value across all the stimulifor a given participant. In addition, the polarity ofthe assignment of stimuli within each stimulusdimension was also randomly assigned betweenparticipants as was the assignment of the categorylabels LORK and THAB to the abstract categoriesA and B in Table 1. Each stimulus was displayedon a computer monitor, and participants indicatedtheir response by mouse clicking in a box contain-ing one of the category labels.

ProcedureThe procedure for both the standard and low-differentiation conditions was the same as theclassification condition in Johansen and Kruschke(2005). Participants from the two conditions wererun simultaneously, half in one condition and halfin the other based on even or odd participantnumbers, and the participant instructions wereidentical throughout. The instructions told partici-pants that they should learn to assign the instancesto categories and would receive feedback. Theywere also warned that there would be a test phaseat the end of the experiment to evaluate howmuch they had learned and that they would notreceive corrective feedback during this phase.

Each training trial displayed one of the nine cat-egory instances from either the standard or low-differentiation conditions shown at the top ofTable 1. After making their response, participantsreceived feedback, either CORRECT! orWRONG!, the correct category label was displayedabove the stimulus, and participants were given upto 30 s to study the correct answer. The messageFASTER was displayed if they did not maketheir initial response within 20 s of the start ofthe trial. They started the next trial by clickingthe mouse on a box that had the message “Afteryou have studied this case (up to 30 seconds),click here to see the next one.” If they did notstart the next trial within 30 s of their initialresponse, the message FASTER appeared andthen the next trial started automatically.

In the training phase, the nine training instancesin each of the two conditions were presented in 25


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randomly ordered blocks for a total of 225 trainingtrials. After the training phase, participants wereinstructed that they would be tested without feed-back but that they should base their responses onwhat they learned when feedback was beinggiven. During the test block, the nine trainingitems and seven test items for the standard andlow-differentiation conditions (Table 1) were pre-sented in random order. Participants were givenno feedback on each trial other than that theirresponse had been recorded.

Results and discussion

The averaged learning curves for all participants bycondition, standard or low-differentiation, are inthe top panel of Figure 1, which shows a systematicdifference between conditions throughout thecourse of learning: The low-differentiation struc-ture was considerably harder to learn than the stan-dard structure as measured by average accuracyacross sets of five blocks, F(1, 79)= 35.053,MSE= 0.028, p, 0.001, in an ANOVA withtraining condition and training block set asfactors. In addition, the proportions of goodversus poor learners in reference to a learning cri-terion (≥0.75 in the last two blocks of training, asin Johansen & Palmeri, 2002), was much higherin the standard condition (17/40 good learners)than in the low-differentiation condition (3/41),χ2(1)= 13.48, p, 0.001. In fact, the differencesin performance for the two learning conditionsoccurred across the course of learning even in therelatively poor learners who did not ultimatelyachieve the ≥0.75 criterion as shown in thebottom panel of Figure 1. (We do not report theresults for the best learners in this way as therewere only three good learners in the low-differen-tiation condition). Overall the standard categorystructure was easier to learn throughout andresulted in higher performance at the end of learn-ing compared to the low-differentiation structure.

However, overall average accuracy does not tellthe complete story. Importantly, we need to askwhether there were response differences betweencategory instances, and we need to examine testgeneralization to new instances. In their study,

Blair and Homa (2003) reported neither of theseanalyses, but they are crucial for differentiatingthe dual-system theory (a prototype-based categor-ization system plus a non-generalizing memory forinstances system) from the single-system exemplartheory, particularly in the context of assessing cat-egory influence.

Figure 2 shows the Category A response pro-portions from the test phase for the nine trainingand seven generalization test items in each trainingcondition (Table 1) based on all participants inboth conditions. The horizontal lines are theapproximate 95% binomial confidence intervalaround 0.5 and provide a useful reference for theamount of learning at the end of training: All but

Figure 1. Experiment 1 training condition accuracy averaged across

sets of five training blocks for all participants (top panel) and for

poorer learners (bottom panel) who did not ultimately achieve the

learning criterion of ≥0.75 in the last two blocks of training

(error bars are standard errors).



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one of the training items fell outside this interval inthe standard condition whereas all but two of thetraining items fell within this interval in the low-differentiation condition. Thus the test phaseresults also show that accuracy on the individualtest items was generally higher in the standard con-dition than the low-differentiation condition.

Further, there were systematic and stable differ-ences in test trial performance within the standardcondition. Figure 3 shows performance by

condition for good versus poor learners, i.e., highversus low end of training accuracy, as specified inreference to the learning criterion. For the standardcondition, similar qualitative patterns of respond-ing occurred in the good versus poor learners,e.g., A1, A2, and A3 (labels from the standard con-dition in Table 1) were the best learned instancesfrom Category A and B3 and B4 from CategoryB. Also the generalization test item correspondingto the prototype of A, T3 1111, was strongly

Figure 2. Experiment 1 test trial response proportions by training condition with an approximate 95% binomial confidence interval on the

population proportion of 0.5 (based on n= 40 for simplicity).


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assigned to Category A while T7 2212 was quitestrongly assigned to Category B in both.Importantly, these patterns of responding also cor-relate closely with the data from Medin andSchaffer (1978), shown at the bottom of Figure 3,r= 0.94 for the good learners. The contrast

between good and poor learners in the low-differ-entiation condition is not informative becausethere were so few good learners, and there wasonly weak evidence for differences between thetest items in the low-differentiation condition,though it was by no means completely absent.

Figure 3. Experiment 1 test trial response proportions by training condition separated for high- and low-accuracy participants in reference to a

learning criterion,≥0.75 average accuracy in the last two training blocks. Data fromMedin and Schaffer’s (1978) Experiment 3 are shown for

reference.



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In addition, the differences in training trial per-formance in the standard condition’s test blockwere quite stable because they correspond tosimilar differences throughout the course of learn-ing. Figure 4 shows learning curves for differenttraining trial types by condition (Table 1) interms of proportions of Category A responses aver-aged into sets of five training blocks and based onall participants. As in the test data in Figure 2,exemplars A1, A2, and A3 as well as B3 and B4were the easiest to learn in the standard conditionand this pattern persisted throughout learning.On the other hand, the training items were onlyweakly different from each other in the low-differ-entiation condition (on the right in Figure 4), asemphasized by the fact that some Category Aitems were not even systematically differentiatedfrom the Category B items.

The most compelling evidence for category influ-ences on learning in the standard condition comesfrom a comparison of individual category instances

that had the same category assignment in both thestandard and low-differentiation conditions andwere learned well in the standard task. ConsiderA2 1212 (shown by squares connected with solidlines in both conditions in Figure 4). There were sys-tematic differences between conditions throughoutlearning for this item, with strong assignment toCategory A in the standard condition and weakassignment to Category B in the low-differentiationcondition (despite the feedback to the contrary in thelow-differentiation condition). Likewise, B4 2222(shown by circles connected by dashed lines inboth conditions in Figure 4) was quite stronglyassigned to Category B in the standard conditionthroughout learning, but weakly assigned to Athroughout most of learning in the low-differen-tiation condition. The remaining category instanceswere not as clearly differentiated between theconditions, but these instances were not learnedparticularly well in the standard condition in thefirst place.

Figure 4. Experiment 1 Category A response proportions by condition and with mean block accuracy averaged across sets of five training blocks

for all participants (error bars are standard errors).


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In summary, category membership in the stan-dard 5-4 structure has a pronounced but differentialinfluence on the learnability of exemplars in refer-ence both to each other and to members of a morepoorly differentiated 5-4 structure. Further, thesedifferences are conceptually not compatible withparticipants treating the standard task pragmaticallyas an identification learning task with no generaliz-ation across instances and no category influences onlearning. Overall, these data indicate that there arecategory influences on learning of the standardMedin and Schaffer (1978) 5-4 category structuredespite a lack of category advantage for that structure(Blair & Homa, 2003) and despite the difficulty oflearning it. In addition, exemplar modelling sup-ports this category influence conclusion.

Exemplar modelling of the results

Results from the 5-4 category structure have beenmodelled and discussed many times in the past(Medin & Schaffer, 1978; Nosofsky, 2000; Smith&Minda, 2000; etc.), so it will come as no surprisethat the exemplar model provides a good account ofthe results from the present experiment as detailedbelow. However, the deeper purpose of this model-ling analysis is to take a closer look at how theexemplar model accounts for the results in thecontext of two contrasting conclusions: firstly,

Blair and Homa’s (2003) no-category-advantageconclusion that this category structure inducesinstance memorization with no generalizationacross instances and, secondly, the fact that thereare clear category influences on learning for thisstructure.

Category learning research has commonly insti-tuted a learning criterion such that only those par-ticipants that have learned the categoriessufficiently well are included in the key data set,which is then used to address primary research ques-tions such as how participants represent categories,use them, etc. Moreover the assessment of the par-ticipant proportions who reach the various criteriafor the 5-4 structure have lead Blair and Homa(2003) as well as Smith and Minda (2002) toemphasize the relative difficulty of learning thisstructure, with substantial proportions of partici-pants not learning to criterion. However, wehave focused on modelling the results for all partici-pants as conceptually a learning criterion has thepotential to compress or mask differences ininstance learnability against a ceiling of perfectperformance.

Figure 5 shows the exemplar model’s best fitpredictions plotted against the data from the stan-dard and low-differentiation conditions respect-ively. (The details of the model and themaximum likelihood modelling procedure can be

Figure 5. Exemplar model best fit predictions for the standard and low-differentiation conditions of Experiment 1, where each point

corresponds to one of the instances in Table 1.



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found in the Appendix.) The model does a reason-able job of accounting for the data in both con-ditions, with an overall fit of G2= 10.270corresponding to a root mean squared deviation(RMSD) of 0.053 for the standard condition2

(with dimensional attention parameters of 0.369,0.108, 0.297, and 0.227, for the four dimensionsrespectively, and a similarity scaling parameter ofc= 4.040) and with an overall fit of G2= 15.146corresponding to RMSD= 0.073 for the low-differentiation condition3 (with dimensional atten-tion parameters of 0.406, 0.100, 0.339, and 0.155,respectively, and a similarity scaling parameter ofc= 2.746).

Tables 2 and 3 also show the exemplar model’spredictions for the standard and low-differentiationconditions by trial type, where the data and modelprediction values for each trial type are the datapoints in the scatter plots shown in Figure 5. Inparticular, the column in Tables 2 and 3 labelled“SumSim A” has the sum of each test item’s simi-larities to all the exemplars in Category A, and“SumSim B” is the sum of the item’s similaritiesto all the exemplars in Category B. If a test itemperfectly matches an exemplar in the category rep-resentation, then its similarity to that exemplar is1.0. Since the training items, A1–B4, all exactlymatch one item, the extent to which the summedcategory similarities for these items are greaterthan 1.0 partly indexes a category influence onresponding; that is, the influence of exemplarsother than the perfectly matching memorizedinstance. As none of the training items A1–B4were members of both categories, a training itemnever perfectly matched an exemplar in the oppo-site category, so the summed similarity to exem-plars of the opposite [category] can be less than1.0, but it doesn’t have to be as the cumulative simi-larity to multiple exemplars has the potential to begreater than 1.0.

The training items from the standard conditioncan be divided into high-accuracy items (A1, A2,A3, B3, and B4) and low-accuracy items (A4,A5, B1, and B2) in Figure 2. It is important toemphasize that this is not an arbitrary division,but one both strongly suggested by the standardcondition learning curves (Figure 4) and widelyreplicated. For example, this pattern of testingtrial accuracies occurred in Medin and Schaffer’s(1978) Experiment 3 shown at the bottom ofFigure 3, in the various additional data sets sum-marized in Figure 7, and in the average data from30 replications of this category structure reportedby Smith and Minda (2000).

For the high-accuracy training items from thestandard condition, the average of the summedsimilarity to members of their own category inTable 2 is 1.92. If self-similarity is removed fromthis by subtracting 1, then the proportion of cat-egory similarity due to other exemplars is 0.92/1.92= 0.48, or roughly half of the category simi-larity. In contrast, the average summed similarityfor low-accuracy training items was 1.36, so theproportion due to other category exemplars is0.36/1.36= 0.26, or only about one quarter of thecategory similarity. Correspondingly, the averagesummed similarities of the high-accuracy trainingitems (Table 2) to members of the opposite cat-egory was quite low, 0.40, while twice as high forthe low-accuracy items, 0.80.

The division of the low-differentiation con-dition training items (Table 3) into a high-accuracyset (A1, A3, A5, B1, and B3) and a low accuracy set(A2, A4, B2, and B4) was somewhat more arbitrarybecause this structure was much harder to learn andthe specific item learning curves in Figure 4 weremore poorly differentiated. However, even in thisvery poorly differentiated category structure, theaverage summed similarity for high-accuracyitems to members of their own category in Table

2Fitting the model with RMSD directly rather than G2 resulted in a virtually identical fit and set of parameters as well as predicted

values: RMSD= 0.053, with dimensional attention parameters of 0.371, 0.102, 0.301, and 0.226, respectively, and a similarity scaling

parameter of c= 4.031. The (unreported) scatterplot of the model’s predictions against the data was virtually identical to the left panel

of Figure 5.3 Fitting the model with RMSD directly rather than G2 also resulted in extremely similar parameters, fit, and predictions for these

data: with dimensional attention parameters of 0.403, 0.126, 0.321, and 0.150, respectively, and a similarity scaling parameter of c=2.959. The (unreported) model predictions were also very similar to those in the right panel of Figure 5.


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3 was 2.02, versus 1.64 for the low-accuracy items.With self-similarity removed, the proportion ofcategory similarity due to other exemplars was0.51 for high-accuracy items and 0.39 for low-accuracy items. So even for this poorly

differentiated structure the amount of categoryinfluence was somewhat larger for high- than forlow-accuracy items, though the difference was notas large as for the standard condition data. Butthe key difference from this account of the standard

Table 3. Exemplar model predictions for the low-differentiation condition from Experiment 1

Trial types Low-differentiation Data Model SumSim A SumSim B

A1 A 2 2 2 1 0.61 0.64 1.83 1.01

A2 A 1 2 1 2 0.46 0.48 1.69 1.84

A3 A 2 1 1 2 0.63 0.70 2.18 0.92

A4 A 1 1 2 1 0.54 0.55 1.66 1.37

A5 A 2 1 1 1 0.63 0.75 2.25 0.74

B1 B 1 1 2 2 0.34 0.42 1.33 1.84

B2 B 1 2 1 1 0.37 0.46 1.49 1.78

B3 B 1 1 1 2 0.32 0.45 1.62 1.99

B4 B 2 2 2 2 0.39 0.50 1.44 1.43

T1 ? 1 2 2 1 0.51 0.54 1.51 1.30

T2 ? 1 2 2 2 0.37 0.44 1.27 1.64

T3 ? 1 1 1 1 0.39 0.47 1.53 1.73

T4 ? 2 2 1 2 0.68 0.67 1.91 0.96

T5 ? 2 1 2 1 0.61 0.67 1.80 0.89

T6 ? 2 2 1 1 0.68 0.71 1.96 0.81

T7 ? 2 1 2 2 0.61 0.53 1.46 1.28

Both the data and model predictions are in terms of Category A response proportions. SumSim A indicates each test item’s summed

similarity to all the exemplars of Category A, and SumSim B to all the exemplars of Category B.

Table 2. Exemplar model predictions for the standard condition from Experiment 1

Trial types Standard Data Model SumSim A SumSim B

A1 A 1 1 1 2 0.78 0.78 2.12 0.59

A2 A 1 2 1 2 0.83 0.83 2.18 0.44

A3 A 1 2 1 1 0.88 0.90 2.00 0.23

A4 A 1 1 2 1 0.68 0.70 1.46 0.63

A5 A 2 1 1 1 0.68 0.66 1.36 0.70

B1 B 1 1 2 2 0.33 0.44 1.00 1.27

B2 B 2 1 1 2 0.40 0.39 0.86 1.34

B3 B 2 2 2 1 0.30 0.23 0.45 1.54

B4 B 2 2 2 2 0.05 0.14 0.28 1.74

T1 ? 1 2 2 1 0.70 0.67 1.19 0.59

T2 ? 1 2 2 2 0.48 0.47 0.89 1.01

T3 ? 1 1 1 1 0.83 0.87 1.83 0.27

T4 ? 2 2 1 2 0.43 0.40 0.74 1.11

T5 ? 2 1 2 1 0.30 0.36 0.62 1.12

T6 ? 2 2 1 1 0.50 0.60 1.07 0.70

T7 ? 2 1 2 2 0.20 0.19 0.34 1.43

Both the data and model predictions are in terms of Category A response proportions. SumSim A indicates each test item’s summed

similarity to all the exemplars of Category A, and SumSim B to all the exemplars of Category B.



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condition was that for the low-differentiation con-dition, average summed similarity to members ofthe contrast category for high-accuracy items was1.13 and for-low accuracy items was 1.54. Hencecontrast category similarity was substantiallyhigher in the model’s account of the low-differen-tiation condition, as would be expected from thepoorer differentiation compared to the standardstructure.

In summary, the purpose of this assessment isnot to argue that prior modelling analysis of datafrom this category structure contrasting exemplarand prototype theory is wrong. Rather thepurpose has been to look at how the exemplarmodel accounts for the data in the context of theclaim that learning is based on instance memoriza-tion without generalization between instances. Theexemplar model explains the differences in trainingitem accuracy observed in the data in terms ofdifferential category influences on learning fromboth the member and contrast categories, that isdifferential generalization across multiple instances.In fact, we propose that it is the relatively poordifferentiation of these category structures thatenhances differential item learnability and makesarguing for nongeneralizing exemplars so implausi-ble. While selective attention helps people and theexemplar model to differentiate the categories andso achieve high training item accuracy in the firstplace, differential within- and between-categorysimilarity compellingly explains differential learn-ability. The latter is very hard to explain, in con-trast, if this categorization task is equivalent to anidentification learning task with no exemplarcrosstalk.

EXPERIMENT 2

The basic claim we have critiqued in Experiment 1is that learning of the 5-4 category structurejust invokes simple instance memorization withno generalization across instances. The purposeof Experiment 2 was to provide a methodologicalcontrast to the standard learning with feedbackparadigm used in Experiment 1 and substantiallyemphasize memorization by explicitly telling

participants to memorize the category instancesfrom a simultaneously presented summary (Figure6). The basic intent of this paradigm was toinduce participants to encode the category instancesfrom the standard condition (column 2, Table 1)into memory in as methodologically simple a wayas possible. In the standard category learning para-digm, participants learn a category structure bycategorizing single instances over a protractedseries of trials with feedback where the resultingerror drives selective attention and graduallyimproves associative performance. Conceptually,selective attention driven by explicit feedbackmight operate to make cross-instance similaritymore differential than it might otherwise havebeen. In contrast, participants in this experimentwere simultaneously presented with the instancesfrom the standard 5-4 structure (column 2, Table1) grouped with category labels (Figure 6) andexplicitly instructed to memorize them in a shortinterval. Thus participants received no feedbackbecause there were no responses and no trialstructure.

Method

ParticipantsThere were 30 participants, who were undergradu-ate students at University College London orCardiff University.

Materials and procedureParticipants were instructed to memorize theinstances from two categories on a categorysummary sheet as shown in Figure 6. The categoryinstances were described as being rocket ships fromPlanets A and B. After participants were given fiveminutes to memorize these instances, the summarysheet was removed, and they were asked to assigneach of the 16 cases from the standard conditionin Table 1 to one of the categories by circling oneof the two possible category labels below theinstance (Planet A or Planet B). For methodologi-cal simplicity, the presentation order of the testtrials was the same for all participants (T1, T4,T2, T3, T5, T6, T7, A1, B4, B1, A5, A3, A4,B3, A2, and B2), as was the assignment of abstract


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to physical dimensions—Dimension 1=wingwidth (1= narrow/2=wide), Dimension 2=cone shape (1= curved/2= pointed), dimension3= booster number (1/2), and Dimension 4=portal orientation (1= down/2= up).

Results and discussion

Overall categorization performance on the nine cat-egory instances resulted in an average accuracy of0.73 based on all participants. Comparison with

various published learning results from the standardparadigm and different numbers of training blocks,on the right in Figure 7, shows that this is similar tothat observed in the learning results from after a full16 blocks of training, 0.72 (Nosofsky, Palmeri &McKinley, 1994), where each block had all ninecategory instances for a total of 144 trials. Thusthe overall performance level obtained with thepresent explicit memorization task is highly con-sistent with one aspect of Blair and Homa’s(2003) argument, that participants in the standardparadigm memorize the instances of the 5-4 cat-egory structure.

The left panel of Figure 7 shows that categoriz-ation performance on the nine category instances,A1–B4, was highly varied, ranging from almostchance accuracy (e.g., instance B1), to more than90% accuracy (instance B4). Importantly, this vari-ation was not random but rather was systematic andhighly correlated with the published learningresults based on different amounts of training inthe standard trial-by-trial learning with feedbackparadigm (the right panels of Figure 7), e.g., r=0.92 with results from after 32 blocks of training(Johansen & Palmeri, 2002). In particular, theseresults duplicated the same differences in trainingitem accuracy observed in the standard conditionof Experiment 1 both at the end of learning(Figure 2) and over the course of learning (Figure4); that is, higher accuracy on A1–A3, B3, and

Figure 6. Category summary sheet from Experiment 2 with

instances from two categories corresponding to the abstract category

structure for the standard condition in Table 1.

Figure 7. Average data for the explicit memorization task from Experiment 2 in terms of Category A response proportions, left panel. The last

three panels are test results after 16 blocks, 25 blocks, and 32 blocks, respectively, of trial-by-trial feedback learning for the standard 5-4 category

structure shown in column 2, Table 1 (Johansen & Palmeri, 2002; Nosofsky et al., 1994; Palmeri & Nosofsky, 1995). The dashed line is the

guessing performance reference at 0.5 because there were two categories.



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B4 than on A4, A5, B1, and B2. And lastly, thegeneralization test results for T1–T7 showed amoderate level of correspondence to those fromthe learning reference data, most notably in termsof a large prototype effect for T3, the prototypeof Category B.

The comparability of these to prior resultsdemonstrates that not only were there differencesin accuracy for the category members, but thismethodologically simple paradigm producedresults that are surprisingly similar to those fromthe far more elaborate multi-trial learning withfeedback paradigm. In the context of the dual-system prototype theory being considered here,there are two contrasting interpretations that canbe drawn from these results depending onwhether they are considered to represent the com-plete ablation or the active facilitation of the mind’scategorization system, as distinct from the nonge-neralizing-exemplar-memorization system.

One perspective is to use the minimalistinstance-memorization paradigm to argue thatthe explicit memorization instructions shouldeven more strongly invoke instance memorizationand hence even more completely ablate the categor-ization system. In addition, the lack of feedbackmight further minimize the effects of selectiveattention and similarity, also arguably key com-ponents of the categorization system, and leaveresponding to be firmly based on the nongeneraliz-ing instance memorization system. From this per-spective, the fact that the differences in trainingitem accuracy in this experiment so closely replicatethose from the standard paradigm strongly arguesagainst nongeneralizing exemplars in the dual-system theory. So even when instances areencoded into memory in as simple a way as possiblethere are still clear category influences, and it is notclear from the perspective of parsimony what thedual-system account adds here.

However, an alternative perspective is that ourinstance-memorization paradigm had the exactopposite of the desired effect; far from completelyablating the categorization system, maybe thisparadigm actively facilitated the categorizationsystem by allowing participants to more easilyobserve the commonalities and differences

between instances, both within and between cat-egories. That is, the summary presentation meth-odology effectively enhanced the perceiveddifferentiation of the categories and thus actuallyactivated rather than ablated the categorizationsystem. Probably the most compelling evidencefor this perspective is that the summary memoriza-tion paradigm produced a large prototype effectduring the testing phase (T3), as large as that inthe extensive training condition from Johansenand Palmeri (2002). But if the summary memoriza-tion results represent enhanced performance of theactivated categorization system then that systemproduced results that look remarkably similar tothose from the standard task in Experiment 1,which are so well accounted for by the exemplarmodel in terms of generalizing across multiple cat-egory instances. Thus from the perspective of par-simony, it is unclear what dual-system prototypetheory with nongeneralizing exemplar memory isadding in this alternative interpretation.

GENERAL DISCUSSION

The two experiments presented here evaluated cat-egory influences on instance learnability in the 5-4category structure (Medin & Schaffer, 1978) fromtwo different methodological perspectives.Experiment 1 contrasted feedback learning in thestandard 5-4 structure with learning in an evenmore poorly differentiated category structure gen-erated by switching the category assignment oftwo pairs of instances. Blair and Homa (2003)compared the standard category learning taskwith an identification learning task and arguedthat the comparable learnability of the two tasksindicated a lack of “category advantage”, whichthey took as evidence that responding was basedon instance memorization with no generalizationacross instances. However, the present results indi-cate that a more poorly differentiated categorystructure was even harder to learn—a difficultresult to explain if multiple category instances arenot influencing responding, particularly as therewere systematic differences in performance acrosscategory instances. Further, as would be expected


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from the history of this category structure, theexemplar model provided a good account of thesedata. In particular, it accounted for the differentiallearnability of the training items in terms of differ-ential similarity to multiple instances both withinand between categories. In essence, Experiment 1uses a variation of Blair and Homa’s categoryadvantage methodology to show an advantage inlearning some instances in the standard 5-4 struc-ture compared to a less differentiated categorystructure. Pure instance memorization withoutgeneralization cannot explain this observation.

Experiment 2 was a minimalist memorizationtask where participants were presented with a sim-ultaneous display of all the category instances(Figure 6) and given five minutes to memorizethem. The results of this task look strikingly likethose from the standard category learning paradigm(e.g., Johansen & Palmeri, 2002; Medin &Schaffer, 1978; Nosofsky et al., 1994; Palmeri &Nosofsky, 1995), despite the large differences inthe methodology. While this suggests that instancememorization is a fundamental part of that para-digm—consistent with the claims of Blair andHoma (2003) and Smith and Minda (2000; alsoSmith, 2005)—these findings also indicate thateven this simple way of encoding instances intomemory resulted in a category influence on learningand generalization. This category influence is basedon comparison to more than one instance andyields clear prototypicality effects, even thoughthis poorly differentiated category structure puta-tively does not lend itself to anything other thanthe memorization of specific instances with no gen-eralization across multiple instances: “The lack of acategory advantage … strongly suggests that par-ticipants who learn these categories learn them bymemorization and receive no benefit from general-izing among members of the same category” (Blair& Homa, 2003, p. 1298).

At minimum, these results suggest that the con-clusions from Blair and Homa’s (2003) categoryadvantage methodology should be viewed withcaution. Their argument is that lack of categoryadvantage for category learning compared to identi-fication learning indicates a poorly differentiatedcategory structure unrepresentative of real world

categories which does not invoke the brain’s categ-orization system and which is dealt with only byinstance memory. Our counterargument is thateven for this poorly differentiated category struc-ture, there are still clear category influences.

We suggest that the problem with Blair andHoma’s (2003) category advantage argument is asfollows: While categorization solely in referenceto single memorized instances certainly predicts alack of a category advantage, a lack of categoryadvantage does not necessarily imply that categoriz-ation performance is based on memorized singleinstances without a category influence of multipleinstances. The lack of category advantage canarise for other reasons in the presence of a categoryinfluence. For example, the crosstalk between indi-vidual instances may be such that learning is facili-tated for some and harmed for others and thusaverages out to being comparable to identificationlearning, but this category influence at the level ofspecific instances may not be apparent fromlooking at an overall learning rate.

More generally, it thus seems that even an elabo-rated dual-system prototype theory that has beenparadoxically motivated to make predictions aboutinstance memory fails. If category decisions arebased on more than one instance in the memoriza-tion system, as our results suggest, then this systemshould generate prototype effects, typicality gradi-ents, and so on and the added theoretical value ofa separate prototype-based “true” categorizationsystem becomes unclear. In effect, prototypetheory’s separate memory store for instanceswould be generating categorization behaviour in asimilar way to exemplar theory’s single system, atwhich point it is reasonable to ask: What is the pro-totype-based categorization system serving toexplain?

There are several possible ripostes to this con-clusion. One is to argue that the dual system proto-type plus nongeneralizing exemplar theory we haveconsidered is effectively just a straw man. However,given past criticisms of the 5-4 structure (Blair &Homa, 2003; Smith & Minda, 2000; etc.) andthe absence of a “category advantage” with thisstructure, the theory is anything but a straw man.It is distinctly non-trivial, explains a range of



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findings, and the experiments reported here could,in principle, have yielded further support. The fol-lowing reasonably summarizes this dual-systemposition (Blair & Homa, 2003, p. 1299): “Datafrom previous research using the 5-4 categorieshas been difficult for prototype models to fit, andthese data are generally seen as supporting exemplartheories. If one assumes a strong relationshipbetween memorization and categorization, thenthe failure of a prototype model can be seen as acritical weakness of the theory. If one assumesthat there is little or no relationship between mem-orization and categorization, then the 5-4 categorylearning task has little to do with categorization andis therefore an inappropriate test of prototypetheory.”

Another possible riposte to our conclusions isthat the theoretical debate has moved on from thecoarse distinction between exemplar generalizationversus nongeneralization to the more subtle distinc-tions between typicality gradients (e.g., Homaet al., 2011). We have summarized our reactionsto the dot-distortion paradigm in the introduction.In addition, our differences in instance and cat-egory learnability provide some convergingsupport for recent developments in theories of cat-egory intuitiveness involving assessments of whatmakes categories hard or easy to learn (Pothos &Bailey, 2009; Pothos et al., 2011a, 2011b). Wewould like to emphasize the overall logic andminimal conclusions of our research. We take ourresults as evidence for exemplar theory and thusstill consider it a viable candidate to explain broadareas of categorization behaviour—perhaps evenall categorization behaviour (with suitable elabor-ation). However, we acknowledge that some mayconsider research on the 5-4 category structure(Medin & Schaffer, 1978) to have reached a stateof theoretical sterility, perhaps because theybelieve that such binary-valued category structuresare unrepresentative of the real world or that proto-types clearly provide a better account of typicalitygradients, even when multiple exemplars areallowed to generalize between each other.Nevertheless, even if both of these are completelytrue, we believe that Blair and Homa’s (2003) anti-exemplar category-advantage argument is not

viable and, at minimum, this evidence againstexemplar theory should be discounted and futureprototype theories suitably constrained.

Manuscript received 13 September 2011

Revised manuscript received 13 September 2012

First published online 13 November 2012

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APPENDIX: EXEMPLAR MODELSPECIFICATION AND MODELLINGPROCEDURE

The exemplar model applied to the results of Experiment 1 was

the generalized context model (Nosofsky, 1986). In overview,

the model calculates the total similarity of a test item to all the

instances in a category and then specifies a category response

probability by contrasting that category’s summed similarity

with the total similarity to all categories. The predictions from

the model for these data were derived using the following two

equations, four free parameters, and a best fitting parameter

procedure.

In detail, each category is represented in the model by the

instances composing it, the exemplars participants were told in

the training phase were in that category (for example, A1–A5

for Category A in Table 1), each composed of features on four

binary-valued feature dimensions. The model specifies the simi-

larity of a given test item, i, to a given category exemplar, j, using

equation 1.

hij = exp −c∑dim k

wk|xik − xjk |( )

(1)

In this equation, xik is the feature value of test item i on feature

dimension k, and correspondingly xjk is the feature value of

exemplar j on the same feature dimension k. The absolute

value of the difference between these two features, ∣xik – xjk∣, isthen multiplied by the dimensional attention parameter for

feature dimension k, wk, which specifies how much a feature

difference on that dimension should matter in the similarity cal-

culation. These weighted differences are calculated for all four

feature dimensions, summed and multiplied by –c to yield the

content of the parentheses in equation 1, where c is an overall

scaling parameter for similarity. This scaled sum of weighted

feature difference values is then exponentiated to give the simi-

larity of test item i to exemplar j, ηij.Using the similarities generated by equation 1, the category

response probability that a test item i will be from Category A

is determined by equation 2. Specifically, the model calculates

P(catA | i) =

∑j[catA

hij∑j[catA

hij +∑

j[catB

hij

(2)

the total similarity of a test item i to all the instances in Category

A by summing across its similarity to each of the specific

instances in that category as in the numerator of equation 2,∑j[catA

hij . This summed similarity to the representation for

Category A is divided by the summed similarity to all the

instances in both categories, Category A on the left and

Category B on the right in the denominator.

The model’s best fitting predictions for the data in a given

condition of Experiment 1 were generated by adjusting the

free parameters to minimize the maximum likelihood statistic

G2. We have not drawn any statistical conclusions about the

goodness of fit of this model because the data substantially

violate independence. In practice, using G2 resulted in very

similar predictions to the more traditional procedure of mini-

mizing root mean squared deviation (RMSD), the discrepancy

between the model’s predictions and the data. So even though

the fits used G2, we also report RMSD to be comparable to pre-

viously reported fits of this model. Of the model’s four dimen-

sional attention parameters, wk, in equation 1, three are free

parameters and the fourth is constrained such that the sum of

the four attention parameters is 1. The overall similarity

scaling parameter c is a free parameter rather than simply

being redundant with the four attention parameters by the dis-

tributive rule. Various sets of initial free parameter values were

chosen and adjusted via a hill-climbing procedure. The

model’s best fitting parameter values and predictions for the

two conditions of Table 1 are reported in the main text.


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Documents

Instance memorization and category influence: Challenging the evidence for multiple systems in category learning