A C om posite H olographic A ssociative R ecall M odel...P sychological R eview 1982, V ol 89, N o. 6, 627-661 C opyright 1982 by the A m erican P sychological A ssociation, Inc. 03

Psychological Review1982, Vol 89, No. 6, 627-661

Copyright 1982 by the American Psychological Association, Inc.0033-295X/82/8906-0627$00.75

A Composite Holographic Associative Recall ModelJanet Metcalfe Eich

University of Toronto, Toronto, Ontario, Canada

In this article, a highly interactive model of association formation, storage, andretrieval is described. Items, represented as sets of features, are associated by theoperation of convolution. The associations are stored by being superimposed ina composite memory trace. Retrieval occurs when a cue item is correlated withthe composite trace. The retrieved items are intrinsically noisy, may be ambig-uous, and may under certain conditions be systematically distorted from theirencoded form. A discrete response is selected by matching the retrieved item toall of the items in semantic memory. The model yields several new predictionsabout errors in single-trial cued recall that depend on similarity relations amongthe to-be-remembered items, and also about the efficacy of extralist cues. Ex-periments are presented that test these predictions against human recall. Themodel is then applied to several well-known results: prototype abstraction, theA-B A-D paradigm—including the independence of the B and D responses—and the Osgood transfer surface.

This article addresses the question of howpeople associate two ideas and store the as-sociation in memory in such a way that atsome later time, when only one of the ideas

I am grateful to the many people who contributed tothis article. Among his many other contributionsthroughout the course of this work, Eric Eich providedthe name for the model described herein. Peter Liepafirst told me about holographic recall, and Bennet Mur-dock incited and kindled my interest in the hypothesis.I thank Endel Tulving for his support and guidance,Fergus Craik for his many insightul suggestions, andWilliam Batchelder for his numerous contributions tothe model. I am grateful to Robert Bjork, Thomas Wick-ens, Norman Slamecka, Gordon Logan, Paul Kolers,and two anonymous reviewers for thoughtful critiquesthat helped shape this article, I also appreciate the en-couragement of Walter Kintsch. I thank Mary Duncan,Brian McElree, Louis Narens, Henry Roediger, and EricEich for facilitating the experiments and the simulations.

This article is based on the author's doctoral disser-tation at the Department of Psychology, the Universityof Toronto. Some of the research was conducted whilethe author enjoyed the hospitality of the School of SocialSciences at the University of California, Irvine and theDepartment of Psychology, University of California, LosAngeles. This work was financially supported by NaturalSciences and Engineering Research Council 'of Canada(NSERC) fellowships to the author, an NSERC grant toBennet Murdock, and a grant to the author from theFoclissed Research Project on Perception and HigherCognitive Processes, University of California, Irvine,through the auspices of Kenneth Wexler.

Requests for reprints should be sent to Janet M. Eich,who is now at the Department of Psychology, 405 Hil-gard Avenue, University of California, Los Angeles,California 90024.

is available, they may use that idea to re-cre-ate or retrieve the other. A second questionthat follows naturally from the first is, Howare people able to retrieve such ideas?

The particular answer to these questionsthat will be investigated and elaborated herehas usually been called the holographic hy-pothesis of associations. It is not the image-like characteristics of holograms that definethe holographic hypothesis; rather, it is theformal operations of convolution and cor-relation that are important. Roughly speak-ing, association by convolution consists ofthe interation of all of the parts of one itemwith all of the parts of another. The resultis an interactive new entity. A number ofthese interactive associations may be storedin a single composite memory trace, some-what resembling a photograph that has beenexposed many times. Retrieval occurs bymeans of the operation of correlation. Theoperations of convolution and correlationwill be explained in a later section of the ar-ticle or the reader may refer to Borsellino andPoggio (1973), Murdock (1979), or Stroke(1969). What we get from this scheme—hol-ographic associations stored in a compositetrace—is a profoundly interactive memory.

Since its invention by Gabor (1948), thehologram has frequently been cited as a met-aphor for human association formation, stor-age, and retrieval, and the neurological apt-

627

628 JANET METCALFE EICH

ness of the metaphor has often been noted(Borsellino & Poggio, 1973;Cavanagh, 1976;Heerden, 1963; Julesz & Pennington, 1965;Longuet-Higgins, 1968; Metcalfe & Mur-dock, 1981; Murdock, 1979, 1982; Pribram,1971; Pribram, Nuwer, & Baron, 1974; West-lake, 1970; Willshaw, 1981; Liepa, Note 1).In addition, J. A. Anderson (1970) has re-marked that the construct of a compositetrace, which is an intrinsic part of all holo-graphic models, may be particularly appro-priate to human memory because it may giverise to creative behavior. Holographic mod-els, however, have only rarely been directedtoward explaining psychological data. Onenotable exception is Cavanagh's (1976) holo-graphic model of recognition for short listsof items. Also, Metcalfe and Murdock (1981)presented a holographic model of single-trialfree recall of unrelated words. Both of thesemodels provide a reasonably good descrip-tion of the data to which they are applied.

In this article, a traditional psychologicalvariable—similarity—will be represented ina holographic model similar to that proposedby Metcalfe and Murdock (1981). This modelwill henceforth be referred to as CHARM,which stands for composite holographic as-sociative recall model. The representation ofsimilarity will allow the highly interactivenature of the holographic association itselfand of the method of storage to becomemanifest. It will also allow the model to makesome predictions about what people will re-call in several experimental situations. Notall of these predictions are intuitively ob-vious.

CHARM initially will focus on an experi-mental situation in which people are pre-sented with a list of pairs of words to studyand remember. The words may vary in theirsimilarity to each other. The subjects will beinstructed to study the pairs as pairs, and itwill be assumed that an association is formedbetween the two words composing each pair.A short time after studying, subjects will bepresented with cue words and asked to recallthe targets. The reason for focusing on thecued recall of a once-presented list of pairedassociates is that this is the simplest situationto which CHARM can be applied. It is also thesimplest situation in which to address the

question of how two ideas may be associatedand stored and how retrieval takes place.

Although the initial focus of this article ison implications of the holographic associa-tion and the composite trace in single-trialcued recall, several extensions of the modelto other paradigms will be presented in a latersection. These extensions—to prototypelearning, the A-B A-D paradigm, and theOsgood transfer surface—provide some in-sight into the generality as well as the limi-tations of CHARM.

Description of CHARM

CHARM is a fairly simple holographicmodel of associative recall. A main assump-tion of the model is that items are representedas patterns of features rather than as discreteindivisible units. These items may vary intheir similarity to each other. Two such itemsare associated interactively by means of theoperation of convolution. The result is storedin a composite memory trace that consistsof the superimposition of other associationsas well. Retrieval occurs by means of theoperation of correlation. Finally, the re-trieved item is identified as a particular re-sponse by being matched to every item in alexicon representing semantic memory.

CHARM stems from a variety of sources,and each of the main constructs in the modelhas precedents in the literature. For instance,the representation of items in terms of setsof features is well known (e.g., Bower, 1967;Estes, 1972;Tversky, 1977; Wickens, 1972).The representation of similarity will be interms of feature overlap. This representationhas often been used before (e.g., Reed, 1973;Smith, Shoben, & Rips, 1974; Tversky, 1977),although, to my knowledge, similarity hasnot previously been studied within a holo-graphic framework.

The holographic association in vector no-tation, as will be used here, has been specifiedbefore (Borsellino & Poggio, 1973). This as-sociation appears in a number of other mod-els (Cavanagh, 1976; Heerden, 1963; Julesz& Pennington, 1965; Longuet-Higgins, 1968;Murdock, 1982; Willshaw, 1981; Liepa, Note1). The model from which CHARM most di-rectly derives was given by Liepa (Note 1),

COMPOSITE HOLOGRAPHIC ASSOCIATIVE RECALL MODEL 629

and work on the present model was begunin collaboration with Bennet Murdock (Met-calfe & Murdock, 1981). Murdock (1982) haselaborated a holographic model that storesboth item and associative information in asingle trace. Murdock's (1982) paper alsodeals with the issue of noise distributions—an issue that will not be covered in the pres-ent article. The main constructs under in-vestigation here—the holographic associa-tion and the composite trace—are the samein CHARM as in the above-cited models, andCHARM depends on the theoretical advancesmade by these investigators.

The construct of a composite trace is anintegral part of all holographic memory mod-els but has also been employed in modelsthat do not use the associative operation ofconvolution and the retrieval operation ofcorrelation (J. A. Anderson, 1970, 1972,1973, 1977; J. A. Anderson, Silverstein, Ritz,& Jones, 1977;Kohonen, 1977, 1980). Someof the psychological as well as neurologicalimplications of this construct have been de-lineated by J. A. Anderson (1977), the mostimportant being that it may give rise to cre-ative behavior.

The distinction between semantic and ep-isodic memory is a familiar one (Tulving,1972). In this article, the composite-holo-graphic trace refers (roughly) to episodicmemory. A pattern recognizer correspondingto semantic memory is included as well.These two levels of representation allowCHARM to solve the problem of response am-biguity that occurs in other holographic anddistributed models (e.g., Willshaw, 1981;Liepa, Note 1). The construct of a semanticpattern recognizer relates to response avail-ability (e.g., Martin, 1965; Underwood, Run-quist, & Schulz, 1959; Underwood & Schulz,1960). The identification process used inCHARM, by which a particular response isselected, bears a semblance to the resonanceprocess given in Ratcliff's (1978) item-rec-ognition model.

Each part of the model is thus familiar(though some parts may be more familiarthan others). What I do in the present articleis to mesh these several parts into a modelthat makes some predictions about recall.

There are, of course, many things one

would like such a model to do and explain.The strategy I adopt in the present article isto specify the model sufficiently to allowsome of the implications of the interactivenature of the association and the compositenature of the trace to become obvious andtestable. Recourse to other constructs (how-ever reasonable) was specifically avoided inan effort to show what sorts of predictionsand results could (and could not) be attrib-uted direcly to the composite-holographictrace. In this section of the article, I explainthe mechanisms for association formation,storage, and retrieval and describe some re-sults of varying semantic similarity. First,however, the manner in which the individualitems are represented needs to be examined.

Representation of Individual Items

In CHARM, items are represented as or-dered sets of features. The work of Tversky(1977) indicates that the individual featuresof items, and not just their point location inmultidimensional space (Hutchinson &Lockhead, 1977), may be important for cer-tain tasks, such as judgements of similaritiesand differences. However, the featural rep-resentation, as opposed to a point-locationrepresentation, is necessary in the presentmodel because the features themselves par-ticipate in both the associative and the re-trieval operations.

In contrast to certain other models (seeMedin & Schaffer, 1978; Reed, 1973), inwhich items are represented by a rather smallnumber of features, CHARM assumes that thenumber of features representing a given itemis quite large. Apart from this quantitativedifference, the concept of similarity as featureoverlap, as it has been developed in earliermodels, applies quite readily to CHARM andsimplifies the analysis of similarity.

The features in each item are coded asnumbers and are assumed to have positiveand negative values, with an expected meanof zero. This coding scheme is analogous tothe semantic differential. However, Batch-elder and Narens (1977) have shown that theidentity of particular features, even underhighly circumscribed conditions, may not beuniquely determinable. Because this is the


case, it seems appropriate to consider the fea-tures to be abstract.

The numerical values of the features mayvary from item to item, and it is the differ-ence in overall pattern that characterizeseach item. The strength of a feature, as givenby its absolute value, is an indication of howimportant that feature is in the representa-tion of the item. In a later section, once someof the implications of similarity have beendescribed, the question, "More important forwhat?" will be addressed in the context ofcued recall. If the average absolute value ofall of the features of one item were greaterthan that of another item, the first itemwould be said to be stronger than the second.

It is assumed that the numerical value ofa particular feature within an item is inde-pendent of the values of the other featureswithin the same item. Though possibly un-realistic, this assumption is made for math-ematical convenience and presumably couldbe relaxed.

More critical is the assumption that thefeatures must be ordered. That is, if Feature15, say, represents a particular attribute inone item, it represents the same attribute inall items. Both the associative formation andretrieval operations depend on the featuresbeing ordered.

Unrelated items will be considered to beitems in which the feature values are statis-tically independent. Knowing the value of aparticular feature in one item gives no in-formation about the value of that same fea-ture in the rest of the set of unrelated items.We may take the dot product between twoitems as a measure of the extent to which thetwo items are similar or unrelated. The dotproduct is found by multiplying the value ofeach feature in one item by the value of thecorresponding feature in the other item andadding all of the products. The dot productof F, coded as (• • • , /_„ /<,, /h • • • ) andG, coded as (• • • , g-h g0, gi, • • •), is F-G,given by

F-G =n-l

22

_ n-\2

figi,

where n is the number of features in theitems. The result is (• • -f-ig-i+ fogo +

f\gi + • • •)• Over the set of unrelated items,the dot product between any two items isexpected to be zero. In the computer simu-lations that will follow, unrelated items willbe constructed by selecting feature valuesrandomly for each feature of each item froma symmetrical distribution centered on zero.The representational assumptions for unre-lated items are the same as those of Metcalfeand Murdock (1981) and differ from thoseof J. A. Anderson et al. (1977) and Liepa(Note 1) only insofar as the unrelated itemsare considered to be statistically independentrather than strictly orthogonal.

To go to the other extreme, suppose thattwo items are identical. Now when the dotproduct between these two identical items istaken, the result is not zero but rather thesum of squares of the values of the features,which is a positive value. Let us, for conve-nience, set this value at 1 so that F • F = 1for all items. Notice that this value is a mea-sure of the strength of the item and that set-ting the value to be the same for all itemsamounts to saying that items begin withequal strength. This is not a necessary as-sumption, and there are no doubt experi-mental manipulations that would affect thisvalue. Identity is taken as the most extremecase of similarity. As has often been pointedout, even when the same item is presentedtwice, it may not be encoded identically onboth occasions. The construct of encodingvariability will not be used in the presentarticle as an explanation, however, althoughthe model is not incompatible with this idea.

One may, of course, have intermediatedegrees of similarity. Suppose, for instance,that half of the features in two items are iden-tical and the other half independent. The in-dependent features, when multiplied andadded to form the dot product, will be ex-pected to sum to zero as before, and the iden-tical features will result in a positive value,as before. Because only one half of the totalfeatures are identical, the expected value ofthe dot product will be .5 rather than 1. Thedot product thus indicates the extent of fea-ture overlap (beyond independence) of twoitems.

In this article, similarity will be repre-sented as the proportion of features that twoitems have in common (i.e., that have iden-


tical numerical values). It will be assumedthat the number of features in each item issome large constant number and that the dotproduct of an item with itself gives a valueof one. These representational assumptionsare very simplified and can probably be re-laxed considerably to be more psychologi-cally plausible. For the present purpose, thesimplicity of the assumptions makes it easierto see what CHARM does when items are as-sociated, stored, and retrieved.

Association FormationIt is postulated that two items in con-

sciousness, each represented as an orderedset of features, may be associated by meansof the operation of convolution. This methodof association formation is fundamental tothe holographic hypothesis and is shared bya variety of other models. The operation hasother applications as well (see Murdock,1979, for a review). Suppose that two itemsF and G are coded in terms of « features(where n is odd), yielding F = (/_<„_ 0/2,• • • , /-i, /o, /i, • • • , /(«-i)/2) andG = (g-(n-l)/2, • • • > £-!> #0> £b • • • . g(n-\)/2)-The convolution of F and G, written as F*G,is a 2n - 1 row vector whose mth term isgiven by

Tm = 2 ' f,gj ,

ITEM FA S S O C I A T I V E

MEMORY

TRACE

ITEM G

where S(m) = {(i, j)\ - (« - l)/2 < i, j ^(n — l)/2, and i + j = m}. If n is equal to3, it is straightforward to compute thatF*G = (/_,£_,, fog-t + f-ig0, f\g-\ +logo + /-i/i> figo + fogi, figi)- Fig-ure 1 presents an illustration of convolutionfor two items each consisting of three fea-tures, and a number of other illustrations canbe found in Lathi (1968). The associativetrace, which is the sum of the products alongthe central line of intersection, is representedin the box in the center of Figure 1 . It issimple to compute the convolution of twoitems by constructing a matrix, such as theone shown in Figure A 1 of the Appendix.

The operation of convolution is itself com-mutative or symmetric, that is, F*G = G*F.This can easily be verified by exchanging theitems in Figure 1; the associative trace re-mains the same. This implies that the for-ward and backward associative strength be-

X

Figure 1. An illustration of the convolution of two items,each consisting of three features.

tween F and G should be the same if every-thing else is equal (cf. Asch, 1968; Ekstrand,1966).

In CHARM, both of the associated items areconsidered to converge on a higher order as-sociative trace. This trace is a complex in-teraction between the two items and does notitself resemble, in any obvious way, either ofthe contributing items. The meaning of thefeatures in the association is not the same asthe meaning of the features in the items. Forinstance, if one were to assign a name to oneof the features in the items, that name wouldnot apply (uniquely) to any of the featuresin the associative trace. Conceptually, thisassociation is nothing like a pathway betweenthe two items (as in, for instance, J. R. An-derson & Bower's, 1973, or J. R. Anderson's,1976, models). As we shall soon see, the re-trieval operation is nothing like a search.

To facilitate the exposition of how con-volution works in combination with corre-lation, consider the special case in which anitem is convolved with a delta vector, de-noted d. A delta vector is an item that hasvalues of zero on all features except the cen-tral feature, which has a value of 1. When anitem is convolved with a delta vector, theresult is the item itself. This may easily beverified by substituting the values of (0, 1,0)


for either F or G in Figure 1 and multiplyingthrough each connection. The result is theother item. Convolving an item with a zerovector, that is, an item with values of zeroon all features, produces a vacuous item —another zero vector. Convolving an item withwhat will be called an attenuated delta vector(i.e., an item with values of zero on all' fea-tures except the central one, which has avalue greater than zero but less than one)produces the other item with a strength thatis equal to the central feature of the atten-uated delta vector.

I do not propose that memory items arethemselves delta vectors. However, if therewere an operation that functionally con-verted one of the items into a delta vector,the other item would be reconstructed. Thisis just what the retrieval operation of corre-lation does.

Item Retrieval

When a retrieval cue is presented and re-call of the item with which that cue was as-sociated is required, it is proposed that thecue is correlated with the associative trace.(Correlation, as used here, is not identical tocorrelation in statistics, which is the dot prod-uct, although the two are related.) Correla-tion may be denned in a manner similar toconvolution. When F and G are coded asF — (/-(n_i)/2, . . . , /-i, JO, /I, . . . , /(n-l)/2)and G = (g-<«-o/2, • • • , g-i, go, 8\, • • - ,g(n-\)/2\ the correlation of F and G, writtenas F#G, is a 2« - 1 row vector whose mthterm is given by

Rm = 2 ftgj ,

where S(m) = {(i, j)\-(n - l)/2 < /, ; ^(«-l)/2, and i-j = m}. It follows thatwhen n is equal to 3, for instance, the resultof correlation F#G = (f-igi, f0g\ + f-{g0,fi8\ + fogo + f-ig-i, figo + fog-i, fig-i)- Ascan be seen, the central feature of correlationisF-G.

If an item is correlated with itself, the valueof the central feature will be one, becauseF • F was set to one. The noncentral featureswill have an expected value of zero (but willnot be exactly zero) because of the indepen-dence of the feature values and the overall

expected value of zero. Thus, autocorrelation(F#F) results in an approximation to a deltavector. If the two items being correlated aresimilar, the central feature will be equal tothe dot product between the two similaritems, that is, equal to their similarity. Thus,the correlation of two similar items resultsin an attenuated delta vector. If the two itemsbeing correlated are unrelated, the expectedvalue of the central feature is zero, as it is forall of the other features. Thus, the correlationof two unrelated items approximates a zerovector.

Relation Between Operations forAssociating and Retrieving

As was given in the Association Formationsection, when an item is convolved with adelta vector, the result is the item itself:

5*G = G. (1)When an item is convolved with a zero vec-tor, the result is a zero vector:

0*G = 0. (2)The result of convolution with an attenuateddelta vector falls between these two extremes.

As was given in the Item Retrieval section,when an item is correlated with itself, an ap-proximation to a delta vector results:

F#F at S. (3)When an item is correlated with an unrelateditem, an approximation to a zero vector re-sults:

F#G^O, where F-G = 0. (4)The result of correlating an item with anothersimilar item falls in between these two ex-tremes, resulting in an approximation to anattenuated delta vector.

The relation between convolution and cor-relation for unrelated items has been givenbefore (Borsellino & Poggio, 1973; Murdock,1979; Liepa, Note 1). It will be simpler togive a more general equation here and thenderive the result for unrelated items. Theequation relating convolution and correla-tion is given byF#(F*G)

= (F#F)*G + (F#G)*F + noise. (5)


The Appendix illustrates the convolutionand correlation matrices that produce thissummary equation and shows the locus ofthe two potentially nonnoise components,(F#F)*G and (F#G)*F.

If F and G are unrelated, we may substi-tute the first four equations into Equation 5as follows:1 F#(F*G) = (F#F)*G + (F#G)*F + noise

<a. 3*G + 0*F + noise& G + 0 + noise

"̂i

If F and G are unrelated, and G is used asa retrieval cue, Equation 5 becomes

G#(F*G) = (G#F)*G + (G#G)*F + noisea 0*G + 6*F + noise^ 0 + F + noise

Thus, when two unrelated items are as-sociated by convolution, and either of theitems is correlated with the resulting associa-tive trace, an approximation to the otheritem is reconstructed or retrieved.

Effects of SimilarityStimulus and response generalization fall

out immediately from the above associativeand retrieval scheme. When two unrelateditems are associated by convolution, andthen an item that is similar to but not iden-tical with one of the associated items is cor-related with the result, an approximation tothe other item is produced. In this case thetwo similar items do not form a delta vectorwith a central feature of precisely one; in-stead, an attenuated delta vector is formed,with a central feature equal to the similarity(dot product) between the two items. Theretrieval operation produces the other itemwith a strength that is proportional to the dotproduct. Thus, if F and G are convolved andthen F' (an item similar to F) is correlatedwith the trace, F and F' will form an atten-uated delta vector that will produce or re-construct G with a strength proportional toF • F'. In a like manner, if G' was used as aretrieval cue, F would be produced with a

strength proportional to G • G'. The fact thatstimulus generalization results directly fromthe method of association formation and re-trieval suggests that the model might be di-rectly applicable to a wide variety of exper-imental paradigms (see Gibson, 1941). Thefact that response generalization occurs forthe same reason gives rise to the counterin-tuitive prediction that an item similar to aresponse will evoke recall of the stimulus—a prediction that will be tested later in thisarticle.

If the two associated items are similar toeach other (i.e., F • G > 0), both of the non-noise components given in Equation 5 areimportant. For example, consider the limit-ing case in which F and G are identical.Equation 5 becomes

F#(F*G) = (F#F)*G + (F#G)*F + noise^ 5*G + 5*F + noise=^ 2G + noisea; 2F + noise.

The item produced will have twice thestrength as would have been the case had itbeen associated with an unrelated item.(Some complications arise from the internalnoise that make this only an approximation,but it is a fairly good one, so long as otherassociations enter into the composite traceas well as the target association.)

Suppose now that instead of the associateditems being identical, they are similar to eachother. For the sake of illustration, supposethat F • G = .5 because about 50% of the fea-tures are identical (and the remainder areindependent). If these two similar items werecorrelated, the result would be an attenuateddelta vector with a central feature equal toF*G = .5. Equation 5 then becomes

F#(F*G) = (F#F)*G + (F#G)*F + noise=s 5*G + .55*F + noise^ G + .5F + noise.

The retrieved item is a linear combinationof the original items F and G. Each featurein G is weighted or multiplied by 1, eachfeature in F is multiplied by .5, and the re-sults are added, feature by feature. This tendsto accentuate the features that are common


to F and G, making them stronger than theywould otherwise be, and to have an interfer-ing effect on the features that are unique tothe target item G. The item that is re-createdis a systematic distortion of the encoded (tar-get) item G such that it is more like the as-sociated item F than would be the case hadthe target been associated with an item thatwas not similar. The fact that the model sys-tematically distorts the retrieved item fromits encoded form when the two associateditems are similar, but not when they are un-related, has experimental implications thatwill be tested later in the article.

In summary, when two items that are un-related are associated by convolution andthen one of the two is correlated with thetrace, an approximation to the other item isretrieved. When an item similar to one of theconvolved items is correlated with the trace,the other item is still produced, but with adecreased strength. When two similar itemsare convolved and then one of the two iscorrelated with the trace, the item that is re-trieved is systematically distorted from itsencoded form such that it is more like bothof the associated items and less like the targetitem itself, taken in isolation. The interactiveassociation itself introduces this distortion.

OLD TRACE

The Composite Associative Memory Trace

In CHARM, associations are stored in acomposite memory trace—termed compositebecause the composite portraits of Gallon(1879), in which photographs of faces weresuperimposed to yield a prototypical face,provide a good visual analogy to such a mem-ory trace. J. A. Anderson and his colleagues(J. A. Anderson, 1970, 1972, 1973, 1977;J. A. Anderson et al., 1977; J. A. Anderson& Hinton, 1981) have argued for the neu-rological and psychological plausibility ofthis same construct.

Figure 2 gives a numerical example of howthe composite trace in CHARM is formed. Thefigure shows how two pairs of items are firstconvolved and then added into the compos-ite trace. The trace starts out with some nu-merical values that are the result of previouspairs that have been added into it. When apair of items (F and G) is presented, con-volution occurs as described earlier. Thematrix in the figure is a convenient way ofcomputing the result of convolution. Thenumerical values in the figure were chosenfor their computational simplicity ratherthan to conform to the independence andstrength assumptions in the model. The re-

v Xxo

0

vO\N

0•»•

'd

-1

0

xj

0•V-

-1

0

0

-2

•»•

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-1

0

-1•»•

V (.

o r

-i

i ,/

0

•»•1 -3

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OLD TRACEFigure 2. A schematic illustration of the formation of the composite memory trace. (Note that theassociations are truncated as in the simulations).


suit of convolution is added, feature by fea-ture, into the trace. When the next pair (Hand I) is associated, the result is also addedinto the composite trace.

How does the composite trace influencewhat is recalled? When the items of a list areall unrelated, the fact that the trace includespairs other than the target pair adds noise tothe recalled item. Suppose a list consists oftwo pairs of four unrelated items: F-G andH-I. When F is given as a retrieval cue, thereconstruction can be characterized as fol-lows:F#[(F*G) + (H*I)]

= (F#F)*G + (F#G)*F + noiseF.G+ (F#H)*I + (F#I)*H + noiseH,i

= §*G + 0*F + noiseF.G + 0*1

+ 0*H + noiseH,i

= G + noiseF.G + noiseH.i.

In this situation, the effect of the nontargetH-I pair is to add noise to the reconstructeditem G. Quite literally, the composite traceproduces interference. Metcalfe and Mur-dock (1981) present a number of computersimulations that illustrate this buildup ofnoise due to an increasing number of pairsin the memory trace, when those pairs areunrelated.

Now consider a situation in which all fouritems are similar to one another. For the sakeof illustration, suppose that the dot productof any item with any other item is .5. Goingthrough the reconstruction computationsgivesF#[(F*G) + (H*I)]

= (F#F)*G. + (F#G)*F + noiseF,G+ (F#H)*I + (F#I)*H + noiseH,i

= 5*G + .56*F + noiseF,G + .55*1

+ .55*H + noiseH.i

= G + .5F + .51 + .5H

+ noiseF.G + noiseH.i •

The main point to note is that in this situ-

ation, the composite trace not only producesnoise but also causes all of the items in thelist to contribute to the pattern that is re-trieved from memory.

As a final illustration, consider the casewhere two unrelated target items (B and D)have been associated with the same cue (A)and both associations (A-B and A-D) havebeen stored in the composite trace. When thecue is correlated with the trace, the singleitem that is retrieved is a combination of bothof the unrelated targets. This situation, whichcorresponds to Barnes and Underwood's(1959) A-B A-D paradigm, can be sche-matized as follows:

A#[(A*B) + (A*D)]

= (A#A)*B + (A#B)*A + noiseA,B

+ (A#A)*D + (A#D)*A + noiseA,D

= 5*B + 0*A + noiseA,B + 5*D

+ 0*A + noiseA,D

= B + D + noiseA.B + noiseA»D •

The fact that the retrieved item is a combi-nation of more than one item in this situa-tion, as well as in situations where to-be-re-membered items are similar to each other,reveals a problem of possible response am-biguity. The construct of semantic memory,detailed below, solves this problem.

To summarize, a quick rule of thumb forsaying what will be retrieved from the com-posite-holographic memory trace is as fol-lows: Take the dot product (i.e., the similar-ity) of the cue item with each of the itemsin the list. If the dot product between the cueand a particular item is about zero, then onlynoise will be produced. If the dot productbetween the cue and Item X is not zero, thenthe complement item, with which Item Xwas convolved, will be retrieved with astrength proportional to the dot product.This calculation may be carried out for everyitem in the list, giving the strength with whichthe complement items are retrieved. All ofthe noise and the retrieved items, weightedby their appropriate strengths, are then addedto give an approximation to the single itemthat is recovered from memory.


Semantic Memory

Because the item that is retrieved from thecomposite trace is intrinsically noisy, andmay be systematically distorted or ambigu-ous, CHARM requires a pattern recognizer ifit is to make predictions about what discretewords will be recalled. This pattern recog-nizer basically identifies the retrieved item assuch and such a word and allows for a dis-crete response.

There are two parts to the pattern recog-nizer. First, because the retrieved item is tobe assigned a particular label, there is a listingof all the possibilities. This listing of respon-ses corresponds in a general way to what isoften called semantic memory, where theterm is interpreted in the restricted sense ofa lexicon. The usage of the term semanticmemory seems most similar to that given byKintsch (1974). Thus, when an item is re-trieved from the composite trace, it is iden-tified by being matched to every item in thelexicon.

Second, there is a matching process thatserves to select one (or more) of the discretepossibilities as, the resporise(s). The matchingprocess is similar to the resonance operationdescribed in RatclifPs (1978) item-recogni-tion model. Each feature in the retrieved itemis multiplied by the corresponding feature ineach lexical item, and the sum of the prod-ucts for all of the features corresponding toa particular lexical item is taken. In this man-ner, a separate dot product is computed forevery lexical item. The better the match be-tween the retrieved item and a particular lex-ical item, the higher will be the dot product—or "resonance" value (see Ratcliff, 1978)—for that lexical item. In the simulations thatfollow, the matching process is allowed to beexhaustive; that is, every feature of every lex-ical item is matched to the retrieved item.(An alternative approach is to halt the match-ing process once sufficient information hasaccumulated—via a random walk to a cri-terion—for a particular response; see Rat-cliff, 1978. Whether the matching processstops at a criterion or is exhaustive probablydepends on the demands of the specific taskat hand.)

Resonance values allow us to determinewhat the retrieved item will be identified as

and to make contact with verbal cued-recallexperiments in which, in most instances, re-sponses are discrete. It is at the identificationstage that the strength of features becomesespecially important. Features that have highabsolute resonance values—that is, strongfeatures—will contribute more to the selec-tion of a response than will weak features.The implementation of a lexicon for patternrecognition is the same as in Metcalfe andMurdock (1981) but is not explicit in anyother holographic model. It allows CHARMto address situations involving response am-biguity and thereby enables the model tomake predictions concerning errors of recalland to deal elegantly with the A-B A-Dtransfer paradigm. In the third and fourthexperiments reported below, evidence for theseparate existence of a semantic memory sys-tem is provided.

For simplicity, no occurrence informationis stored at the lexical level. The matchingprocess is thus properly considered to be anidentification process rather than a recogni-tion-memory process. CHARM is a model ofrecall, not recognition.

Experimental Tests of CHARM

In the preceding discussion, I described theworkings of the model. I said little, however,about explicit experimental predictions. Inthis section, I will describe several simple sin-gle-trial cued-recall experiments and outlinethe predictions of the model. I will presentcomputer simulations of the model that dem-onstrate the predictions in a more concretefashion. These simulations were run predic-tively (before the experiments were con-ducted) and thus are attempts not to fit databut rather to make qualitative predictions.I will present several experiments that seekto determine whether people, when in recallsituations that should conform fairly closelyto those simulated, produce patterns of recallthat correspond to the predictions of themodel.

Intralist Intrusions

The first simulation is directed at a situ-ation in which people are presented with a


list of cue-target word pairs to study and re-member. The list may consist of words thatare all unrelated to each other or that are allsimilar to each other. After studying, subjectsare given the cue words as retrieval stimuli,and the question asked is, What will be re-called?

Simulation 1Method. The entire simulation that I will describe

here was run 100 times for each of the two conditions:similar list and unrelated list. The only difference be-tween these runs was that each had a different randomassignment for the initial representations of the items.One run of this simulation for the unrelated-list con-dition will first be detailed. Then the alteration in theprogram that gives rise to the similar list condition willbe described.

A small lexicon consisting of 12 items was con-structed. Six of these items were designated to be listitems and six were unrelated extralist items. Each featureof each lexical item was a number randomly selectedfrom a unit normal distribution with a mean value ofzero. The randomization subroutine RANDR was usedand care was taken that the computer specificationsmatch those for which this subroutine was originallydesigned. Each item consisted of 63 features. The 63-tuple composing each item was then normalized so thatthe dot product of any item with itself equaled one.Because of the random selection of feature values, thedot product of any item with any other item was ap-proximately equal to zero.

The associative memory trace was formed by con-volving Items 1 and 2, Items 3 and 4, and Items 5 and6. The results of the three convolutions were added intoa single 63-tuple made up of the central 63 features ofthe convolutions. Once this composite trace was formed,the program attempted to recall.

In order to recall, each of Items 1,3, and 5 was cor-related with the composite trace, resulting in three re-trieved patterns that were again truncated to the central-

63 features. Each retrieved pattern was then matched toeach of the 12 lexical items by multiplying each featurein the retrieved item by the corresponding feature in thelexical item and summing the products, yielding a reso-nance score for each lexical item. For purposes of illus-tration, the program also chose the lexical item that hadthe highest resonance score (as long as it was greaterthan zero) to give as a response. This responding crite-rion is arbitrary but will illustrate the pattern of recallmore concretely than do the resonance scores them-selves.

In the similar-list condition, the lexicon was initiallyconstructed in exactly the same way as in the unrelated-list condition. Then the values of every other feature inthe first six items were altered so that they were all ex-actly the same as the feature values originally assignedto Item 1. Thus, the items that were to make up the listhad identical values on 32 features and independentvalues on 31 features. This representation of similarityis crude, but a later simulation'on protoypes that usesa more refined representation gives about the same re-sults. The convolution, correlation, and identificationprocedures were the same in the similar-list conditionas in the unrelated-list condition.

Results. As evidenced by the results pre-sented in Table 1, the model predicts that thediscriminability of the target relative to otherlist items is worse when the list is composedof similar rather than unrelated items. Thus,a distinctive pattern of intrusion errors shouldbe found when the responses to a list of sim-ilar items are compared to those to a list ofunrelated items. When the list consists ofunrelated items, intralist intrusions shouldbe quite infrequent, whereas when the listitems are all similar, the frequency of intralistintrusions should be considerably higher.The resonance scores show this pattern andalso show that there should be no differencein the rate of intrusions depending on whether

Table 1Mean Resonance and Recall for Each Type of Response in Simulation 1

Type of response

Condition Target CueNontargetresponse

Nontargetstimulus

1.50 (.60)21.7%

Unrelatedextralist

.00 (.20) .00 (.20)Unrelated

Resonance .80 (.20) .00 (.30) .00 (.20)Recall 98.6% .6% .6%

SimilarResonance 1.70 (.60) 1.50 (.60) 1.50 (.60)Recall, 42.0% 14.6% 21.7%

No. (out of 12) of lexical itemscorresponding to response type 1 1 2

.00 (.40).0%

Note. Standard deviations are in parentheses.


a given item had been a stimulus or a re-sponse item.

The differential pattern in the two condi-tions stems from the fact that in the model,the pattern that is retrieved from the com-posite trace is a combination of all of theitems that are stored in the composite tracewhen those items are similar to each otherbut consists only of the target item when thelist items are unrelated. This intrusion pat-tern is thus expected even though there maybe lexical items in the unrelated-list condi-tion that are equally similar to the target itemas are the list items to the target in the sim-ilar-list condition.

The table shows the levels of recall giventhe arbitrary decision criterion of the bestmatched item. These numbers are not quan-titative estimates because no attempt wasmade to quantify the degree of similarity inthe simulation as compared to the experi-ment that will follow, to equate the numberof pairs in the trace, or to estimate the num-ber of features. The recall figures do serve toillustrate that even though the resonance ofthe target item was higher in the similar-listas compared to the unrelated-list condition,correct recall in the similar-list condition isexpected to be worse than in the unrelated-list condition. This occurs because the re-trieved item provides little of the informationon the nonshared features of the similaritems that is necessary to discriminate thetarget item from the other list items.

The simulation also produced the coun-terintuitive prediction that there should becue intrusions—that is, recall of a cue wordto itself as a cue—in the similar-list but notin the unrelated-list condition.

Experiment 1Method. In this experiment, people's recall to a list

of similar pairs was compared to recall to a list of un-related pairs.

Four sets of materials were constructed such that eachset consisted of two lists: one in which the words wereall from a single category and one in which each wordwas from a different category. Each list consisted of 14pairs of words. In order to construct the similar list ineach set, a category was randomly selected from theToronto categorized word pool (Murdock, 1976). Wordswere randomly selected from the category until 14 pairsresulted. The uncategorized list in each set was con-structed from the same word pool. Twenty-eight cate-gories were randomly selected (with the exclusion of thecategory that was used in the similar list in the same

set). A word was randomly chosen from each of the 28categories, and the words were then randomly paired.

Each of the 16 subjects in the experiment (volunteersfrom the social sciences subject pool at the Universityof California, Irvine) received two lists of pairs (one set)to study. Four subjects were assigned to each of the foursets of materials. Two subjects studied and were testedon the categorized list first, whereas the remaining twosubjects studied and were tested on the unrelated listfirst. The lists were typed in uppercase letters on sheetsthat were given to subjects to study for 4 minutes. Afterstudying, subjects counted backwards from a large num-ber by threes for 1 minute and wrote down their finalcount. They were instructed that the right-hand mem-bers of the pairs were the targets or responses and thatthey would be given the left-hand items as cues.

Cued recall was written in booklets that contained onecue per page. The order of presentation of cues was ran-domized for every subject. Beside each response, subjectswere asked to write their degree of confidence about thecorrectness of the response on a scale of 1 to 6, where1 was guessing and 6 was highly confident. Recall wassubject paced, and subjects were instructed not to lookback to previous responses or forward to upcoming cuesuntil all attempts to respond had been made.

Results. The mean number of correct re-sponses, intralist intrusions, and extralist in-trusions in each of the two conditions arepresented in Table 2, along with the confi-dence ratings. As can be seen from the table,the entire pattern of recall and intrusionscorresponded quite well to the predictions ofthe model. In particular, the nontarget listitems were poorly discriminated from thetarget items in the categorized-list conditionbut not in the uncategorized-list condition.An analysis of variance was conducted inwhich the factors were condition (categorizedor uncategorized), response type (correct,stimulus intrusion, response intrusion, andextralist intrusion) and set (1 to 4). There wasa significant interaction between responsetype and condition, F(3, 36) = 34.47, p <.05. There were no other significant effectsor interactions. A chi-square test, where theobservations were treated as if they were in-dependent, was also performed. There wasa significant relation between the frequencyof correct and intralist intrusions and thecategorized or uncategorized conditions,X

2(l)= 30.67.There was no statistical difference between

intrusions that were originally stimulus itemsand response items, t( 15) = .81, although theslight tendency was in favor of the stimulusitems. This result offers some support for thesymmetrical nature of the association in themodel.


Table 2Mean Number of Correct Responses andConfidence Rating for Each Type of Response inExperiment 1

Type of response

Condition

Other Extra-list list

Target Cue item item

UncategorizedNo. recalled8

Confidence ratingb

CategorizedNo. recalled"Confidence rating11

11.25.9

7.95.7

0—

0—

.83.8

3.12.6

.13.5

.51.4

aOut of 14. "Out of 6.

In summary, the predictions of the modelgiven in Simulation 1 were largely supportedby the results of the present experiment. Theone prediction that absolutely failed to ma-terialize was that of intrusions of the cue itemto itself as a cue: No subject ever said thatthe target item was A when A was given asa cue. It seems likely that because an itemwas never paired with itself in the experi-ment, subjects were able to use a rule to in-hibit this particular response. Nevertheless,the prediction of cue intrusions is important,not necessarily for its own sake, but becauseit is a direct result of the interactive natureof the postulated association.

It is of interest to note that the predictionof differential intrusion errors in the similaras compared to the unrelated condition de-rives directly from the property of the modelthat, in the former condition, the compositetrace causes the retrieved item to be system-atically distorted towards a "prototype" ofthe list. The results of both the simulationand the experiment indicate that CHARMshould be extendable to prototype learningexperiments. Further, errors of recall, ac-cording to the model, are related to people'sability to form concepts. The extension ofthe model to prototype learning will be madein a later section of the article.

Extraassociative-List Context Effects

For the same reason that intralist intru-sions were predicted in the first experiment,the model predicts that the makeup of the

whole list of paired associates, not only theto-be-remembered pair, will influence thegoodness of recall. Consider a situation inwhich a given pair, say NAPOLEON-ARIS-TOTLE, is embedded in a list of pairs of namesof famous people (homogeneous list) or isembedded in a list containing a variety ofconceptually different pairs such as RED-BLUE, 14-22, and so forth (heterogeneouslist). As was pointed out to the author (Tulv-ing, Note 2), CHARM makes precisely theright predictions about the difficulty of recallunder these conditions. NAPOLEON-ARIS-TOTLE should be more difficult in the ho-mogeneous-list condition because, in thatcondition, the composite trace will cause aprototype of the entire list rather than justthe appropriate target response to be pro-duced. In an experiment that included thiscomparison, Tulving (Note 3) found that thetarget association was indeed harder to learnin the homogeneous- than in the heteroge-neous-list condition.

Cue Intrusions

The predictions of differential cue intru-sions between the similar and unrelated con-ditions was not confirmed in Experiment 1,probably because subjects were able to usea rule to eliminate these responses. This pre-diction is, nevertheless, an important onebecause it bears directly on the structure ofthe interactive association postulated inCHARM and, further, because it is a counter-intuitive or high-risk prediction. The ques-tion that will be addressed in the present ex-periment is whether cue intrusions are morelikely to occur when a cue and target are sim-ilar rather than unrelated. Tulving (1974) hasreported the presence of cue intrusions in astudy in which some of the pairs had identicalcues and targets, so the inclusion of this typeof pair in the list appears to override, at leastto some extent, a rule excluding these intru-sions.

CHARM makes the prediction that cue in-trusions will be more frequent when the cue-target items are similar to each other becausethe item that is retrieved from memory re-sembles both the cue and the target. It is be-cause the retrieved item in the similar con-dition is a combination of both A and A',where the common features are accentuated


and the contrasting features suffer interfer-ence, that one expects this retrieved item tobe sometimes mistakenly (from the experi-menter's point of view) identified as A—thecue itself. When the two associated items Aand B are unrelated and A is presented as acue, the cue item is not itself reconstructed,and so cue intrusions are not expected.

It is not clear that other models make thisprediction. In models such as FRAN (J. R.Anderson, 1972), in which the probability offorming an association depends on the sim-ilarity of the to-be-associated items, it wouldseem that the probability of recall might behigher in the similar as compared to the un-related condition (in contrast to the previousexperiment). There is no indication, how-ever, of whether there should be more orfewer cue intrusions in the similar as com-pared to the unrelated condition. Theremight be more if a selection of nodes (dif-ferent from the central node for a given item)occurs, as is suggested by J. R. Anderson(1976). On the other hand, there might befewer cue intrusions in the similar conditionif the subject guesses the cue in the absenceof a tagged pathway to a different tagged node(as presumably occurs more frequently whenthe items are not similar). There is littledoubt that either result could be accommo-dated after the fact, but no a priori predictionis clear. Bower's (1972) multicomponentmodel makes reference only to the propertiesof the stimuli and so can make no predictionsabout phenomena attributable to the relationbetween the two associated items. The samemay be said for Medin and SchafFer's (1978)feature model, which represents similaritybut does not consider the responses, only thestimuli. This is also the case for the J. A.Anderson et al. (1977) model, which containsa forward-directional association, althoughthis model is in other respects like CHARM.Because Flexser and Tulving's (1978) gestal-ten model does not include any representa-tion of similarity, it makes no predictions inthis situation. To my knowledge, there areno other models that make the prediction ofcue intrusions. If subjects were guessing someof the time when they had no informationabout the correct response, one would expectthat the conditional probability of a cue in-trusion given an intrusion should be the samein both conditions.

Simulation 2Method. In this simulation, the similarity of the cue-

target pairs was varied within a single list. Three levelsof similarity were used; identical, similar (50% featureoverlap), and unrelated. As in the first simulation, a lex-icon of 12 items was constructed such that each itemwas a random normalized 63-tuple. Items 1 and 2 werereassigned feature values so that they were identical;Items 3 and 4 were reassigned feature values so that 32of the 63 features were identical and the remaining 31features were independent; and Items 5 and 6 were leftwith their original independent feature values. Items 7through 12 were not included in the study list but wereconsidered to be unrelated extralist possibilities in thelexicon. To make the simulation somewhat more real-istic, Item 7 was assigned the same feature values as wereItems 1 and 2 on half its features, Item 8 was similarlyrelated to Item 5, and Item 9 was related to item 6.

The associative memory trace was constructed by con-volving Items 1 and 2, Items 3 and 4, and Items 5 and6 and adding the results into a single 63-tuple repre-senting the composite trace. Then Items 1,3, and 5 werecorrelated with the trace to produce three retrieveditems. These retrieved items were matched to the itemsin the lexicon by means of the matching process de-scribed in Simulation 1. The simulation was run through100 replications, and the means and standard deviationsof the resonances of the lexical items to each of the threeretrieved items were computed.

Results. The main point to note from theresults shown in Table 3 is the difference inthe resonances of the cues for the similar andunrelated conditions. When the original twoitems in a pair were similar, the resonanceof the cue was almost as high as was that ofthe target. In the unrelated condition, theresonance of the cue was essentially zero,whereas the target itself was fairly stronglyevoked.

I note parenthetically that if a rule can beused to eliminate the cue as a response, thelevel of recall is proportional to the resonancescores of the target, in this simulation. Recallwill then be a direct function of the similaritybetween the stimulus and the response. Thisis the case because, unlike Simulation 1, theonly competing response is the cue itself.However, in the experiment that follows, anattempt is made to deliberately inhibit theuse of such a rule. Thus, no prediction ismade about the level of recall: The only clearprediction is that there should be relativelymore cue intrusions in the similar-pair con-dition than in the unrelated-pair condition.

Experiment 2Method. The lists in the present experiment each

consisted of three types of pairs: identical pairs, synonym


Table 3Mean Resonance for Each Type of Response inSimulation 2

Type of response

Condition

UnrelatedMSD

SimilarMSD

IdenticalMSD

Target

.76

.20

.94

.29

1.42.32

Cue

.02

.32

.85

.41

1.42.32

Otherlist

item

.00

.27

.07

.30

-.01.32

UnrelatedExtralist

item

.00

.22

-.02.24

.02

.26

Note. The unrelated, similar, and identical conditionswere all within a single list.

pairs, and unrelated pairs. There were 20 pairs of eachtype in each list, for a total of 60 'pairs. Although thecue-target words varied in their similarity to each otherwithin a pair, there was no obvious relation among thepairs in the list. Four different lists were constructed.The words that constituted the four lists in the experi-ment were chosen from the 80 highest ranked synonymsof Whitten, Suter, and Frank (1979). The lists were con-structed so that the same response term occurred equallyfrequently as a response in each of the three conditions,over lists, and the mean synonymy was about the samefor all lists.

To construct the lists, each of the four pairs that werethe highest ranking four synonym pairs given by Whittenet al. (1979) were assigned by means of a Latin squareto the four lists in four nominal conditions: identical,synonym, cue of the unrelated pair, target of the unre-lated pair. The synonym given first in Whitten et al.'s(1979) listing was the particular member of the synonympair that was used in these four nominal conditions. Inthe synonym condition, both words from the synonymlisting were used. The assignment of words to conditionsand lists was repeated for each successive tetrad of syn-onym pairs given in the norms until there were 60 pairsin each list. The order of pairs in each list was thenrandomized. There were two random test orders for eachof the four lists.

Thirty-two subjects, who were volunteers from thesocial sciences subject pool at the University of Califor-nia, Irvine were tested. Eight subjects were assigned toeach list.

The lists were read to subjects at a rate of 10 sec perpair. Following study, subjects wrote the names of thestates of the United States in alphabetical order for 6minutes. They were then given a booklet containing the60 cue items—always the first item in a pair—and wereasked to write their responses along with a rating of thecertainty of their responses on a scale of 1 (guessing) to6 (highly confident). Ten minutes were allowed for cuedrecall.

Results. The prediction that there wouldbe more cue intrusions in the synonym thanin the unrelated condition was confirmed.When the probability of a cue intrusion,given an intrusion, was calculated for eachsubject in both conditions, the resultantmean conditional probability was .60 in thesynonym condition and .46 in the unrelatedcondition, r(31) = 1.89, p < .05. The samepattern resulted when the data were pooledover subjects. The conditional probability ofa cue intrusion was then .50 in the synonymcondition and .39 in the unrelated condition.

Table 4 shows the frequency of cue andnoncue intrusions for the synonym and un-related conditions when these were dividedinto highly confident (with ratings of 4 orhigher) and low-confident (with ratings of 3or lower) intrusions. There was a dispropor-tionate number of highly confident cue in-trusions in the synonym conditions,X2(l) = 5.19, p < .025, but not in the unre-lated condition x2(l) = -00) ns. The confi-dence-rating results provide converging evi-dence that these intrusions were not due sim-ply to some complicated guessing strategy.

The level of correct recall was .63 in thesynonym condition and .22 in the unrelatedcondition. When the cue-target pair hadoriginally consisted of identical words, thelevel of correct responding was .59.1 thoughtthat as long as subjects actually associatedthe identical words with each other, the levelof recall would be better in the identical thanin the synonym condition rather than show

Table 4Comparison of Cue Versus Other Intrusions asa Function of Condition and Confidence inExperiment 2

Synonymcondition

Type ofintrusion

CueOther

Highconfi-dence

3115

Lowconfi-dence

2834

Unrelatedcondition

Highconfi-dence

3046

Lowconfi-dence

6397

Note. A total of six intrusions for which no confidenceratings were obtained have been excluded. Of these sixintrusions, two occurred in the synonym condition andfour in the unrelated condition; within each condition,the excluded intrusions were divided equally accordingto type (cue versus other).


no difference. One should note that in Tulv-ing's (1974) study, recall of identical pairswas worse than that of similar pairs. In otherexperiments it has been shown that the levelof recall increases with increased similaritybetween the cue and target (McKoon & Rat-cliff, 1979, for instance). It seems that per-formance in the identical condition, whichis not usually included, is most puzzling.

The cue-intrusion prediction was madebecause the item recreated from the holo-graphic association is, under some condi-tions, a combination of the cue and targetand, hence, is likely to be mistakenly iden-tified as the cue. It would be of some interestto tap experimentally an item that is itself acombination rather than rely on the intru-sion probabilities as the only evidence for thiscombinatorial property. An experiment byLoftus (1979) may be relevant. Loftus showedsubjects slides of people going about routineactivities. One of the slides showed a personreading a green book. Later, a leading ques-tion suggested that the book had actuallybeen blue. When subjects were asked to selectthe remembered color on a color wheel, their"choices tended to be a compromise betweenwhat they actually saw and what they weretold on their questionnaire, that is, they se-lected a bluish-green" (p. 123). One plausibleinterpretation is that the subjects actually re-trieved a superimposed combination of thetwo events, as both the composite trace andthe holographic association in CHARM pro-duce. Gibson (1941) has also noted that ina paired-associate learning task in which sub-jects are given two different nonsense sylla-bles as responses to the same stimulus, a fre-quent error was the combination of the twononsense syllables. Bartlett (1932) noted thatin an experiment in which subjects weregiven name-face pairs and were later askedto describe the face corresponding to a par-ticular name, details from other faces wereoften incorporated into the descriptions.These results suggest that what is retrievedis not simply a degraded but essentially ve-ridical copy of the target item but may ac-tually be a combination of a number ofevents.

The finding of differential cue intrusionsin the present experiment is an indicationthat the item that is retrieved from memorymay be a combination of the items that were

associated when those items are initially sim-ilar to each other. This finding was predictedbecause of the interactive nature of the as-sociation in CHARM. It is a counterintuitivefinding that is not predicted by other modelsof recall.

Extralist CuingIn the preceding experiments, I tested sev-

eral predictions of the model with respect toerrors of recall. In this section, a rather dif-ferent question will be addressed: the efficacyof extralist cues. These two areas of investi-gation have in common the fact that the in-teractive association model yields predictionsabout both. They are linked not by the ex-perimental paradigm but rather by the con-cept of the interactive association.

Consider a situation in which a personstudies a list of pairs of unrelated words. Thesubject is told that the right-hand word ineach pair is the target word that will later becued for recall. We now ask the question,What sorts of cues will be effective in elicitingthe target items? Three possibilities will beconsidered, namely, the word that was pre-sented with the target item in the list (i.e., thelist cue), a word that is similar to the list cue,and a word that is similar to the target itself.Before presenting the simulation of this sit-uation, let us consider for a moment whatmight be expected.

If one simply assumes that an associationis formed between the list cue and the targetitem, then it seems likely that the list cuewould serve as an effective reminder for thetarget. Presumably, all associative models,including the present one, are in accord onthis point. One might also expect that an ex-tralist cue similar to the list cue should giverise to recall of the target. This is a classiccase of stimulus generalization, and althoughthe term stimulus generalization does notitself explain the phenomenon, there are anumber of feature models (e.g., Bower, 1967;Estes, 1955; Medin & Schaffer, 1978) in ad-dition to the present one that can address it.

Because the phenomenon of stimulus gen-eralization is well known and well substan-tiated, it is probably intuitive that the itemsimilar to the cue should allow recall of thetarget. More obscure is the question of whatthe item that is similar to the target will causeto be recalled. There is a considerable amount


of data that show that an item that is preex-perimentally related to a list item may facil-itate recall of the list item (Bahrick, 1969;Bilodeau, 1967; Bilodeau & Blick, 1965;Light, 1972; Santa & Lamwers, 1974). It isnot clear, however, that items that are similarto each other in the sense that they sharefeatures are related in this same sense. If theyare, then perhaps they should cause the targetitem to be recalled. However, there are otherdata (e.g., Santa & Lamwers, 1974; Thomson& Tulving, 1970) that show that even preex-perimentally related cues do not necessarilycause the target item to be recalled. Intuitionsuggests that an extralist word such as BUYmight be an effective retrieval cue for a targetword such as PURCHASE. '

The most interesting prediction of CHARMin this extralist cuing situation is that a syn-onym of the target word, rather than causingthe target word itself to be recalled, will tendto retrieve the unrelated intralist cue. Thisprediction, as well as the stimulus-general-ization prediction, will be demonstrated inthe simulation that follows.

Simulation 3Method. In this simulation, the efficacy of extralist

cues was examined. A 12-item lexicon was constructedas in the previous simulations. The items consisted of63-tuples, where each feature value was drawn from aunit normal distribution and then normalized so thatthe dot product of an item with itself equalled one. Thefirst six items were designated as list items. Item 7 wasreassigned feature values so that it showed 84% overlapwith Item 1; Item 7 would thus be considered to be likean extralist item similar to the cue. Item 9 was reassignedfeature values to show 84% overlap with Item 2 and wasthus like an item similar to the target. Item 11 was alsoused as an extralist cue, but one that was unrelated toeither the cue or the target and its feature values werenot changed.

Items 1 and 2, 3 and 4, and 5 and 6 were convolved,and the results of the three convolutions were added intoa 63-tuple representing the composite trace. Then Items1 (the list cue), 7 (an extralist item similar to the listcue), 9 (an extralist item similar to the target), and 11(an unrelated extralist cue) were correlated with thetrace. The means and standard deviations of the reso-nance scores of the retrieved items with each of the lex-ical items were computed from the 100 runs of the sim-ulation.

Results. Table 5 provides a summary ofthe mean resonances and their standard de-viations as obtained from Simulation 3.When the list cue was correlated with thetrace, the target was strongly evoked. The

Table 5Mean Resonance for Each Type of Responsein Simulation 3

Response type

Cue condition

List cueMSD

Cue synonymMSD

Target synonymMSD

Unrelatedextralist cue

MSD

Listtarget

.75

.20

.52

.19

.02

.23

.02

.20

Listcue

.00

.30

.05

.26

.51

.19

.01

.22

Intralistintrusion

.01

.21

.00

.20

.01

.21

-.02.19

Extralistintrusion

.00

.19

.00

.20

.00

.19

.00

.18

extralist cue that was similar to the list cuealso retrieved a pattern that had a high reso-nance with the target, though not as high asthat evoked by the list cue. This indicatesthat stimulus generalization should occur.The extralist cue that was similar to the targetproduced a pattern that was not at all likethe target. Instead of retrieving the target, theextralist cue similar to the target retrieved anapproximation to the list cue!

Experiment 3Method. Lists of pairs of unrelated words were pre-

sented for study. Subjects were then given as cues forthe recall of each right-hand target word either (a) theleft-hand cue word that had initially been presented, (b)a synonym of the left-hand cue word, or (c) a synonymof the target.

The design of the experiment included two within-subjects factors: type of cue (list cue, cue synonym, ortarget synonym) and trials (one to three). There wereeight cues of each type in a given list. At recall, eightunrelated extralist cues were also presented as lures.

Three lists were constructed from the 144 highestranked synonym pairs of Whitten et al. (1979). Of thethree highest ranking synonym pairs, one word was ran-domly selected and then randomly assigned either toList 1, 2, or 3. Thus, at this stage in list construction,each of the three lists contained only one word. Of thenext three highest ranking synonym pairs in the norms,one word was again randomly selected and then ran-domly assigned to either of the three lists. At this stage,each list contained two words, which were then matedto form the initial cue-target pair in each list. Theseprocedures were repeated until a total of 24 pairs hadbeen formed for each list. One half of the pairs in eachlist were then reversed so that a word that was originallyassigned as the cue for a given pair became the target


for that pair, and the original target became the cue.This equated the synonymy of the extralist cues to thecue (or stimulus) and target (or response) members ofthe pairs over the list. The order of presentation of thepairs in each list was then randomized.

For each list, three test sets were constructed. Acrossthe three test sets for a given list, every pair was assignedto every cuing condition. Thus, if in Set A of List 1 thefirst pair was cued with the list cue, in Set B it might betested with a synonym of the cue, and in Set C with asynonym of the target. For each test set within each list,there were three random orders.

The entire experiment was counterbalanced so thatLists 1, 2, and 3 occurred equally often on Trials 1, 2,and 3 and the three test sets for each list occurred equallyoften on every trial.

Subjects were given two set-establishing lists beforebeginning the experiment. One of these lists consistedof similar pairs and the other of unrelated pairs (seeExperiment 1 for more details). Subjects were then givenbooklets in which three study lists, three blank pages,and three test lists were interleaved. The subjects wereinstructed to study the first list for 4 minutes, keepingin mind that they would soon be asked to recall thecapitalized right-hand words and,that the uncapitalizedleft-hand words should be studied in conjunction withthe targets because these might assist later recall. Fol-lowing study, subjects turned to the next (blank) pageof their booklets and wrote the alphabet in reverse orderfor 1 minute. The subjects were then told that they wouldbe given an equal number of cues that were list cues,synonyms of the list cues, synonyms of the targets, orunrelated extralist cues and that their task was to usethese cues to recall the right-hand members of the pre-viously presented pairs (i.e., the target items). On Trial1, subjects were unaware, while they were studying, ofthe differences among the various types of cues to whichthey would soon be exposed during the recall test. OnTrials 2 and 3, these differences were known to the sub-jects at the time of list presentation and study.

Eighteen subjects, who were volunteers from the so-cial sciences subject pool at the University of California,Irvine participated in the experiment. The subjects weretested in small groups.

Results. The data resulting from Experi-ment 3 are presented in Table 6. As can beseen from the table, the level of target recallwhen a synonym of the list cue was givenwas the same as when a synonym of the targetwas given. This finding is in contrast to theprediction of the model, which was that asynonym of the target should produce theoriginal list cue rather than the target itself.

There were a number of other discrepan-cies between the data and the predictions ofCHARM. Cue synonyms and target synonymsproduced equal numbers of list-cue respon-ses. According to the model, synonyms of thetargets shbuld cause recall of the original listcues, and synonyms of the list cues shouldnot. Again, in contrast to the predictions of

Table 6Percentage of Response Types as a Function ofCue Type in Experiment 3

Response type

List List Intrusion OmissionCue type target cue error error

List cueCue

synonymTarget

synonymLure

34

14

16—

0

8

10—

15

9

913s

51

69

6587

* Only 5 of these 58 responses were synonyms of thelures.

the model, a rather large number of responsesto the unrelated extralist cues was found.

In an attempt to rescue CHARM, an anal-ysis of the intercorrelations of each of thethree cue-type conditions (list cue, cue syn-onym, and target synonym) was conducted.Each subject contributed three scores to eachcorrelation, one for each of the three trials.There was no correlation between correctrecall in the two synonym conditions,r(52) = —.01. There was also no correlationbetween recall to the target synonyms andrecall to the list cues, r(52) = -.08. Therewas, however, a positive correlation betweenrecall to the cue synonyms and recall to thelist cues, r(52) = .44.

Correlations were also computed betweencorrect (target) recall in the two synonymconditions and responses to the unrelatedextralist cues (or lures). Responses to theselures give some indication of guessing. A pos-itive correlation was found between recall tothe target synonyms and responses made tothe lures, r(52) = .33. A negative correlationwas found between responses to the luresand correct recall to the cue synonyms,r(52) = -.22.

In summary, it appeared that correct recallto the cue synonyms was positively corre-lated with normal cued recall and negativelyrelated to guessing. Correct target recall tothe target synonyms was unrelated to normalcued recall and positively correlated withguessing. The regression equations, showingthe relative weightings of correct (target) re-call in the two synonym conditions in pre-dicting correct recall given the list cues and


in predicting guessing to the lures, are givenbelow,Z '(list cue)

= ' '44Z(Cue synonym) ~ •""^(target synonym) j

^ (responses to lures)

QUJ

synonym) ' -JJ target synonym) •

These correlations suggest that there mightbe two different processes or levels of infor-mation that combine to give rise to the (un-predicted) equal level of target recall in thecue-synonym and target-synonym condi-tions as well as the equal level of intrusionsof the list cues in these two conditions. Toillustrate these ideas, I divided the data intothose lists in which subjects made two ormore responses to the unrelated extralist cuesof lures (high-guessing lists) and those inwhich no responses were made to the lures(low-guessing lists). The data segregated inthis fashion are shown in Figure 3. As canbe seen from the figure, the data for the low-guessing lists conformed more closely to thepredictions of CHARM than did the data fromthe experiment as a whole. In particular, inthese lists, when a synonym of the target wasprovided as a retrieval cue, the original listcue tended to be recalled in preference to thetarget itself. On the high-guessing lists, thistrend was dramatically reversed. The list cuewas hardly ever recalled to the synonym ofthe target, whereas the target itself was re-called quite frequently. The holographic as-sociation and composite trace in CHARM can-not account for the pattern of recall observedin the high-guessing lists.

The correlations obtained in Experiment3 suggest that there might be two factors,processes, or levels of information that con-tribute to the overall pattern of recall foundin the experiment. One of these factors seemsto produce results consistent with CHARM,whereas the other factor produces results thatare at odds with the model. CHARM has noth-ing to say about this second factor, but thedata suggest that it is in some way related toguessing. It seems unlikely that it is justguessing, because the responses that weregenerated to the lures were rarely synonyms(although the lures also had synonyms). Thissecond factor was nevertheless related toguessing and not to normal recall, where the

-Oa:0-

I Little guessingI I Much guessing

LIST CUE TARGET TARGETCUE SYNONYM SYNONYM SYNONYM

(TARGET) (TARGET) (CUE) (TARGET)

Figure 3. Proportion of list cues or target items recalledas a function of cue type and guessing level (Experiment3). (The abscissa gives the ,type of cue presented at re-trieval—not in parentheses—and the response given—in parentheses.)

stimulus or cue is given and the response ortarget is recalled. The next experiment wascarried out in an attempt to isolate the pat-tern of recall that is consistent with CHARM.

Experiment 4Method. In the present experiment, as in Experiment

3, subjects studied a list of paired associates and werethen given list cues, cue synonyms, and target synonymsas retrieval cues. The question of interest, as before, waswhat would be recalled to the extralist cues. The mostcounterintuitive prediction was that extralist target syn-onyms would result in recall of the list cues rather thanthe targets.

There were three main differences between the presentexperiment and the previous one. The first differencewas that subjects in the present experiment were notinformed that some of the cues would be target syn-onyms and some would be cue synonyms. (I thoughtthat by not informing subjects, it might be possible toattenuate what was a guessing-related strategy in theprevious experiment.) The second difference was theproportion of synonym cues in the test lists. In the pres-ent experiment, 16 of the 20 total cues were list cues.Only two cues were critical target synonyms, and onlytwo were cue synonyms. I thought that this change mightinduce subjects to respond to the extralist synonym cuesin the same way that they responded to the list cues.This is, after all, what the simulation did. Finally, nounrelated extralist lures were presented because I feltthat their inclusion might disturb the set that the ex-periment was designed to induce. In summary, Exper-iment 4 sought to encourage subjects to use only theretrieval operation or strategy that is normally used torecall target items from a list when intralist cues areprovided.

The experiment conformed t o a 3 x 4 x 2 X 3 mixeddesign, with cue type (list cue, cue synonym, and targetsynonym) serving as a within-subjects factor and list,study order, and test order serving as between-subjectsvariables.


Four lists, each consisting of a unique collection of20 unrelated cue-target word pairs, were generated viathe synonymy norms of Whitten et al. (1979) in a man-ner similar to that used in Experiment 3. Every subjectin the present experiment studied one of these four lists.Two different random presentation or study orders ofeach list were prepared and assigned randomly to sub-jects. The cue-target pairs were typed in lowercase anduppercase letters, respectively, on the first page of athree-page booklet. Immediately prior to list presenta-tion, the subjects were read the following instructions:

In this experiment, you will be given a list of pairsof words. Your task is to remember the right-handwords. However, you should study the right-handwords in conjunction with the left-hand words—trying to form meaningful pairs. You will have threeminutes to study the pairs. When the three minutesare up, I will ask you to turn to the last page of yourbooklet [the second page was blank], where you willfind some cues that may help you to recall the right-hand target words. Most of the cues will be the left-hand cue words. You will have four minutes to recall.Do you have any questions?"

A total of 20 cues appeared on the final page of thebooklet. The cues were typed in lowercase letters. Of the20 cues, 14 were original list cues that the subject hadseen minutes before. Of the remaining six cues, two wereextralist cue synonyms, two were extralist target syn-onyms, and two were (additional) list cues. These lattersix cues provided the experimental data of chief interestand will be referred to as "critical" cues.

On the recall page of the subject's booklet, the top sixserial positions were reserved for a corresponding num-ber of "noncritical" list cues, whereas the critical cueswere randomly allocated to the bottom 14 positions. Onthe initial pass through the cues, subjects were asked toread and, if possible, to respond to the cues in their orderof presentation from the top of the page to the bottom.

A total of three different test orders were constructedfor a given set of six critical cues. These test orders wereprepared such that, across all subjects, any given targetitem that corresponded to a critical cue was probedequally often with (a) a cue synonym, (b) a target syn-onym, and (c) the original list cue. The critical extralistcue and target synonyms, like all of the words in thelists, were drawn from the synonymy norms of Whittenet al. (1979). Every extralist cue was approximately bi-directionally synonymous with its applicable intralistcue or target item (see Whitten et al., 1979, for detailson directional synonymy).

A total of 72 students at the University of Torontodonated a portion of their class time to take part in theexperiment. Three subjects were randomly assigned toeach of the 24 conditions that were defined by the cross-ing of the three between-subjects factors (list, study or-der, and test order). Of the 72 subjects, 69 providedusable data. One subject's data were discarded becauseof prior knowledge of the hypothesis. The data from twoother subjects were also discarded because analysis oftheir responses to the cue and target synonyms was com-plicated by the fact that they produced both membersof the original pair when probed with the extralist cues.

Results. Data obtained via the criticalcues are summarized in Table 7 and can beseen to correspond quite closely to the pre-dictions of CHARM. In particular, target syn-onyms produced recall of the correspondinglist cues rather than the targets themselves,whereas the reverse was true of the cue syn-onyms, x20) = 34.07, p < .001. It has beenpointed out to me that if the present exper-iment was considered in isolation, it is con-ceivable that subjects used a strategy of notresponding with a synonym, even thoughsynonyms were recalled (Slamecka, Note 4).This strategy, though possible, does not seemlikely, because it would not account for whythe pattern of recall found in the present ex-periment was also found in the previous ex-periment, but only when there was evidencethat subjects were doing little guessing. Whenthe results of the present experiment aretaken in conjunction with those of the pre-vious experiment, it seems more likely thatthe present experiment largely succeeded indoing what it was designed to do, namely,to attenuate the guessing strategy found inthe previous experiment and to induce sub-jects to use the extralist target synonyms inmuch the same manner that they use listcues.

The only inconsistency between the dataand the predictions of the model was that theextralist synonyms of the target did some-

Table 7Proportion of Response Types as a Function of Cue Type in Experiment 4

Cue type

List cueCue synonymTarget synonym

List target

.68

.29

.15

List cue

.00

.02

.27

Response type

Intralistintrusion

.04

.03

.03

Extralistintrusion

.01

.02

.02

Omissionerror

.27

.64

.53

Note. Each proportion is based on 138 observations—69 subjects X two presentations of each cue type per subject.


times produce recall of the targets them-selves. As Table 7 shows, this happened rel-atively infrequently. It is possible that despitesteps that were taken to dissuade subjectsfrom using a guessing-related strategy likethat observed in Experiment 3, such a strat-egy was not wholly eliminated. On balance,though, the pattern of results found in thepresent experiment was quite consistent withthe predictions of CHARM.

Extensions of CHARMIn the preceding section, CHARM was used

to make several predictions about what wouldbe recalled in a number of simple, single-trialcued-recall situations. These predictions, byand large, were confirmed by the experimentsthat sought to test them. In the present sec-tion, the model will be extended to threemore complex areas of investigation—pro-totype learning, the A-B A-D paradigm, andthe Osgood transfer surface—in which thecomposite-holographic trace might be ex-pected to exert a major influence on perfor-mance. These extensions are carried out withsome trepidation, because there are, no doubt,factors and processes other than associationformation, storage, and retrieval that are im-portant in the data observed in each of thethree chosen areas. The aim of the presentextensions isv exploratory: to determine whateffects may be attributable to the holographicassociation itself and to the composite traceand also what effects do not fall out in a nat-ural way. Therefore, I have specificallyavoided embellishing the model by includingother constructs such as encoding variability,stimulus or response differentiation, contex-tual associations, list markers, unlearning,spontaneous recovery, decay, item recogni-tion, response availability, response integra-tion, and the like, even though some of theseconstructs may be compatible with CHARMand may also be quite appropriate and rea-sonable. To reiterate, the aim of the presentextensions is to illustrate what the current,unembellished version of CHARM does anddoes not do, without recourse to other con-structs.

Prototype LearningIn the discussion of Experiment 1,1 noted

that the reason the model made the predic-

tion of intrusion errors in the similar-list con-dition was that the composite-holographictrace produced an item that was a combi-nation of the items in the list. I suggested thatin effect, CHARM was producing a list pro-totype. In this section, an attempt will bemade to apply the model in a more formalway to the formation of prototypes.

The experimental paradigm that will bemodeled was introduced by Posner and hiscolleagues (Posner, Goldsmith, & Welton,1967; Posner & Keele, 1968, 1970) and hasbeen studied by a number of other investi-gators (Franks & Bransford, 1971; Hintzman& Ludlam, 1980; Homa, Cross, Cornell,Goldman, & Shwartz, 1973; Medin & Schaf-fer, 1978; Strange, Keeney, Kessel, & Jen-kins, 1970). Basically, subjects are given sev-eral patterns to study that may be consideredto be category exemplars generated from acategory prototype. Usually three or foursuch constructed categories are included inthe study list, and subjects are instructed tolearn that Exemplar E is an instance of Cat-egory C. This paradigm is quite similar to theanalysis of natural category learning as out-lined by Rosch and Mervis (1975; Mervis& Rosch, 1981) insofar as the exemplars donot specify the category in terms of definingfeatures (i.e., features that must be present)but rather show an overlap or correlationwith each other. Subjects, at time of study,are not presented with the prototype itselffrom which the exemplars were generated.At time of test, subjects are given (a) the oldexemplars, (b) the prototype, (c) new exem-plars that are formally equivalent to the oldexemplars in terms of their similarity to theprototype, and, frequently, (d) new exem-plars that are more like the prototype thanwere the old exemplars. Subjects are askedto sort the materials into different responsecategories that are provided by the experi-menter. In the simulations that follow, theresponse possibilities will be limited to thosegiven by the experimenter rather than en-compassing all of semantic memory.

The simulation will focus on the procedureused by Homa et al. (1973), who varied thenumber of presented exemplars in each cat-egory. They found that when only a few(three) exemplars of a category were given,the old instances were classified best, the clas-sification of the prototypes was considerably


worse, and new instances were worse yet.When many category instances were given,however, there was little difference betweenthe correct classification of the old instancesand the prototype; the new instances werealso classified somewhat better, but correctresponding did not improve as much for thenew instances as it did for the prototype. Itis this approximately Z-shaped interaction(where the prototype gives the crossbar onthe Z) that will be simulated below.

Simulation 4Method. I ran the entire simulation three times with

three levels of similarity. The high-similarity conditionwill be described first, and then the changes in the pro-gram that produced the medium and low similarity con-ditions will be detailed.

A lexicon of 12 unrelated items, each consisting of 63features, was constructed as in the previous simulations.Three of the lexical items (10, 11, and 12) were desig-nated as responses that would be associated with thecategory exemplars and would be the targets of recall.These three items were left unchanged. Two categories-one with few (one) and one with many (four) exem-plars—were constructed as follows: Lexical Item 1 wasconsidered to be a prototype, and Items 2 and 3 weredesignated to be category exemplars. Items 2 and 3 werereassigned feature values so that 42 of the 63 featureswere identical to those in Item 1. In order to do this, 42features were randomly selected and reassigned the samevalues on Item 2 as those of the corresponding featuresin Item 1. A different random selection of 42 featureswere assigned to have identical values in Item 3 as thoseof the prototype, Item 1.

The large category was constructed in the same way.Forty-two features from each of Items 5 through 9 wererandomly selected (with a different random selection foreach) to be replaced with the corresponding values fromthe large-category prototype, that is, Item 4.

In order to construct the memory trace, Item 3 (anexemplar of the small category) was convolved withResponse Item 10. Four exemplars of the large category(Items 6, 7, 8, and 9) were convolved with ResponseItem 11. All five associations (Item 3*Item 10, Item6*Item 11, Item 7*Item 11, Item 8*item 11, and Item9*Item 11) were added into a 63-tuple representing thecomposite trace.

Then Items 1 (the prototype of the small category),2 (a nonpresented exemplar of the small category), 3(the presented exemplar of the small category), 4 (theprototype of the large category), 5 (a nonpresented ex-emplar of the large category), and 6 (a presented ex-emplar of the large category) were correlated with thecomposite trace to produce six retrieved patterns. Thesesix patterns were matched to the three response possi-bilities, namely, Items 10, 11, and 12, by the same pro-cedure used, in the previous simulations. The best matchof the three was taken to be the response (or classifi-cation) that would be given. Means and standard devia-tions of the resonance scores were calculated for the 100replications of the simulation.

The entire simulation was run twice more, with only2 lor 11 features being replaced in both categories, toyield the medium- and low-similarity conditions, re-spectively.

Results. The results of the simulation forthe three levels of similarity of the exemplarsto the prototype are given in Table 8. Resultsobtained with few presented exemplars showan effect of similarity of the test probe to theencoded item. The presented exemplar wasa better cue for the correct response or clas-sification than was the prototype, which inturn was better than the nonpresented ex-emplar, as Homa et al. (1973) reported.These relations are basically the same asthose revealed by Simulation 3, which in-vestigated the efficacy of extralist cues, andmay be viewed as manifestations of stimulusgeneralization. (The prototype was moresimilar to the presented exemplar than wasthe nonpresented exemplar by virtue of theway in which the exemplars were generatedin the simulation and presumably in the ex-periment that it was designed to mimic.)

One can also see from the results in Table8 that when many exemplars were presented,the difference in correct responding betweenthe prototype and the presented exemplarwas decreased. In fact, in the high-similaritycondition,- the prototype was actually moreeffective at producing the correct responsethan was a presented exemplar. This is notobvious from the recall data because of aceiling effect but is readily apparent in theresonance scores. Also, new exemplars wereconsistently least effective at evoking correctrecall. Again, this is not obvious from thepercentage-correct scores in the high-simi-larity condition owing to a ceiling effect butcan be deduced from the underlying reso-nance scores.

On the whole, this simple simulation dida good job of producing the Z-shaped inter-action found for correct classification whenthe type of probe (presented exemplar, pro-totype, and nonpresented exemplar) wascrossed with the number of exemplars pre-sented, as found by Homa et al. (1973).

Simulation 5Method. A second major finding with respect to the

prototype learning paradigm is that with a delay in test-ing, there is a greater loss in the accuracy of classificationof the presented exemplars than the prototypes. This


Table 8Prototype Abstraction in Simulation 4

Number of exemplarspresented

Probe Few Many

High-similarity conditionPresented exemplar

Mean resonance , .72 (.34) 1.71 (.41)% recall 88 100

PrototypeMean resonance .40 (.31) 1.96 (.39)% recall 62 100

Nonpresented exemplarMean resonance .25 (.34) 1.29 (.36)% recall 45 100

Medium-similarity conditionPresented exemplar

Mean resonance .76 (.25) .98 (.34)% recall 96 98

PrototypeMean resonance .24 (.24) .92 (.33)% recall 66 100

Nonpresented exemplarMean resonance .05 (.23) .27 (.30)% recall 34 61

Low-similarity conditionPresented exemplar

Mean resonance .79 (.26) .84 (.33)% recall 96 100

PrototypeMean resonance .11 (.26) .49 (.35)% recall 41 79

Nonpresented exemplarMean resonance .01 (.26) .03 (.34)% recall 36 36

Note. The table represents the relation between numberof exemplars presented and efficacy of three types ofprobes for correct classification under three conditionsof similarity. Standard deviations are in parentheses.

finding has been reported by Posner and Keele (1970),Strange et al. (1970), and Homa et al. (1973). This dif-ference has usually been interpreted (e.g., Posner &Keele, 1970) as evidence for the differential storage ofprototype and exemplar information, although Medinand Schaffer (1978) and Hintzman and Ludlam (1980)have developed models that account for this effect bymaking use only of exemplar information.

In order to mimic a delay in testing, I assumed in thissimulation that several unrelated pairs were convolvedand entered into the composite memory trace. Thisamounts to making the assumption that something,though unrelated to the experiment, was stored in thecomposite trace in the delay interval of about 1 week.

In a preliminary simulation, only two random pairs wereadded, and no forgetting was systematically produced.In the simulation I will describe here, these two inter-vening pairs were multiplied by five in order to increasethe distortion they introduce into the trace.

This simulation was the same as the medium-simi-larity condition of Simulation 4, except that four addi-tional unrelated lexical items (designated 13-16) wereconstructed. These four items were unrelated tof eachother and were also unrelated to any of the other 12lexical items. The four extra items were simply randomnormalized vectors, each composed of 63 features.

The composite trace was constructed in the samemanner as in Simulation 4. In addition, though, Item13 was convolved with Item 14 and multiplied by five,Item 15 was convolved with Item 16 and multiplied byfive, and the results of these convolutions were addedinto the trace.

The three probes in each of the large and small cat-egories were correlated with the trace, as before, and thematching and response-selection operations were iden-tical to those used in Simulation 4.

Results: The results of this simulation,summarized in Table 9, may be directly com-pared to those reproduced in the center panelof Table 8, because the two simulations wereidentical except for the addition of the in-tervening unrelated associations. As revealedthrough comparison of the two tables, thepresence of the intervening unrelated asso-ciations did give rise to forgetting. What didnot occur, however, was differential forget-ting of the presented exemplars and the pro-totypes.

In summary, whereas CHARM readily pro-duces a prototype that becomes more dom-inant as the number of category exemplarsincreases, it does not readily yield differentialforgetting of presented exemplars and pro-totypes. Such differential forgetting might beobtainable if we assume, in keeping with Pos-ner and Keele (1970) and Strange et al.(1970), that subjects store two types of in-formation—exemplar information and ab-stracted prototype information—that are lostfrom memory at somewhat different rates.CHARM abstracts prototypes quite readily (asin Simulation 4). It is possible that there ex-ists another level of information storage atwhich individual items or exemplars are tem-porarily stored in a discrete fashion (cf.Hintzman & Ludlam, 1980; Medin & Schaf-fer, 1978). This possibility is particularly in-teresting when taken in conjunction with theresults of Experiment 3, which provide evi-dence for a level of memory storage otherthan that of the composite-holographic trace.


Table 9Prototype Abstraction in Simulation 5

No. of exemplarspresented

Probe Few Many

Presented exemplarMean resonance% recall

PrototypeMean resonance% recall

.72 (.66)60

.25 (.72)44

1.05 (.71)76

1.04 (.74)74

Nonpresented exemplarMean resonance% recall

-.02 (.71) .38 (.77)29 44

Note. The table represents the relation between numberof exemplars presented and efficacy of three types ofprobes for correct classification under the delay (mediumsimilarity) condition. Standard deviations are in paren-theses.

Elio and Anderson (1981) have providedother evidence in an abstraction paradigmfor two types of information.

Non-Association-Specific InterferenceIn the immediately preceding simulation,

the addition of unrelated pairs of items intothe composite memory trace produced a de-crease in the level of correct recall. This in-terference was not specific to the associationsthat had been stored; that is, the interferingassociations were in no way related to thestored target associations.

The buildup of interference that results inthe model as the number of unrelated pairsadded into the composite trace increases hasbeen demonstrated in several computer sim-ulations reported by Metcalfe and Murdock(1981). In essence, these simulations indicatethat, everything else being equal, the level ofrecall is inversely related to the number ofunrelated associations that have been storedin the composite memory trace.

The model's property of non-association-specific interference appears to be directlyanalogous to McGovern's (1964) finding thatsubjects who learned a C-D list of pairedassociates following an A-B list snowedpoorer recall of the B terms than did subjectswho studied only the A-B list. The sameproperty might also be related to Under-wood's (1957) classic description of an in-

verse relation between probability of recallof a given serial list and number of lists pre-viously learned.

Association-Specific InterferenceBarnes and Underwood (1959) conducted

a classic experiment in which a list of A-Bpairs was learned to criterion. Followinglearning, subjects were given a variable num-ber of trials on an A-D list, in which thestimuli were the same as those of the first listand the responses were different. Subjectswere then presented with the stimuli andwere asked to recall both the B and D terms.The important finding was that when onlya few A-D trials were given, recall of B wasmuch higher than recall of D. As more A-Dtrials were given, recall of D increased andrecall of B correspondingly declined. Subse-quently, Martin (1971) showed that in theA-B A-D paradigm with modified modifiedfree recall (MMFR) testing (as was used byBarnes & Underwood, 1959), recall of B isindependent of recall of D. Over a variety ofmethods of pooling the data, the relationP(B)P(D) = P(B and D) was found to obtain(Martin, 1971, 1972, 1981).

It is the trade-off between B and D recall,depending on the number of A-D trials, incombination with the independence of B andD responses, that is modeled in the computersimulation described below.

Simulation 6Method. A lexicon of 12 unrelated items was con-

structed. There were 15 features in each item, and theitems were normalized so that the dot product of anitem with itself was equal to one. Fifteen features wereused, rather than 63 as in the previous simulations, inorder to place recall in an appropriate range. (Metcalfeand Murdock, 1981, have shown that with unrelateditems, recall is directly proportional to the number offeatures in the items.)

Item 1 was designated as A, Item 2 as B, and Item 3as D. Item 1 was convolved with Item 2 and the resultwas multiplied by four to correspond to four trials onthe A-B association. Item 1 was then convolved withItem 3 and multiplied by either 1,3,5, or 7 to correspondto an equivalent number of trials on the A-D associa-tion. The results of the four repetitions of A*B, and ofthe variable number of repetitions of A*D, were addedinto a single 15-tuple representing the composite trace.

In order to recall, Item 1 (or A) was correlated withthe trace, producing a single retrieved item. This itemwas matched to each of the 12 lexical items as in priorsimulations, producing a resonanace score for each lex-ical item. Then the program selected as the recalled items


the two lexical items with the highest resonance scores,provided that each score exceeded a lower limit of zero.The selection of two items was made in order to mimicthe MMFR testing procedure introduced by Barnes andUnderwood (1959).

The simulation was replicated 100 times for each ofthe four A-D repetition conditions. A count was madeof the number of trials, in each repetition condition, onwhich B, p, and both B and D were recalled. Meansand standard deviations of the resonance scores werealso computed.

Results. Results of the present simula-tion, summarized in Table 10, coincideclosely with the actual results reported byBarnes and Underwood (1959): As the num-ber of A-D trials or repetitions increases, re-call of D increases whereas the recall of Bdecreases.

The reason that the model generates Barnesand Underwood's finding becomes apparentwhen the particular features of B and D areconsidered. In all cases in the present sim-ulation, Cue Item A produced a combinationof B and D. If a feature happened randomlyto have the same sign in B and D, then whenthe item produced by correlation wasmatched to all of the possibilities in the lex-icon, this feature tended to favor the selectionof both B and D. On those features wherethe signs of the values happened randomlyto be different between B and D, the numberof repetitions became especially important.Suppose, for instance, that the A-B associ-ation was repeated more frequently than wasthe A-D association. In this instance, the signof the contrasting features tended to be thatof the B item. Alternatively, if the A-D as-sociation was repeated more frequently, thesign of the contrasting features in the re-cre-ated item tended to favor selection of the Ditem. To give a specific example, suppose that

feature n had a value of -1 in Item B and+ 1 in Item D. If B had been presented onlyonce whereas D had been repeated fourtimes, the value of this feature in the recon-structed item would have been +3—favoringD. Had B been repeated four times and Dpresented only once, the value would havebeen -3—favoring B.

Because nothing was done to alter the in-dependence of the Lexical Items B and D,independence, as shown by Martin (1971),emerged as a natural consequence. The con-tingency tables produced by the simulationfor the four conditions of A-D repetition aregiven in Table 11. Inspection of these tablesreveals that in all four repetition conditions,the quantity P(A)P(B) was very close to P(Aand B), indicating independence.

Osgood Transfer SurfaceIn the final simulation that will be pre-

sented here, the Osgood (1949) transfer sur-face, as revised by Martin (1965) in his Fsurface, will be modeled. This surface pro-vides a summary of the transfer relations thatare expected, depending on the similarity ofthe stimuli of two lists and the responses oftwo lists. The four edges of the surface maybe described as follows: (a) When the stim-ulus terms in the two lists are unrelated andthe response terms of the second list varyfrom being identical to similar to unrelatedto those of the first list, no transfer is expected(i.e., A-B C-B = A-B C-B' = A-B C-D). (b)When the stimulus terms in the second listvary from being identical to similar to un-related to those in the first list, and the re-sponse terms are identical in the two lists,transfer ranges from maximum positive to

Table 10A-B A-D Paradigm With MMFR Testing in Simulation 6

Response

Number of repetitions of A-D pair

BMean resonance% recall

DMean resonance% recall

2.92(1.01)100

.76(1.11)21

2.92(1.32)88

2.26(1.19)62

2.93(1.76)59

3.76(1.40)91

2.94 (2.26)46

5.26(1.69)99

Note. Standard deviations are in parentheses. MMFR = modified modified free recall.


Table 11Contingency Tables Illustrating ResponseIndependence in the A-B A-DParadigm in Simulation 6

Item B B Total

One repetition of A-DDD

Total

2179

100

000

2179

100

Three repetitions of A-DDD

Total

533588

93

12

6238

100

Five repetitions of A-DDD

Total

527

59

392

41

919

100

Seven repetitions of A-DDD

Total

451

46

540

54

991

100

neutral (i.e., A-B A-B > A-B A'-B > A-BC-B, where A-B A-B gives maximum pos-itive transfer and A-B C-B gives no transfer),(c) When the stimulus terms in the two listsare identical and the response terms of thesecond list range from being identical to sim-ilar to unrelated to those of the first list, trans-fer ranges from maximum positive to max-imum negative (i.e., A-B A-B > A-B A-B' >A-B A-D, where A-D A-B gives maximumpositive transfer and A-B A-B yields maxi-mum negative transfer), (d) When the re-sponses are unrelated in the two lists and thestimulus terms of the second list range frombeing unrelated to similar to identical tothose of the first list, transfer ranges frommaximum negative to neutral (i.e., A-BC-D > A-B A'-D > A-B A-D, where A-BA-D gives maximum negative transfer andA-B C-D is neutral).

Martin (1965) has argued that the Osgoodsurface is attributable to the nature of the(forward) associations. He has further arguedthat two other surfaces may contribute toobserved transfer relations. One of these isa backward-association surface—the mirrorimage of the forward-association, or Osgood,surface. If CHARM can produce the forward-association surface when the stimulus terms

are presented as cues, it will also generate thebackward-association surface when the re-sponse terms are given as cues, by virtue ofthe fact that the association in the model issymmetric.

The third surface delineated by Martin(1965) was the R surface. In contrast to eitherthe forward- or backward-association sur-face, Martin attributed the R surface not tothe associations themselves but rather to re-sponse learning or availability. Because thisarticle is concerned with the problem of howitems are associated, stored, and retrieved,and not with other processes or stages oflearning, such as response learning or avail-ability, no attempt will be made to modelthis third, R surface, even though it is notquestioned that the stage of learning reflectedby this surface may influence observed trans-fer relations in particular experimental situ-ations.

A problem that I immediately encoun-tered in attempting to simulate the Osgoodsurface was that if a single association is con-sidered in isolation, it makes no differencewhether that association is repeated. A-BA-B does not produce a higher level of recallthan does A-B alone. The reason for thisanomaly in the model is that when a singleassociation is doubled, for instance, both thesignal and the internal noise are doubled, andexactly the same selection errors will occurwhen the retrieved item is compared to thelexical items as would occur had the associ-ation not been doubled. This anomaly occursonly when the composite trace is assumed tostart with values of zero on all of its features.It is because there was another associationin the composite trace in Simulation 6 thatthe problem was not obvious in that simu-lation. When the composite trace does notstart out as a blank slate, the problem doesnot arise. Accordingly, in the simulation thatfollows, two extraneous unrelated associa-tions, whose purpose was to provide "back-ground noise," were stored in the compositetrace in each condition, as were the associ-ations of main interest.

Simulation 7Method. A lexicon of 14 unrelated 31-feature items

was constructed as in the previous simulations. Item 1was designated as A, Item 3 as B, Item 5 as C, and Item7 as D. In order to mirnic the similarity relation between


A and A', Item 2 was reassigned feature values to beidentical with those of Item 1 on 15 randomly chosenfeatures. In a similar manner, though with different ran-domizations, Item 4 was reassigned values on 15 featuresto be identical with those of Item 3 and, likewise, Item6 with Item 5 and Item 8 with Item 7.

Nine separate traces were constructed to represent thefollowing conditions: (a) A-B A-B, (b) A-B A-B', (c)A-B A-D, (d) A-B A'-B, (e) A-B A'-B', (f) A-B A'-D,(g) A-B C-B, (h) A-B C-B', and (i) A-B C-D. These•nine conditions define a 3 X 3 design in which threelevels of stimulus similarity (identical, similar, and un-related) are factorially combined with three levels of re-sponse similarity (identical, similar, and unrelated) toproduce the main conditions represented in the Osgoodsurface.

In all nine conditions, two unrelated pairs—Item9*Item 10 and Item ll*Item 12—were convolved andadded to the 31-tuple representing the composite mem-ory trace. In addition to these two unrelated pairs, thenine conditions were constructed, respectively, as fol-lows: (a) Item 1 *Item 3 + Item 1 *Item 3, (b) Item 1 *Item3 + Item l*Item 4, (c) Item l*Item 3 + Item l»Item7, (d) Item l*Item 3 + Item 2*Item 3, (e) Item l*Item3 + Item 2*Item 4, (f) Item l*Item 3 + Item 2»Item7, (g) Item l*Item 3 + Item 5*Item 3, (h) Item l*Item3+ Item 5*Item 4, and (i) Item l*Item 3 + Item5*Item 7,

To simplify the programming, Item 1 was correlatedwith each of the nine traces, and recall of Item 3 wascompared across conditions. The correlation of Item 1with each of the nine traces produced nine retrieveditems, each of which was matched, as in prior simula-tions, to all (14) lexical items. The best match (i.e., themost resonant lexical item) was chosen as the item thatwould be recalled. The simulation was replicated 100times, using different random values of the lexical items.Means and standard deviations of the resonance scoresfor each lexical item were computed.

Results. The pattern of correct (Item B)recall produced by the simulation is' shownin Table 12 and can be seen to correspondclosely to the transfer relations represented

by the Osgood surface. More specifically, thesimulation produced all of the ordinal rela-tions that define the four edges of the Osgoodsurface: (a) A-B C-B = A-B C-B' = A-BC-D, (b) A-B A-B > A-B A'-B > A-B C-B, (c) A-B A-B > A-B A-B' > A-B A-D,and (d) A-B C-D > A-B A'-D > A-B A-D.I have rerun this simulation using differentrandomizations, different numbers of extra-neous unrelated pairs, and different numbersof features in the items. In all cases, the re-sults were similar to those obtained in Sim-ulation 7, as illustrated in Table 12.

Relation to Other Models

In the preceding sections, I showed thatCHARM makes a number of predictions aboutwhat would be recalled in several cued-recallsituations. By and large, these predictionswere confirmed experimentally. I also showedthat the model can account for a variety ofwell-known results that have been obtainedin associative-learning paradigms. In this sec-tion I will compare CHARM to several otherassociative models.

Liepa's Holographic Model

CHARM was developed from the holo-graphic model proposed by Liepa (Note 1;also see Murdock, 1979) and so, in manyrespects, it is similar to that model. In par-ticular, the convolution-correlation algebraof Borsellino and Poggio (1973) and the con-struct of a composite memory trace are com-mon to both models. Liepa's model is more

Table 12The Osgood Transfer-Retroaction Surface in Simulation 7

Stimulus similarity

Identical (A)Mean resonance% recall

Similar (A')Mean resonance% recall

Unrelated (C)Mean resonance% recall

Identical (B)

1.54 (.39)98

1.14 (.35)93

.77 (.34)72

Response similarity

Similar (B')

1.1 5 (.36)54

.94 (.32)73

.76 (.31)73

1

Unrelated (D)

.76 (.34)36,

.77 (.34)66

.76 (.32)72

Note. Standard deviations are in parentheses.


general than CHARM insofar as it applies toitem, associative, and serial-order informa-tion, which are stored in a single trace. It isless general than CHARM, however, in thatit deals only with orthogonal vectors—sim-ilarity is not represented. One reason for theorthogonality constraint in Liepa's model(and other holographic models as well; e.g.,Willshaw, 1981) is that when this constraintis relaxed, the retrieved item may be ambig-uous.

In CHARM, the orthogonality assumptionis abandoned and similarity is represented ina traditional psychological way. The resultingambiguity in retrieval produces some of themost psychologically interesting properties ofthe model: that certain types of errors of re-call will be made, that prototypes will beformed, and that interference will occur. Tobe sure, CHARM is not a maximally efficientmemorizing device in terms of producing averidical copy of the original items or events.However, it is precisely because CHARMtransforms and combines events that themodel is psychologically interesting.

A second major difference between CHARMand Liepa's model is that the former includesa semantic-memory-pattern recognizerwhereas the latter is a single-layer model.This pattern recognizer is essential for CHARMto be applied to experimental situations inwhich the items retrieved by correlation areeither ambiguous or represent combinationsof two or more items, and yet, the responsesemitted by subjects are discrete. Further, asMartin (1965) has noted and schematized inhis R surface, there appears to be a stage oflearning that is separable from associationformation itself. The results of Experiments3 and 4, and also those of Simulation 5 con-cerning prototype retention, point to the im-portance of a level of information distinctfrom that represented by the composite trace.Thus, the construct of a semantic-memory-pattern recognizer is formally necessary ifCHARM is to be broadly applicable to psy-chological data and also appears to be in-dependently supported by the data them-selves.

J. A. Anderson's Neural Model

CHARM uses the idea of a composite mem-ory trace, and this idea derives, in part, from

the neural model given by J. A. Anderson etal. (1977). Both models account for the for-mation of prototypes by allowing for the su-perimposition of items in the compositetrace.

However, the associations in the two mod-els are different. The association in the J. A.Anderson et al. (1977) model is directionalrather than symmetric, as it is in CHARM. Assuch, the J. A. Anderson et al. (1977) modelcannot account for or predict backward in-trusions (Experiment 1), differential cue in-trusions (Experiment 2), or recall of the cuewhen an item similar to the target is givenas a retrieval cue (Experiments 3 and 4).J. A. Anderson (1977) has noted that thereis a problem in associating two responses toa single stimulus in his model. It is not ob-vious that the feedback mechanism Ander-son proposed in conjunction with the asso-ciation in his model solves this problem. Thesemantic-memory-pattern recognizer in-cluded in CHARM does allow for the removalof ambiguity of responses in situations wheretwo responses are associated with a sin-gle cue.

Multicomponent or Feature Models

A number of feature models of recall havebeen proposed for purely psychological rea-sons (e.g., Bower, 1972; Medin & Schaffer,1978; Underwood, 1969). CHARM, too, usesthe idea that items are composed of sets offeatures, making explicit the link between thevector elements in neural models and the fea-tures that have been proposed for psycho-logical reasons, as was suggested by Estes(1979). Similarity is represented in CHARMin much the same way as it is in featuremodels—that is, in terms of feature over-lap—and I showed that this variable pro-duces a number of psychologically interest-ing results, such as the Osgood transfer sur-face, prototype formation, and intrusions inrecall.

CHARM differs from other feature modelsin that all of the associations are stored in asingle composite trace. However, it may notbe possible to distinguish psychologically theconstruct of a composite trace from the ideathat associations are stored separately but arecombined at time of retrieval. Mathemati-cally, it makes no difference to the end result


whether associations are combined at timeof storage or at retrieval. Thus, there is a for-mal similarity between CHARM and modelssuch as those proposed by Medin and Schaf-fer (1978) and Hintzman and Ludlam (1980)that add the results of a variety of retrieveditems at time of retrieval. Similarly, featureshave usually been coded as positive values,with the absence of a feature coded as zero.In CHARM, features are coded as positive andnegative values around zero, which permitsrepresentation of common as well as con-trasting features (Tversky, 1977). However,it may be that the apparently different viewsof feature coding will in some sense proveequivalent. Nevertheless, the combination ofthe construct of a composite trace and thezero-centered feature coding makes it easyto see certain relations among phenomenathat might not otherwise be obvious. For in-stance, interference and the abstraction ofprototypes both depend on the addition offeatures and differ only in the expected re-sultant values. The same combination ofconstructs also allows for the observation ofcertain conceptual differences. For instance,a loss of discriminability in CHARM reflectsan increase in the randomness of retrieveditems and is not conceptually equivalent toan increase in the similarity of retrieved items(as it is in Medin and Schaffer's, 1978, modelof prototype learning).

CHARM uses a symmetric association,whereas the association in other feature mod-els is directional. The association in CHARMallows it to address phenomena that dependon the similarity relations between the stim-ulus and response terms of a single pair. Italso gives rise to the predictions of equal fre-quencies of stimulus and response intrusions(Experiment 1), cue intrusions (Experiment2), and the efficacy of extralist items similarto the target to generate the cues (Experi-ments 3 and 4). These predictions are notmade by other feature models.

Martin's Encoding-Variability Model

Martin (1972) proposed that associativerecall depends critically on recognition of thefunctional stimulus, reviving Hoffding's ear-lier view of recall (see Rock, 1962). This isin marked contrast to CHARM, which doesnot consider or include item recognition.

When convolution and correlation serve asthe associative encoding and retrieval oper-ations, it is not necessary that cue or stimulusrecognition precede target or response recall(although a pattern-identification process thatmight be related to recognition is includedin CHARM).

Martin has also argued that the constructof variable encoding of stimulus terms is nec-essary for a person to recall multiple respon-ses to a single stimulus, as in the A-B A-Dsituation. As Martin (1972) has stated, "If RIand R2 are two distinct behaviors and if Stis the presumed stimulus for RI, then anyassertion that Si can also be the stimulus forR2 is a mistake. . . . A learner cannot retainboth A-B and C-D where A and C are iden-tically encoded" (p. 71). This "mistake" isprecisely what was committed in Simulation6 that modeled the A-B A-D paradigm. Theresult of that simulation was not only a goodapproximation to the trade-off between Band D recall but also showed independenceof recall of the two responses. The implica-tion, then, is that it is not necessary to invokethe assumption of encoding variability inorder to account for the capacity of a singlenominal stimulus to control two or moredistinct behaviors or responses. This does notimply, however, that the representations inCHARM are incompatible with the idea ofencoding variability. Indeed, CHARM goesbeyond the assumption of encoding vari-ability by providing a memory mechanismthat may actually change the representationof an item from encoding to retrieval, de-pending on the nature of the associated itemand also the nature of the list.

Node/Network Theories

CHARM is radically different from node/network theories of associative recall (e.g.,J. R. Anderson, 1972, 1976; J. R. Anderson& Bower, 1973). To cite just a few obviousdifferences, network theories do not considerthe question of how new associations areformed (see Postman, 1975), which is a mat-ter of prime importance in CHARM. Also,CHARM places no emphasis whatever on itemrecognition, whereas this process is quite im-portant for recall in network theories. Therepresentation of items as conceptual nodesin network theories differs from the feature


representations in CHARM. Further, the ideathat retrieval is a search or that it consists ofspreading activation is metaphorically far re-moved from the filterlike operation of cor-relation proposed in CHARM. And the single-layer semantic memory given by networktheories differs from the dual memory sys-

tem—composite-holographic trace and se-mantic-memory-pattern recognizer—em-ployed in CHARM.

The basic assumptions, or the approachto the problem of recall, are also different.It seems that one assumption made about thenature of the association in network theories

Table 13Predictions and Applications O/CHARM

Prediction or phenomenon

Favorable

Simulation Yes No Evidence

Interaction between correct recalland intralist intrusionsdepending on whether paired-associate list consists entirely ofsimilar or of unrelated items

Equal frequency of stimulus- andresponse-term intralist intrusions

Greater proportion of cueintrusions when cue and targetitems are similar than when theyare unrelated

Stimulus generalization

Extralist item similar to targetevokes recall of cue rather thantarget

Responses of a particular pairlearned less well in ahomogeneous than in aheterogeneous list

Interaction between number ofcategory exemplars presentedand cue efficacy of prototype ascompared to exemplars

Prototype more resistant toforgetting than presentedexemplars

Non-association-speciftcinterference: A-B C-D gives 'worse recall than A-B alone

Trade-off between B and D recallin A-B A-D paradigm withMMFR testing

Independence of B and D responsesin the A-B A-D paradigm

All of the transfer or retroactionrelations given in the Osgoodsurface

X

X

X

X

X

X

Metcalfe andMurdock, 1981

X

X

X

X

Experiment 1

Experiment 1

Experiment 2

Experiment 4;Gibson, 1941.

Experiment 4

Tulving, Note 3

Homa, Cross,Cornell,Goldman, andSchwartz, 1973

Posner and Keele,1970; Strange,Keeney, Kessel,and Jenkins,1970

McGovern, 1964

Barnes andUnderwood,1959

Martin, 1971

Osgood, 1949;Martin, 1965

Note, MMFR = modified modified free recall.


is that if the association between two itemsA and B has been tagged and the tag is stillpresent at time of retrieval, A will automat-ically lead to B. When this assumption ismade about the nature of associations, theproblem then becomes one of inferring,whether, and with what probability, thetagged association exists. An additional prob-lem is that of delineating what is associatedwith what; for instance, is Item A associatedwith context, which meaning node of A isassociated with B, and so on.

In CHARM, the problem of recall is notformulated in terms of inferring what is as-sociated to what and with what probability.Rather, it was assumed early on that the ex-perimenter had control over what was asso-ciated with what. Thus, if an A-B pair waspresented by the experimenter, it was allowedthat A and B were associated. The explana-tory burden in CHARM was placed on howassociations are formed, stored, and re-trieved.

The approach taken in CHARM of focusingon the microstructure of association forma-tion, storage, and retrieval seems to have sev-eral advantages over the "higher level" ap-proach taken in network theories. For in-stance, in discussing how human associativememory (HAM) accounts for some of thebasic findings of interference theory, Ander-son and Bower (1973) appeal to context, rec-ognition, a construct roughly equivalent tounlearning, spontaneous recovery, rehearsaldifferences in some conditions, mediated se-mantic associations, and both forward andbackward associations between stimuli andresponses. In contrast, as has been demon-strated, CHARM can account for a consider-able number of paired-associate learning re-sults by detailing only how the pairs pre-sented by an experimenter are associated,stored, and retrieved. In addition, CHARMcan account for list-context effects, associa-tive-context effects, and the abstraction ofprototypes. Further, CHARM makes predic-tions about errors of recall (see Experiments1,2,3, and 4) that network theories certainlydo not predict and may not be able to ac-commodate. The simplicity with which bothwell-known and counterintuitive (but exper-imentally confirmed) findings are producedby CHARM indicates the value of attempting

to specify at a "micro" level how associationsare formed, stored, and retrieved.

Conclusion

In this article, a composite holographicassociative recall model was proposed as asolution to the problem of how it is that peo-ple associate pairs of items, store the asso-ciations in memory, and then later, whengiven a retrieval cue, use that cue to evokerecall. The model yielded predictions aboutwhat people would recall in several cued-re-call experiments. It was also applied in anunelaborated form to a variety of well-estab-lished phenomena that ostensibly depend onassociations. The results of the model aresummarized in Table 13. As can be seen fromthe table, the model seems to be doing some-thing similar to what people do when theyassociate, store, and retrieve from memory.

CHARM is a highly interactive model ofhuman association formation, storage, andretrieval. Nearly all of the predictions andapplications depend on the interactive natureof the holographic association and of thecomposite trace. The events stored in sucha memory combine and interfere with oneanother so that the output from memory isdifferent from the input to it. Under certainconditions, as when unrelated items are as-sociated, the difference from input to outputmay be that the retrieved items are noisierthan the encoded items. Under other con-ditions, as when the items are similar to oneanother, the retrieved items are systemati-cally transformed from their encoded form.

It is an old notion that memory is not justa passive store for holding ideas withoutchanging them but may in fact transformthose ideas. The Gestalt psychologists gavea number of demonstrations showing thatwhat is retrieved may differ from what wasinitially given. It seems intuitive that peopledo not simply take ideas and passively storethem. Rather, people seem all the time to bealtering and mentally transforming what wasgiven. The holographic hypothesis of asso-ciations may have many implications for thestudy of human memory. It may turn outthat the most important of these is that itmay not only increase our understanding ofhow ideas are associated, stored, and re-


trieved but also provide some insight into thequestion of how it is that people are able totake old ideas and transform them into ideasthat are new. .

Reference Notes1. Liepa, P. Models of content addressable distributed

associative memory (CADAM). Unpublished manu-script, University of Toronto, 1977.

2. Tulving, E. Personal communication, August 1981.3. Tulving E. Organization and interference. Paper pre-

sented at the meeting of the American Associationfor the Advancement of Science, New York, Decem-ber 1967.

4. Slamecka, N. J. Personal communication, December2, 1981.

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Appendix

Computational Illustrations of Convolution and Correlation

The convolution of two items A = ( • • • , a_i,OQ, a\, • • •) and B = ( • • • , b-\, b0, bt, • • •) isconveniently computed by constructing a matrixas shown in Figure Al. The trace T that resultsfrom summing across the positive diagonals isgiven by T = ( • • - , t-2, t-,, t0, /,, /2, • • •) =

atb0 + Oobi, aibi), which conforms to the defini-tion of convolution given in the text in the As-sociation Formation section.

In order to correlate one of the items, say B,with the trace T, a new matrix is formed as shownin Figure A2. The retrieved item is R = (r_(, r0,rt). The central « features of this retrieved itemprovide an approximation to A, provided that theinitially convolved items are unrelated.

To illustrate the nonnoise components in theresultant item R, it is necessary to expand the jointconvolution-correlation matrix. In the expandedmatrix, given in Figure A3, the components thatproduce the retrieved item A have been under-lined. Regardless of the dimension of the vectors(i.e., the number of features in the items), if theitems are unrelated, there is one signal componentin each cell of the joint convolution-correlationmatrix for the central n features of R. It can be

seen that

b02

= a_i(B-B) + b\a\b-\ += a-i + noise.

Similar computations can be carried out for allof the central features of R and one will see thatthe rfl = fl0 + noise and r\ = at + noise. Thus,B#(A*B) = A + noise.

Had A been correlated with T = A*B, the re-trieved item would be an approximation to B. Inthat case, r-l is as follows:

+ aoa-tbo += b-i(a2 + ao2 + a-2) +

+ aia^bi + Ood-ibo= b-i + noise.

Similar computations can be carried out for r0 andrt, and they too produce the corresponding fea-

»-2 t-1 to »1 »2

Figure Al. A computational illustration of the convo-lution of two items A = (a_,, Oo, «i) and B = (£_,, b0,bt) to produce an association T = (t-2, t-i, t0, tt, t2).

b,t_2 b,t.

b-1(2

Figure A2. A computational illustration of the correla-tion of an item B = (b\, b0, 6,) with-the association givenin Figure Al to produce a retrieved item R = (/•_,, ra,r{).

COMPOSITE HOLOGRAPHIC ASSOCIATIVE RECALL MODEL

o,b.,

661

a.,b0

'-2

a0b,

t|

Figure A3. An expanded version of the joint convolution-correlation matrix that was given in FigureA2. (The underlined components produce the retrieved item A when the initially convolved items A andB are unrelated.)

tures of B, namely, b0 and b\. Thus, A#(A*B) =B + noise.

Suppose A and B are convolved, as dia-grammed in Figure Al, and then an item similarto B is correlated with the result. A "weak" ap-proximation to A is retrieved. For instance, sup-pose that the retrieval cue B' = (b-\, b0, x\) so thattwo features are identical to the correspondingfeatures in B and one feature has a value inde-pendent of the value of the corresponding featurein B. In this case, the bottom two rows of the jointexpanded convolution-correlation matrix will beidentical to those given in Figure A3. However,no nonnoise components will be systematicallyproduced in the top row, that is, for the x\ feature.Thus, instead of producing A + noise, B' will re-trieve (n common/H)A + noise. It may be notedthat all of the features of A are still retrieved, butwith a decreased strength.

If A = B, and B is correlated with the resultanttrace,

r-i = a_,(B'B)= a-i + b-i(a{

2 + a02) + bi

The term (a\2 + ao2) results in a positive value butis not quite equal to A • A. In particular, there isone missing component: in this case fl-i2. Themissing component stems from the cases, in theoriginal convolution matrix, where the a and bsubscripts were the same (i.e., from the negativediagonal of the original convolution matrix).There is thus exactly one missing component fromthe dot product A • A in each reconstructed fea-ture. However, as the number of features in theconvolved items becomes large, the difference be-tween (n - 1/n) and 1 becomes vanishingly small,and so \

r-i = a-i + b-i + noise

= 2a_, + noise.

A similar result may be computed in a like man-ner for all features.

Received October 19, 1981Revision received April 5, 1982

Documents

A C om posite H olographic A ssociative R ecall M odel...P sychological R eview 1982, V ol 89, N o. 6, 627-661 C opyright 1982 by the A m erican P sychological A ssociation, Inc. 03