The TECO Connectionist Theory of Recognition Failure

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The TECOConnectionist Theoryof Recognition FailureSverker P. SikstromPublished online: 10 Sep 2010.

To cite this article: Sverker P. Sikstrom (1996) The TECO ConnectionistTheory of Recognition Failure, European Journal of CognitivePsychology, 8:4, 341-380, DOI: 10.1080/713752535

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The TECO Connectionist Theory of Recognition

Failure

Sverker P. SikstroÈ mDepartment of Psychology, UmeaÊ University, UmeaÊ , Sweden

Data from experiments on the phenomenon of recognition failure of recall-able words show moderate dependence between recognition and recall.TECO, a connectionist theory, is proposed to account for the phenomenon.Cued recall is assumed to be cued with the cue word and the event. Recog-nition is assumed to be cued with the event and the copy cue. Moderatedependence is predicted because recall and recognition are cued with theevent. The large degree of independence is predicted because recognitionlacks the word cue and recall lacks the copy cue. TECO predicts exceptionsfrom the regularity of independence when recognition is cued and recall isuncued. Dependency increases when both tests are cued with the cue wordand when recall is uncued. Functions for the various levels of cue informa-tion are derived. A comparison with experimental data shows a better ® tfor the TECO theory than for the Tulving± Wiseman function, especially forthe cued recognition and free recall exceptions.

INTRODUCTION

The generation ± recognition theory (Bahrick, 1970; Kintsch, 1978; Martin,1975) stated that recognition is a prerequisite for recall. This theorybecame more or less obsolete when researchers revealed a remarkableinvariance between recognition and recall (Watkins & Gardiner, 1979).

EUROPEAN JOURNAL OF COGNITIVE PSYCHOLOGY, 1996, 8 (4), 341± 380

Requests for reprints should be addressed to Sverker P. SikstroÈ m, Department of Psy-chology, UmeaÊ University, S-901 87 UmeaÊ , Sweden. E-mail: [email protected]

I would like to thank my supervisor, Lars-GoÈ ran Nilsson, for introducing me to therecognition failure paradigm, and for his stimulating critique and careful reading of my pre-vious drafts of the manuscript. John Gardiner’s and Endel Tulving’s comments of the modelare greatly appreciated, as are Anders Lansner’s on the mathematics. Lars Nyberg, UlrichOlofsson, Bo Molander and others in the memory group at UmeaÊ contributed to the stimu-lating research environment that made this paper possible. Finally, thanks to the anonymousreviewers for their careful and constructive comments.

� 1996 Psychology Press, an imprint of Erlbaum (UK) Taylor & Francis Ltd

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This phenomenon has been called `̀ recognition failure of recallablewords’ ’ or ``recognition failure’ ’ for short (Tulving & Thomson, 1973).Recognition failure has been studied in an experimental setting consistingof three phases. First, subjects are instructed to study word pairs eachconsisting of a cue word and a target word. In the second phase, thesubjects are tested for recognition of target words presented at study.Third, the subjects are tested for recall of the target in the presence of thecue word. The results from such experiments show that subjects often,but not always, fail to recognise words that they will subsequently recall.This phenomenon may not be attributed to the e� ect of the recognitiontest on the cued recall test, because studies have shown that the recogni-tion test does not a� ect the cued recall test to a signi® cant extent (e.g.SikstroÈ m, 1996) . The recognition failure phenomenon can be visualisedby plotting the conditional probability of recognition given recall,P(Rn | Rc) against the overall probability of recognition, P(Rn). Tulvingand Wiseman (1975) demonstrated that the data from all 40 conditionsreported at the time adhere to the following function:

P(Rn | Rc) = P(Rn) + c [P(Rn) ± P(Rn)2] (1)

where c is a constant equal to 0.5.This function was empirically derived by minimising a polynomial

function on the set of data. Recognition failure has been shown to berobust for a wide variety of to-be-remembered items (e.g. Neely & Payne,1983), for di� erent kinds of contextual materials (e.g. Bartling &Thomson, 1977), for naive and familiar subjects (e.g. Tulving &Thomson, 1973), for young and old subjects (e.g. Rabinowitz, 1984) , fordi� erent distractor items in the recognition test (e.g. Watkins & Tulving,1975) and over di� erent retention intervals (e.g. Begg, 1979; Rabinowitz,1984). Nilsson and Gardiner (1993) gathered a database consisting of all302 conditions published between 1973 and 1993. These conditions andthe Tulving ± Wiseman (TW) function are plotted in Fig. 1.

Subsequent research has found deviations from the Tulving ± Wisemanfunction (Begg, 1979; Bryant, 1991; Fisher, 1979; Gardiner & Tulving,1980; Jones & Gardiner, 1990; Muter, 1984; Nilsson, Dinniwell, &Tulving, 1987; Nilsson, Law, & Tulving, 1988). Nilsson and Gardiner(1993) classi® ed all known conditions of recognition failure into one ofthree categories. In the ® rst category, which they labelled `̀ no-excep-tions’ ’ , all of the conditions conformed to the TW-function. In the othertwo categories, nearly all of the conditions did not conform to the TW-function, and thus they were labelled ``exceptions’ ’ . The ® rst category ofexceptions occur when the cue and target words are poorly integrated.These exceptions are generally referred to as `̀ poor integration’ ’ or ` f̀reerecall’ ’ exceptions. The second category of exceptions is referred to as

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``cue overlap’ ’ or ``cued recognition’ ’ exceptions, because the contextualinformation is, to a large extent, already available at the recognition test.These exceptions have a greater probability of recognition given recallthan expected from the Tulving ± Wiseman function. In this paper, allconditions where the cue ± target words pairs are poorly integrated will becalled `̀ free recall’ ’ exceptions. Nilsson and Gardiner (1993) suggested theCV-measurement for classifying exceptions; that is, conditions thatdeviate more than 0.14 from the TW-function. Most, but not all, of thefree recall exceptions deviate signi® cantly above the TW-functionaccording to the CV-criteria. Similarly, all conditions where the cue isretrievable from the target will be called `̀ cued recognition’ ’ exceptions.Most, but not all, of these conditions also deviate signi® cantly above theTW-function according to the CV-criteria.

The Need for a New Theory

``The relation between recall and recognition remains one of the mostfundamental and long standing theoretical problems in the scienti® c studyof memory’ ’ (Nilsson & Gardiner, 1991). A number of theories have been

FIG. 1 . Three hundred and two conditions of recognition given cued recall from Nilssonand Gardiner’s (1993) database. The data set is divided into no-exceptions, free recall excep-tions and cued recognition exceptions. The TW-function is included for comparison.

TECO CONNECTIONIST THEORY OF RECOGNITION FAILURE 343D

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suggested to explain the phenomenon, including Vandal Theory (Begg,1979), Dual Mechanism Theory (Jones, 1978, 1983, 1987), RetrievalIndependence Theory (Flexser & Tulving, 1978, 1982) and BackwardRetrieval (Rabinowitz, Mandler, & Barsalou, 1977). General memorymodels have also been proposed to account for the phenomenon. Thegeneral memory models that have claimed to account for recognitionfailure, but not simulated the phenomenon in detail, include ACT*(Anderson, 1983), SAM (Gillund & Shi� rin, 1984), Matrix Model(Humphreys, Bain, & Pike, 1989) and TODAM (Murdock, 1979, 1982,1983). Hintzman (1987) simulated recognition failure in MINERVA II.An extensive account of the phenomenon has also been given by Metcalfe(1982, 1985, 1991) in the CHARM model. However, most of theseaccounts are unsatisfactory (Nilsson & Gardiner, 1991). CHARM andRetrieval Independence might be regarded as the most developed of thetheories of recognition failure.

Research has focused mainly at a descriptive level rather than at anexplanatory level. The Tulving ± Wiseman (1975) function yields a fairlygood approximation of the set of data, but does not Ð and does not claimtoÐ explain the recognition failure phenomenon. Furthermore, theTulving ± Wiseman function does not hold in general. It is restricted byboundary conditions. Successful e� orts have been made to specify theboundary conditions (Nilsson & Tulving, 1986; Nilsson et al., 1987) , andall of the conditions that are known to deviate widely, de® ned by thecritical ratio, have been shown to adhere to one of the two types ofexceptions. But no function that describes these exceptions has yet beenproposed. No theory has yet been able to deal with both types of excep-tions satisfactorily. The robustness and the remarkable regularity of thephenomenon remain a puzzle to researchers in the ® eld.

There is a need for a theory that can explain the quantitative level ofrecognition failure. The aim of this study, therefore, was to propose suchan explanation of the phenomenon. The TECO (Target, Event, Cue andObject) theory of recognition failure is a mathematical description of thephenomenon which, in contrast to the Tulving ± Wiseman function, is notbased on a least-square approximation. It is suggested on theoreticalgrounds.

There is also a need for a theory that can account for the two types ofexceptions, cued recognition and free recall. TECO suggests such atheory. Functions are proposed for predicting the dependency in theexceptions. This gives a uni® ed theoretical framework, without anyboundary conditions.

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Theoretical Accounts of Recognition Failure

Flexser and Tulving (1978) proposed three criteria that any model ofrecognition should account for. First, it should explain why recognitionfailure occurs. Second, why is it so robust? Third, it should explain thequantitative level of dependency. This demands an explanation of whyrecognition and recall are not independent and why they are not comple-tely dependent. Tulving (pers. comm.) has since proposed a fourthcriterion, the explanation of exceptions. Each of these criteria will now bediscussed in relation to CHARM and Retrieval Independence Theory.

Metcalfe (1982, 1985, 1991) has claimed, in the framework of theCHARM model, that the phenomenon occurs because (a) recognitionand recall are similar (i.e. it uses convolution and correlation) and (b) theinformation is stored in the same composite memory trace. The simula-tion of CHARM can be criticised for not meeting some of Tulving’scriteria:

· Quantitative criterion: CHARM largely overestimates the independence,giving a value of c = 0.2 instead of c = 0.5, as with the Tulving ±Wiseman function (E. Tulving, pers. comm.).

· Exception criterion: CHARM cannot predict retrieval exceptionswithout the unjusti® ed assumption that relatively few features areencoded.

Flexser and Tulving (1978) have proposed Retrieval IndependenceTheory to account for the recognition failure phenomenon. A similarexplanation has been given by the Matrix Model (Humphreys et al.,1989) and ACT* (Anderson, 1983). Retrieval Independence Theory isbased on three assumptions, the ® rst of which, ` t̀race identity’ ’ , statesthat recognition and recall share the same underlying memory trace. Thesecond, `̀ goodness of encoding’ ’ , states that there are variations to howwell a to-be-remembered item is encoded. The dependence is explained bythese two assumptions. The third assumption, `̀ retrieval independence’ ’ ,accounts for the independence between recognition and recall. It statesthat only a small number of the total features are used at the time ofretrieval and that they are independent. But the cue as a whole (in recall)and the target as a whole (in recognition) are indeed presented to thesubject. It is argued here that the presence of a cue makes all or most ofthe cue’s features salient and therefore available to the subject. Totaldependence between recognition and recall is produced by a specialversion of the Retrieval Independence Theory, when the parameters areset to make all features salient at retrieval. Furthermore, the theory hasnot been claimed to handle free recall exceptions.


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THE TECO THEORY

TECO, a general memory theory, is introduced here to account for recog-nition failure. It is based on a connectionist conceptualisation that usesthe brain as an analogy, which is aimed at biological realism.

An Internal Representation of the Learning Episode

TECO assumes an internal representation of the learning episode calledthe `̀ event’ ’ . The event represents the speci® c point in time whenlearning takes place. Examples of events are `̀ the memory test that Itook last week’ ’ and `̀ the ski trip last year’ ’ . The event may be relatedto concepts like schema, frame or script. Events should be distinguishedfrom to-be-remembered items, which are called `̀ objects’ ’ in this paper.An example of objects are the words in the learning list. Objects andevents are represented in populations of nodes. A particular object isrepresented by the pattern of activity in the object population and aparticular event is represented by the pattern of activity in the eventpopulation. The event population might be related to the rememberingstate of awareness, whereas the object population might be related to theknowing state of awareness, or to a feeling of familiarity (Gardiner &Java, 1993; Tulving, 1983). Each event is uniquely related to the learningsituation and therefore makes a clear distinction between two di� erentencoding situations Ð for example, the experimental situation and priorknowledge.

One problem with this type of implementation of events is that, as timepasses, an in® nitely large number of event patterns is used. A plausiblesolution to this is that the event patterns are re-used, which may berelated to forgetting in episodic memory. Viewing the event as a schemaor script may lead to a more economical and less event-node-consumingrepresentation of episodic information.

TECO’s interpretation of the event is di� erent to that of CHARM,which represents an event Ð or, preferably, the context Ð as the `̀ sum’ ’ ofthe items at the time of encoding (e.g. of cues and target pairs). Theevent in CHARM is therefore not seen as something separate fromencoded items. Rather, it includes items, or is a function of them: Event= Function (Items). In TECO, the items are connected to the event,rather than included in the event (see Fig. 2). Note that the event inTECO is not intended to be the same thing as the context. For example,two quite di� erent events (e.g. a lecture and an examination) may occurin the same context (e.g. a classroom). Furthermore, very similar events(e.g. meeting a friend) may occur in two completely di� erent contexts(e.g. in a pub or at home).

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Another theory of episodic memory is SAM (Gillund & Shi� rin, 1984).SAM is a multiple-trace model that uses the concept of images (compareevents): an image contains item information as well as contextual infor-mation. The Matrix Model (Humphreys et al., 1989) uses the event in asimilar manner as TECO.

Encoding

A biologically realistic implementation of encoding is Hebbian learning.Hebb (1949) postulated that `̀ learning takes place by synaptic changewhen pre-synaptic and post-synaptic cells are ® red simultaneously’ ’ . Therepresentation of an item can be expressed as a pattern of activation in anetwork. Assume that the cue, the target and the event are represented inthree populations of nodes. Encoding can then be conducted using thefollowing learning rule:

D wij = h ( x in ± a) ( x j

n ± a) (2)

where D wij is the change in the weight between node i and node j, x in is

the activation of node i in pattern n , and a is the average activity level.Connections between the event population and the object population

might be regarded as the episodic memory system (Tulving, 1983; Tulving& Schacter, 1990) . Connections within an object population (i.e. intra-item connections) may be regarded as familiarity.

Retrieval operation

Parts of the original pattern can be used to retrieve the original pattern(Anderson, 1968, 1970) . This process is known as `̀ pattern completion’ ’ .TECO sees retrieval as pattern completion, where the cue population

FIG. 2. The event in CHARM and TECO.


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forms the starting pattern and the target population forms the patternthat is completed. Successful retrieval occurs when the completed patternrepresents the to-be-remembered item. The cue patterns represent theinformation that is presented to the subjects and the target patterns repre-sent the to-be-retrieved items.

Retrieval of a node can be conducted by ® rst calculating the net input;that is, by multiplying the activation of the node by the appropriateweight and summing over all incoming nodes. The activation of the nodeis then set to high (e.g. + 1) if the net input exceeds a certain threshold(T ) and to low (e.g. ± 1) otherwise:

x i = sgn ( å j wij x jn ± T ) (3)

The probability of correctly retrieving a node is now analysed.Following Hertz, Krogh and Palmer (1991), the learning rule (i.e.equation 2) may be inserted into the calculation of the net input (hi

n , i.e.equation 3) for one node as:

hin = å j wij x j

n = 1/N å j å m x im x j

m x jn =

x in + 1/N å j

N å mp¹ n x i

m x jm x j

n = x in + Ci

n (4)

where m is the index of the number of encoded patterns (N) and thelearning rate ( h ) is set to 1/N. The point of this exercise is to divide the

FIG. 3. Encoding in TECO.

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net input into the to-be-remembered activation ( x in ) and a term respon-

sible for the error (Cin ). The latter term is called the crosstalk term and an

error in retrieval occurs if the crosstalk term can change the sign of theto-be-remembered activation. The probability of correctly retrieving atarget node ( z ) is thus:

P( z ) = P(Cin < 1) = P(1/N å j

N å pm ¹ n x i

m x jm x j

n < 1) (5)

The crosstalk term thus consists of Np random variables. Given theassumption that the activation of the patterns is uncorrelated, the cross-talk term may, from the theory of random coin tosses (Feller, 1968), beseen to be binomially distributed with a mean zero and variance ( s ) of:

s = 1/N (pN)1/2 = (p/N)1/2 (6)

This may be approximated by Gaussian distribution given that Np islarge (i.e. larger than 10, which typically is the case). Using the variance,the maximal number of stored patterns per number of nodes can becalculated (for details, see Hertz et al., 1991). However, this paper is notconcerned with a formal relationship of capacity; however, successfulretrieval can be formalised as the probability that the crosstalk term isbelow a certain retrieval threshold (T ). The probability of correctlyretrieving a target node for Np cue populations of nodes can then bewritten as:

P( z ) = P(1/Np å k Ckn < T ) (7)

A common measurement of memory, P(d), is the probability ofretrieval minus the probability of false alarms for one node (i.e. 1/2)divided by 1, minus the probability of false alarms for one node:

P(d) = (P(1/Np å k Ckn < T ) ± ô ) / (1 ± ô ) =

2P(1/Np å k Ckn < T ) ± 1 (8)

Note, however, that the false alarm rate for one node should not beconfused with the false alarm rate for the tests (i.e. for recognition or forrecall). False alarm rates for recognition and recall may be described by astandard signal detection theory using the net input to one node.

Encoding may also occur to a certain extent during retrieval. It isassumed that item that are scored as hits are also encoded. The rate oflearning at retrieval is an empirical question, but it is likely to be smallerthan the learning rate during encoding. It is now suggested how recogni-tion and recall are conceived in this theoretical framework.


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Recognition as Cued by the Event and the Target

TECO proposes that recognition uses the event as a cue. In recognition,the target object (Ot, i.e. the target word) and the event (E, i.e. the timeof encoding) are presented to the subjects as cues. This yields two popula-tions of connections for recognition. The ® rst population of connectionsis E ® Ot, where the event functions as a cue for the target. The secondpopulation of connections is mediated by the target-to-targe t connection,Ot ® Ot, where the target word (i.e. copy cue) activates itself. Thispopulation of connections may be regarded as a familiarity process inrecognition. Recognition is thus not an active retrieval process Ð that is,no new patterns are activated. Successful recognition occurs when thestrength of the event-to-target connections plus the strength of the target-to-target connections exceeds some threshold.

Recognition is seen as the activation of the target by the event and theactivation of the target by itself (Fig. 4):

P(Rn) = 2P(1/2[C(E ® Ot) + C(Ot ® Ot)] < T rn) ± 1 (9)

where Rn is recognition, E is the event and Ot is the target object, T rn isrecognition, E is the recognition threshold, and C(E ® Ot) is the cross-talk term for the population of connections between the event and thetarget.1 It is well known that recognition tests do not signi® cantly a� ectperformance on a cued recall test (e.g. SikstroÈ m, 1996). The learning rateat the recognition test is therefore set to zero.

The Event as Cue in Recall

TECO suggests a mechanism in cued recall that uses the event as a cue.In cued recall, the object cue (Oc, i.e. the cue word) and the event cue (E,i.e. the time of encoding) are presented to the subjects as cues to retrievethe target (Ot, i.e. the target word). The subjects, by using the event as acue, are then able to distinguish between the study-list episode andknowledge from other episodes. If the events were not given as a cue,

1Note that the account of recognition suggested here does not necessarily mean that high-frequency words are more easily recognised than low-frequency words. It is assumed thatthe retrieval threshold (T rn) is adjusted upwards for high-frequency words (the false alarmrates would otherwise be unacceptably large for high-frequency words) and adjusted down-wards for low-frequency words. This adjustment to the threshold may account for theempirical ® nding that high-frequency words are less well recognised compared with low-fre-quency words.

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then the subjects could simply adopt free association from the word cueand retrieve a target word from prior knowledge or the study-list. Theevent cue corresponds to the speci® c point in time when encoding takesplace, and therefore makes the retrieval operation unique to the learningepisode. This can be formalised by two populations of connections: E ®Ot, where the event cues the target, and Oc ® Ot, where the cue wordcues the target (Fig. 5). Cued recall is the successful activation of a targetpattern by connections from the cue pattern and by connections from theevent pattern to the target pattern. The probability of cued recall maythen be written as:

P(Rc) = 2P(1/2 [C(Oc ® Ot) + C(E ® Ot)] < T rc) ± 1 (10)

where P(Rc) is the probability of cued recall, E is the event, Ot is theobject target, Oc is the object cue, T rc is the threshold for cued recall, andC(Oc ® Ot) is the crosstalk term from the cue population to the targetpopulation. The crosstalk terms may be seen as the strengths of theconnections, that is, small crosstalk terms yield strong connections,whereas large crosstalk terms yield weak connections. Learning is likelyto occur at the recall test; however, this learning does not a� ect theresults in the recognition failure paradigm, because no testing isconducted after the recall test. The TECO theory therefore predicts adi� erent degree of dependency when the test order is reversed; that is,when cued recall precedes the recognition test.

FIG. 4. Recognition in TECO.


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TECO’s Explanation of Why Recognition FailureOccurs

TECO’s explanation of the recognition failure phenomenon is based onthe notion that recall and recognition share one population of connec-tions. TECO’s retrieval operation of recognition is based on the C(E ®Ot) + C(Ot ® Ot) connections and the retrieval operation of recall onC(E ® Ot) + C(Oc ® Ot). So both recall and recognition share E ® Ot

as a common connection. A strong population of common connectionsincreases the probability of recognition; however, a strong population ofcommon connections also increases the probability of recall because it isdependent on the same connections. A weak population of commonconnections reduces both recall and recognition. This explains the depen-dence between recall and recognition.

Recall and recognition also have one separate population of connec-tions each (i.e. Oc ® Ot and Ot ® Ot). The strength of Oc ® Ot a� ectsrecall but not recognition, whereas the strength of Ot ® Ot a� ects recog-nition but not recall. This explains the independence between recall andrecognition. This, in essence, is TECO’s explanation of the phenomenonof recognition failure. A small covariation of recognition and recall thatis neither absolute nor absent. This covariation may be viewed as``subject-cue variability’ ’ , rather than subject variability, item variability,or item± subject variability. Recognition failure of recallable words occurs,according to TECO, because recall and recognition possess two separatepopulations of connections (independence) and one common population ofconnections (dependence).

FIG. 5. Recall in TECO.

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Assumptions of the TECO Model

One of the crucial goals in connectionist models is to study the restric-tions that the empirical data have on possible implementations of thetheory. This may be done by analysing the assumptions of the model.TECO’s account of the recognition failure phenomenon is based on threeassumptions:

1. The separate-event assumption, i.e. the event is seen as a separateentity from the cue and the target.

2. A largely non-overlapping representation of the cue, target and theevent. This assumption allows a distinction to be made between connec-tions that are shared between the two tests (i.e. those that account fordependence) and connections that are not shared (i.e. those that accountfor independence) .

3. The assumption that the uncorrelated strengths of the connections[i.e. C(E ® Ot), C(Ot ® Ot) and C(Oc ® Ot)] are uncorrelated. Consideronce again the crosstalk terms discussed above. The probability of correctretrieval is a function of the interference with previously stored patterns.The crosstalk terms are a function of the activation of the cue populationand the target population. Based on the assumption that the activation ofcue, target and event population are uncorrelated, it follows that thecrosstalk terms and the strengths of the connections are uncorrelated.Note, however, that other psychological variables such as study time andlevels of processing may a� ect the strength of all the connections in asimilar manner and thus introduce a correlation. However, experimen-tally, these variables are kept as constant as possible (i.e. a ® xed studytime for each item and instructions to control for levels of processinge� ects) .

Relating TECO to CHARM and other models

The three assumptions that TECO uses to account for recognition failuremay be compared with the underlying assumptions of other memorymodels such as CHARM, SAM, ACT* and the Matrix Model.

A major di� erence between CHARM and TECO is the use of theevent as a cue. Recognition in CHARM is seen as a retrieval processbetween a copy cue and the target cue [compare C(Ot ® Ot)]. In TECO,however, recognition is seen as a two-way association between the eventand the target [i.e. C(Ot ® Ot) + C(E ® Ot)]. CHARM sees recall as aretrieval process where the cue is associated with the target [compareC(Oc ® Ot)], whereas TECO also uses an event cue [i.e. C(Oc ® Ot) +C(E ® Ot)]. CHARM thus lacks the separate event assumption.


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Another fundamental di� erence between CHARM and TECO is thedegree of distributed representation of the information. CHARM repre-sents each item distributed over all nodes. One particular node may there-fore be included in both the cue and the target (and context). TECOrepresents items in a non-overlapping way so that one node belongs tothe cue or to the target or to the event, but not to more than one ofthese. However, one item may be represented in more than one node (i.e.in a population of nodes). TECO is therefore not a localist model. Thefully distributed representation of CHARM makes it di� cult to applyTECO’s concepts of `̀ common connection’ ’ and `̀ separate connection’ ’ toaccount for dependence and independence. For example, it is not possiblewith CHARM to state that one connection connects the cue with thetarget but not the cue with the event. Furthermore, the dependence inTECO is accounted for by the event as a cue, which CHARM does nothave. CHARM thus lacks the second assumption of non-overlappingrepresentation of items. This means that CHARM possesses a fundamen-tally di� erent account of recognition failure than TECO.

Metcalfe (1991) argued that an understanding of the recognition failurephenomenon may be achieved by violating critical assumptions. Metcalfeviolated the assumption of one composite trace and stored recognitionand recall in two di� erent traces. This resulted in a complete indepen-dence that cannot account for the recognition failure data. It was there-fore concluded that recognition failure occurs because both recognitionand recall involve retrieval of the same type and the underlying traces ofrecognition and recall are stored in the same trace. These requirementsare ful® lled in TECO, since a similar mechanism for recognition andrecall is used and recognition and recall are stored in one compositetrace. Despite these similarities, TECO states other mechanisms fordependency between recognition and recall.

The Matrix Model (Humphreys et al., 1989) uses context (cf. event) asa cue in recall and recognition. In addition, the cue, the target and theevent are stored in separate dimensions. This yields a non-overlappingrepresentation similar to the representation of TECO. There are alsosome di� erences between TECO and the Matrix Model. The most impor-tant is that the Matrix Model uses an interactive combination of thecontext and the cue to retrieve the target and not separate cues.However, a detailed discussion of recognition failure has never beenattempted using the Matrix Model. Nilsson and Gardiner (1991) arguedthat the Matrix Model may use a similar explanation as the RetrievalIndependence Theory to explain recognition failure.

ACT* (Anderson, 1983) uses a non-overlapping representation of itemsand assumes independence between retrieval of the cue from the targetand retrieval of the target from the cue. The reason for the slight devia-

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tion from independence is, according to ACT*, due to cases where atrace was not formed. In such cases, neither recognition nor recallsucceeds, which would account for a small dependency.

SAM (Gillund & Shi� rin, 1984) sees the phenomenon of recognitionfailure as an induction of di� erent meaning caused by contextual shift ofthe to-be-remembered words in the two tests. SAM uses images andcontext embedded in the images (cf. event). This yields an overlappingrepresentation of items which makes it di� cult to divide the connectionsinto shared and non-shared.

The criteria that TECO requires to account for recognition failure arenot always ful® lled in the models discussed above (these models have alsoused other explanations of the phenomenon). However, it may bepossible to modify these models to meet some of the criteria required byTECO. For example, Humphreys et al. (1989, pp. 213 ± 214) suggested away to use the event as a cue in CHARM, MINERVA II (Hintzman,1987) and TODAM (Murdock, 1979, 1982, 1983). However, the degree ofoverlap in the representation of items may be di� cult to modify in someof the other models, as for example in CHARM.

The Quantitative Level of Recognition Failure

Tulving and Wiseman (1975) empirically derived the TW-function forrecognition given recall. Theoretically it is possible for TECO to suggestfunctions to predict the probability of recognition given recall. TECOstates that the connections can be divided into shared connections andconnections that are not shared. Recall and recognition would show totaldependence (ignoring reliability) if all the connections were common. Ifthere were no common connection at all, there would be completeindependence between recognition and recall. This implies that depen-dence is a function of the number of shared connections. Thus depen-dence can be normalised by dividing by the total number of connections.Dependence can now be expressed as a quotient between the number ofcommon connections and the total number of connections. This quotientis denoted by b . Beta = 1 means that all the connections are shared andb = 0 that there are no common connections. Recall and recognitiontogether have three connections, one of which is common, thus yielding aquotient of b = 1/3.

The dependency between recognition and cued recall is thus one-thirdas a consequence of TECO’s interpretation of the cueing. The problem isthus to ® nd an expression for the conditional probability of recognitiongiven cued recall. A formal derivation of this in the TECO model isdependent on the probability distribution of the crosstalk terms. No suchexplicit solution is known when the crosstalk terms have a Gaussian


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distribution (which is the case for the Hop® eld network). However, anexplicit algebraic solution of the conditional probability in the TECOmodel exists, given the assumption that the crosstalk terms have a rectan-gular distribution. A formal derivation of the conditional probability ofrecognition given cued recall is given in the Appendix. Results using thissolution will be presented in the Results section.

Prior research on recognition failure has expressed dependency as theconditional probability of recognition given recall. However, expressingdependency with a conditional probability tells us little of the underlyingsystem in the TECO model. An alternative is to use a measurement ofcontingency that more directly corresponds to the degree of overlap ofcueing between the tests. A measurement of dependency is suggestedbelow which achieves this objective. Note, however, that the dependencymeasurement that is suggested is not formally derived from the assump-tion of the model.

Let Ar1 be the ® rst arbitrary retrieval test operation, Ar2 the secondarbitrary retrieval test, P(Ar1) the probability of the ® rst test, P(Ar2) theprobability of the second test and P(Ar1 | Ar2) the conditional probabilityof the ® rst test given the second test. The conditional probability can becalculated using Bayes’ law:

P(Ar1 | Ar2) = P(Ar1 & Ar2) / P(Ar2) (11)

where P(Ar1 & Ar2) is the probability of Ar1 and Ar2 being a successfulpairwise item. The problem is thus to ® nd an expression for P(Ar1 &Ar2).

I suggest here that P(Ar1 & Ar2) may be expressed as a powerfunction of b . It is ® rst shown how such a function can be written whenthe tests are independent (i.e. b = 0) and then when the tests are depen-dent (i.e. b = 1).

Assume ® rst that Ar1 and Ar2 are independent (i.e. b = 0). P(Ar1 &Ar2) may then be written as:

P(Ar1 & Ar2) = P(Ar1) P(Ar2) = P(Ar1)1± b /2P(Ar2)1± b /2 (12)

Next, consider the case where Ar1 and Ar2 are dependent (i.e. b =1) Ð that is, all the connections are shared. This means that Ar1 and Ar2are identical. It is therefore necessary to impose an additional restrictionthat is not generally true for other measurements of contingency (e.g.correlation). This requires that the probability of Ar1 is equal to theprobability of Ar2. P(Ar1 & Ar2) may then be written as:

P(Ar1 & Ar2) = P(Ar1) = P(Ar2) = P(Ar1)1/2P(Ar2)1/2 =

P(Ar1)1± b /2P(Ar2)1± b /2 (13)

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The functions for P(Ar1 & Ar2) for independence and for dependenceare identical (except that b is either 0 or 1).

Now let b vary between 0 and 1:

P(Ar1 & Ar2) = P(Ar1)1± b /2P(Ar2)1± b /2 (14)

The conditional probability of Ar1 given Ar2 can now be calculatedusing Bayes’ law:

P(Ar1 | Ar2) = P(Ar1)1± b /2P(Ar2)1± b /2/P(Ar2) =

P(Ar1)1± b /2P(Ar2) ± b /2 (15)

The ® nal expression is:

P(Ar1 | Ar2) = Min[P(Ar1)1± b /2P(Ar2) ± b /2, 1] (16)

This function is called the TECO-function. The Min(A, B) operatorcalculates the minimum of A and B. This operator is included because itwould otherwise be possible to have a probability that is > 1 whenP(Ar2) is low. I will show later that the Min ( )-function has an empiricalinterpretation.

The TECO-function can now be applied to recognition given cuedrecall by inserting Ar1 = Rn, Ar2 = Rc and b = 1/3:

P(Rn | Rc) = P(Rn)5/6P(Rc) ± 1/6 (17)

where P(Rn | Rc) is the probability of recognition given recall, P(Rn) isthe probability of recognition and P(Rc) is the probability of recall. Thisfunction will later be tested on empirical data.

The TECO theory makes speci® c predictions of the value of b

depending on the type of exception and no-exception. To verify thisprediction, the b -constant may be broken out of the equation:2

b = ± 2 log[P(Rn | Rc)/P(Rn)] / log[P(Rn)P(Rc)] (18)

The suggested dependency measurement may not be the only functionthat can predict recognition given cued recall. The phi-coe� cient (i.e. the

2Note, however, that b is unde® ned for P(Rn | Rc) close to 1, since the Min-operator cutso� the TECO-function. The b value is thus predicted to be less than otherwise expected forP(Rn | Rc) close to 1.


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correlation for binary values) may also be used. Phi can be calculated as:

} = [P(Rn | Rc) P(Rc) ± P(Rn) P(Rc)]/([P(Rn) ± P(Rn)2][P(Rc) ±

P(Rc)2])1/2 (19)

Breaking out P(Rn | Rc) yields the phi-function:

P(Rn | Rc) = (P(Rn) P(Rc) + } ([P(Rn) ± P(Rn)2][P(Rc) ±

P(Rc)2])1/2/P(Rc) (20)

where } = b = 1/3 for recognition given cued recall.

EXCEPTIONS

Much e� ort has been put into explaining exceptions from the TW-function. Encoding exceptions have been accounted for by VandalTheory (Begg, 1979) , Dual Mechanisms (Jones, 1978, 1983, 1987), ACT*(Anderson, 1983) and MINERVA II (Hintzman, 1987). Retrieval excep-tions have been accounted for by Retrieval Independence (Flexser &Tulving, 1978, 1982), Backward Retrieval (Rabinowitz et al., 1977) andthe Matrix Model (Humphreys et al., 1989). But none of these theorieshas successfully dealt with both exceptions (Nilsson & Gardiner, 1991).

CHARM is the only model that has been claimed to account for bothexceptions. Free recall exceptions are called `̀ impoverished stimuli’ ’ , sincethe stimuli are assumed to be impoverished because of route encoding.CHARM simulates these exceptions by assuming that fewer features areencoded in the item vectors, which, according to the model, increases thedependency. However, recent data have shown that free recall exceptionsmay occur without manipulating encoding. SikstroÈ m (1996) has recentlydemonstrated free recall exceptions for well-integrated word pairs anddeep encoding simply by omitting the cue at retrieval (i.e. by a free recalltest). This shows that free recall exceptions can occur when the memorytrace is intact. Impoverished stimuli are thus not a su� cient criterion forfree recall exceptions.

CHARM denotes cued recognition exceptions as similarity exceptions.These exceptions were simulated by assuming that the cue ± target vectorsare similar. This assumption did not yield exceptions without theadditional assumption of fewer features in the items vectors. Both theseassumptions may be questioned. Cued recognition exceptions are foundwhen the cue is retrievable from the target. This does not necessarilymean that the cue and the target are similar. For example, SikstroÈ m

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(1996) has recently shown that cued recognition exceptions may be foundwith standard (i.e. well integrated) word pairs by presenting the cue atthe recognition test. The second assumption of fewer features in the itemsvectors was proposed without motivation or experimental support(Metcalfe, 1991). Without this justi® cation, CHARM cannot claim tohandle cued recognition exceptions (Nilsson & Gardiner, 1991).

Flexser and Tulving (1978) distinguished between a special and ageneral version of the Retrieval Independence Theory. The generalversion can handle cued recognition exceptions by assuming that theretrieval independence assumption is violated when the information fromthe target overlaps with the cue. This gives rise to a larger dependence.However, the Retrieval Independence Theory cannot account as readilyfor free recall exceptions. Nilsson and Gardiner (1991) argued that, whenthe cue and target are poorly integrated, di� erent episodic memory tracesare accessed. This would suggest more independence rather than moredependence for free recall exceptions.

Free Recall Exceptions

Exceptions from the TW-function occur when the cue and the target arepoorly integrated. These exceptions have therefore been called `̀ poorintegration exceptions’ ’ or ``encoding exceptions’ ’ , since they emanatefrom the encoding situation. Gardiner and Nilsson (1990) have pointedout that when the cue and the target are poorly integrated, a nominallycued recall test becomes functionally like a free recall test. This occursbecause the cue fails to provide useful contextual information about thetarget. The term `̀ free recall exceptions’ ’ will be favoured here.

Bryant (1991) combined the recognition failure paradigm with a levelof processing manipulation. Subjects were instructed to encode the itemsby phonetic encoding, shallow encoding or in a deep meaningful way.The shallow condition and the phonetic condition resulted in a largepositive deviation from the TW-function, whereas the deep encodingconditions conformed to the function. Sandberg (1990) used materialswhere the word pairs could form a word (e.g. foot BALL) or word pairsthat formed a nonword (e.g. cup PEAK). The predictions were thatnonwords would be more di� cult to integrate and thus lead to an excep-tion, which was con® rmed by the experimental data. Other free recallexceptions have been found by instructing subjects to focus their attentionon the cue and the target separately or by using word pairs that are di� -cult to integrate (Begg, 1979; Fisher, 1979; Gardiner & Tulving, 1980;AÈ rlemalm & Nilsson, 1992).

A drop in recall performance can be expected in free recall exceptions,since there is less association between the cue and the target, whereas the


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probability for recognition is largely una� ected. Empirically, this is alsothe case. All conditions of free recall exceptions in Nilsson and Gardiner’s(1993) database have a probability of recognition. The TECO-functioncan predict free recall exceptions, because a low level of recall yieldshigher dependence. But there is another factor that in¯ uences this depen-dence Ð namely, that the cue word fails to be an e� cient cue when thecue and the target are poorly integrated. This means that for free recallexceptions, the cue term can be omitted from the retrieval operation. Theconnections present in recall are C(Oc ® Ot) + C(E ® Ot). Omitting thecue word gives the following retrieval operation for free recall:

FRc = 2P(C(E ® O) < T f rc) ± 1 (21)

where FRc stands for free recall. This is clearly in line with a free recalltest where subjects are supposed to retrieve items from an event (Fig. 6).

The conditional probability of recognition given free recall canformally be derived from the TECO-model given that the crosstalk termis assumed to have a rectangular distribution. The results of such aderivation are presented in the Appendix.

Free recall shares one population of connections (i.e. the event-to-target connections) with recognition. Free recall and recognition togetherhave two connections. This means that b is one-half for free recall excep-tions and not one-third as for no-exceptions. One-half is larger than one-third, which yields a higher degree of dependence for free recall excep-tions. However, note that there is no clear-cut distinction between freerecall exceptions and the no-exception case. Free recall exceptions occur,

FIG. 6. Free recall in TECO.

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according to TECO, because free recall and recognition have one sharedpopulation of connections and one separate population of connections. Theconditional probability can be calculated by inserting b in the TECO-function.

P(Rn | FRc) = P(Rn)3/4P(FRc) ± 1/4 (22)

where Rn is recognition and FRc is free recall.

Cued Recognition Exceptions

The second type of exception occurs when the cue is present or retrie-vable from the target already in the recognition test. This category ofexceptions have been called `̀ retrieval exceptions’ ’ , since they occur at thetime of retrieval. Another name is `̀ cue overlap exceptions’ ’ , because thecue is assumed to be functionally present both in recognition and recall. Ifavour the term ``cued recognition exceptions’ ’ .

The retrieval of the cue from the target in cued recognition exceptionshas been conducted in three di� erent ways by manipulating the cue andtarget items. First, the cue can be retrieved from the target by thesystematic use of target words that are category exemplars of the cuecategory (e.g. body part ARM). Studies of this kind have yielded excep-tions (Gardiner, MaÈ ntylaÈ , & Nilsson, 1995; Nilsson & Shaps, 1980, 1981).Second, Muter (1984) used unique or common famous names. In theunique ± famous condition, the surname was retrievable from the familyname (e.g. First President of the Republic of Turkey, ATATURK). Thiscondition yielded a positive deviation, whereas common names, where thecues were not predictable from the targets, did not show deviations fromthe TW-function. Third, Tulving (1974) used identical cues and targets.In this case, positive deviations were found, but only when guessing wasprohibited (Jones & Gardiner, 1990).

Gardiner and Nilsson (1990) have pointed out that in cued recognitionexceptions, a nominally uncued recognition test becomes functionally likea cued recognition test. The retrieval operation of recognition does notinclude a cue word. This means that cued recognition must be cued di� er-ently from uncued recognition. This is accomplished by adding a cue tothe retrieval operation of recognition. The retrieval operation of normal(or free) recognition includes the E ® Ot and Ot ® Ot connections.Adding a cue to the recognition test gives the cue-to-target connection(Oc ® Ot) which cues the target in the same way as in cued recall. Thecue-to-event connection does not include the target and can thereforearguably not be included in cued recognition of the target. This yields thefollowing retrieval operation for cued recognition (Fig. 7):


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P(CRn) = 2P(1/3[C(E ® Ot) + C(Ot ® Ot) +

C(Oc ® Ot)] < T crn) ± 1 (23)

where CRn stands for cued recognition.The conditional probability of cued recognition given cued recall can

formally be derived for the TECO-model given that the crosstalk termshave rectangular distributions. The results of this derivation are presentedin the Appendix.

It is possible, in principle, to use the TECO-function for any pair ofsuccessive episodic tests given that the ® rst test does not signi® cantlya� ect the second test. The level of dependency, b , will vary depending onthe tests. Cued recall shares both the event-to-target and the cue-to-targetconnections with cued recognition. Altogether there are three populationsof connections in cued recognition and cued recall. This means that b , orthe proportion of shared connections, is two-thirds for cued recognitionexceptions and not one-third as is the case for no-exceptions. Thisexplains why cued recognition exceptions occur: two out of three connec-tions are shared in cued recognition exceptions. This gives a larger depen-dence than the no-exception case, where only one of three connections isshared. Cued recall exceptions have a higher b (2/3) than free recallexceptions (1/2). This does not necessarily mean that cued recognitionexceptions are more dependent than free recall exceptions, since depen-dency is also a function of P(Rc). Free recall exceptions generally have avery low level of recall, which is often su� cient to increase the condi-tional probability beyond the cued recognition level. The conditional

FIG. 7. Cued recognition in TECO.

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probability can now be calculated by inserting b into the TECO-function:

P(CRn | Rc) = P(CRn)2/3P(Rc) ± 1/3 (24)

where CRn is cued recognition and Rc is recall.

The Reliability Constant

Reliability refers to the fact that a re-test often yields a somewhatdi� erent result compared with the ® rst test. This phenomenon has notbeen dealt with in previous models of recognition failure. It is suggestedhere that reliability should be controlled for in recognition failure.

The ® rst step is to ® nd an empirical estimation of the degree of relia-bility. This is done by using data from test ± retest experiments. Anempirical value for reliability (R) can then be estimated by calculating b

on these conditions. Wallace (1978) and Gardiner (1994) have made relia-bility tests on recognition, recall and cued recognition. Table 1 lists sixconditions with the probabilities for the tests [i.e. P(Rn), P(Rc), P(CRn)],the probabilities for the retest, the conditional probability and the R-constant. The average R-constant was found to be 0.86 over the sixconditions. It is assumed that such test ± retest reliability also occurs forP(Rn | Rc), P(Rn | FRc) and P(CRn | Rc). Although this assumption maybe questioned, it is argued that not taking reliability into account is abigger mistake and therefore even more questionable.

The empirical b for test ± retest conditions (R) can now be comparedwith the theoretical b -value. The theoretical b -value for two identical testsis 1, since all connections are shared between two identical tests. Thetheoretical value of 1 should therefore be adjusted to R to account for

TABLE 1The Reliability Constant for Two Successive Identical Testsa

Author T 1 | T 2 P(T 1) P(T 2) P(T 1 | T 2) R

Gardiner (1994) CRn | CRn 0.55 0.59 0.90 0.88Wallace (1978) CRn | CRn 0.67 0.68 0.93 0.83Wallace (1978) Rn | Rn 0.38 0.32 0.97 0.89Wallace (1978) Rn | Rn 0.62 0.60 0.92 0.80Wallace (1978) Rn | Rn 0.58 0.49 1.00 0.87Wallace (1978) Rc | Rc 0.22 0.25 0.80 0.89

Average = 0.86

aFrom left to right, the columns denote the study from where the data were taken, thetwo successive tests, the probability for the ® rst test, the probability for the second test, theconditional probability and the R-constant (i.e. the b -constant for the two identical tests).


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reliability. Two tests that are independent (i.e. b = 0) are not a� ected byreliability, since reliability adjusts towards independence. This shows howto adjust for reliability when the theoretical b is 0 or when the theoreticalb is 1. A function for adjusting for reliability when 0 < b < 1 can nowbe derived by assuming a linear relationship:

b c = [R ± 0] / [1 ± 0] b t = R b t (25)

where b t is the theoretical degree of dependency, b c is the corrected valueof dependency and R is an empirically derived constant for test ± retestreliability, which was found to be 0.86. Using the same method for phiyields an estimate of reliability for } of R } = 0.81.

SIMULATIONS

The no-exceptions, free recall exceptions and cued recognition exceptionsare simulated here in a Hop® eld-type neural network (Hop® eld, 1982) . Anetwork consisting of 24 nodes was created. The network was dividedinto three populations of nodes, called the `̀ cue’ ’ , the `̀ target’ ’ and the``event’ ’ populations. Each population consisted of eight nodes. Twenty-® ve patterns were created by assigning 25% of the nodes in each popula-tion to + 1 and the remaining nodes to 0 (i.e. the activity level a = 0.25) .The encoding phase was simulated by applying the learning rule as speci-® ed above. Retrieval was conducted by activating the appropriate cuepopulation. The event population was activated in all the retrieval tests.The cue population was activated in cued recall and cued recognition andthe target population was activated in recognition and cued recognition.The activation of nodes in the populations that were not activated wereset to the average activity level (i.e. 0.25). The network was then allowedto relax one step using the equation speci® ed above and an optimisedthreshold (the same for all nodes). Successful recall and successful recog-nition occurred when all nodes in the target population after relaxationwere identical to the target population of the corresponding encodedpattern. The simulation was run 40 times (i.e. with 40 subjects and 1000observations) for each condition and the probability of successful recogni-tion, successful recall and successful conditional probability calculated.The results of the simulations are shown in Table 2. First, note that theprobability of retrieval is a monotonically increasing function of thenumber of cue populations (i.e. 0.24, 0.40, 0.50 and 0.62 for free recall,cued recall, recognition and cued recognition). These probabilities ofretrieval are in reasonable correspondence with what is generally foundfor the empirical data. Second, the degree of dependency is signi® cantlylarger for the free recall exceptions and cued recognition exceptions

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compared with the no-exceptions. Third, there is reasonable agreementbetween the simulated degree of dependency and the theoretical degree ofdependency. The b -values are 0.39, 0.52 and 0.59 for the no-exceptions,free recall exceptions and cued recognition exceptions, respectively. It willlater be seen that these values are in correspondence with the b -valuesthat are found empirically.

RESULTS

The predictions of the TECO theory will now be compared with theempirical data. The data are taken from Nilsson and Gardiner’s (1993)database of recognition failure. Only conditions where recognitionpreceded cued recall are included in the database. The experimental dataconsist of a wide variety of experimental conditions. This provides goodexternal validity.

The TECO-function with b corrected for reliability, the TECO-functionwith b not corrected for reliability, the explicit solutions, and the phi-function are tested by comparing the predicted and the observed data ofP(Rn | Rc). The Tulving ± Wiseman function is included as a comparison,since it represents an alternative view of looking at the phenomenon.Unfortunately, it is not possible to make a comparison with other simula-tions (e.g. CHARM), because there are no explicit functions available tomake quantitative predictions. The deviation between the predicted andobserved values of P(Rn | Rc) is calculated. No-exceptions are studied® rst, followed by free recall exceptions and then cued recognition excep-tions. Finally, b is studied for di� erent exceptions.

No-exceptions

Conditions that are not predicted to be exceptions in Nilsson and Gardi-ner’ s (1993) database were selected. This means that none of the condi-

TABLE 2Simulations of the TECO Modela

Exceptions n P(Rn) P(Rc) P(Rn | Rc) b

No-exceptions 1000 0.50 0.40 0.69 0.39Free recall 1000 0.50 0.24 0.88 0.52Cued recognition 1000 0.62 0.40 0.93 0.59

aFrom left to right, the columns denote the number of observations (n), the probability ofrecognition, the probability of recall, the conditional probability of recognition given recalland the b -value.


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tions selected was manipulated, so that the word pairs were poorlyintegrated and none of the conditions included cues that were retrievablefrom the targets. Altogether, 269 conditions were selected. [Note thatnine conditions classi® ed as no-exceptions according to Nilsson andGardiner’s CV criteria (i.e. they deviated less than 0.135 from Tulving ±Wiseman) were predicted to be exceptions. Those conditions are furtherspeci® ed when the appropriate exceptions are dealt with.]

Five predictor functions are compared:

1. The TECO-function with b corrected for reliability: P(Rn | Rc) =P(Rn)5R /6P(Rc) ± R/6, where R = 0.86 (i.e. b = R/3) .

2. The TECO-function with b = 1/3: P(Rn | Rc) = P(Rn)5/6P(Rc) ± 1/6 .3. The Tulving ± Wiseman function: PTW (Rn | Rc) = P(Rn) ± c[P(Rn) ±

P(Rn)2], where c = 1/2.4. The explicit solution of the TECO-model, where the crosstalk terms

have a rectangular distribution (see the Appendix) .5. The phi-function as a predictor (see above), where } = R } /3 and R}

= 0.81.

The deviations were measured as the di� erence between observed andpredicted conditional probabilities. Two ways of summing the deviationover the selected conditions are used. First, by simply averaging thedeviation (i.e. positive and negative deviations may cancel out):

1/N å Pobserved(Rn | Rc) i ± Ppredicted(Rn | Rc) i (26)

This gives a measurement of the ® t of the overall dependence. Theseresults are shown in the ® rst row of Table 3.

TABLE 3General Table of Resultsa

TECOÐ Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð

Exceptions b Corrected b Not Corrected TW Explicit Phi

No-exceptions 0.000 ± 0.017 0.001 0.008 ± 0.016Free recall ± 0.003 ± 0.041 0.190 0.011 ± 0.136Cued recognition 0.028 ± 0.021 0.175 0.010 ± 0.025

aFrom left to right, the columns denote the average deviation for the TECO-function withb corrected and not corrected for reliability, the TW-function, an explicit solution of theTECO model and the phi-function.

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The results show that the TECO-function with b corrected for relia-bility, the TW-function and the explicit solution yielded a very good ® t tothe overall degree of dependence. The deviations were 0.000, 0.001 and0.008, respectively. The TECO-function without b corrected for reliabilityand the phi-function show higher degrees of dependence, yielding averagedeviations of ± 0.017 and ± 0.016, respectively. This is to be expected forthe TECO-function, since correction of b for reliability decreases depen-dency.

A second way of measuring the deviation is by averaging the absolutevalue of the deviations:

1/N å ABS(Pobserved(Rn | Rc) i ± Ppredicted(Rn | Rc) i)] (27)

This gives a measurement of the degree of lawfulness of the model. Theseresults are shown in the ® rst row of Table 4.

The best predictor, when this measurement was used, was the TECO-function with b corrected for reliability. It deviated on average by 0.034.The TW-function, the TECO-function with b not corrected for reliability,the explicit solution and the phi-function deviated by 0.037, 0.038, 0.040and 0.041, respectively. Figure 8 shows the predicted data using theTECO-function corrected for reliability, the predicted data using the TW-function and the observed data.

Free Recall Exceptions

Twenty experiments in Nilsson and Gardiner’ s database were classi® ed asfree recall exceptions. These conditions also deviate more than 0.135 fromthe Tulving ± Wiseman function. All these free recall conditions havepoorly integrated cue and target words. Some conditions in the databaseare predicted to be free recall exceptions, although they do not deviate

TABLE 4General Table of Resultsa

TECOÐ Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð

Exceptions b Corrected b Not Corrected TW Explicit Phi

No-exceptions 0.034 0.038 0.037 0.040 0.041Free recall 0.059 0.059 0.190 0.054 0.146Cued recognition 0.050 0.055 0.175 0.068 0.062

aFrom left to right, the columns denote the average absolute deviation for the TECO-function with b corrected and not corrected for reliability, the TW-function, an explicit solu-tion of the TECO model and the phi-function.


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su� ciently from the TW-function to be classi® ed as exceptions. Theseconditions are Salzberg’s (1975) condition 57, Bartling and Thomson’s(1977) conditions 78 and 79, Begg’s (1979) condition 120 and Fisher’s(1979) condition 143. Four conditions were omitted, since they are basedon very few correctly recalled items, making it di� cult to achieve reliablestatistics. These conditions are Sandberg’s (1990) condition 271 andBegg’s (1979) conditions 128, 131 and 132. The total number of correctrecall responses in these conditions are 6, 4, 16 and 8, respectively.

The same predictor functions as for the no-exceptions case were used,with the exception that b and } were 1/2. The explicit solution washowever di� erent, as speci® ed in the Appendix. The average deviationsare shown in the second row of Table 3 and the average absolute devia-tions in Table 4. The results show a good ® t for the TECO-function withcorrected b . The average deviation was ± 0.003, whereas the TW-functiondeviated by 0.190. The average deviation for the explicit solution was0.011. The phi-function seemed to deviate signi® cantly below theobserved value (i.e. by 0.13). The absolute deviations were 0.059, 0.059and 0.056 for the TECO-function with corrected b , for the TECO-function without corrected b and for the explicit solution, respectively.

FIG. 8. The 272 no-exceptions in Nilsson and Gardiner’s (1993) database. The predictedP(Rn | Rc) from the TECO-function, the Tulving± Wiseman function and the observedP(Rn | Rc) are shown.

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The TECO-function with b = 1/3 (i.e. the no-exceptions function)deviated by 0.099 from the observed data, which is a fairly good predic-tion compared with the TW-function. Figure 9 plots the TECO-functionwith b = R/2, the observed data and the TW-function. Deviations fromthe TECO-function are also shown.

Cued Recognition Exceptions

Cued recognition exceptions are de® ned as experiments where the cuewords can implicitly be derived from the target words by semantic knowl-edge. Six conditions in Nilsson and Gardener’ s (1993) database wereclassi® ed as exceptions in this category. Three additional conditionsful® lled the criteria for where cued recognition exceptions should occur,although they did not deviate su� ciently from the CV criteria to becategorised as exceptions. Nilsson and Gardiner (1993) claimed that thiswas due to a ceiling e� ect at the recognition level [exceptions from theTW-function de® ned by the CR criteria cannot occur when P(Rn) >0.88]. In addition, Gardiner et al. (1995) recently conducted 10 cuedrecognition exceptions that were published after Nilsson and Gardiner’s(1993) database.

FIG. 9. Free recall exceptions plotted according to the observed data, the TECO-function ( b= R/2) and the Tulving± Wiseman function. The deviations of the TECO-function from theobserved values are connected with lines.


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The conditions listed above were compared with the predictions. TECOpredicts a b that is 2/3 for cued recognition exceptions. The observeddata are compared with the same predictor functions as for the no-excep-tions case, with the exception that b and phi were 2/3. The explicitsolution was however di� erent, as speci® ed in the Appendix.

The average deviations are shown in the third row of Table 3 and theaverage absolute deviations in Table 4. The results show an averagedeviation of 0.028 for the TECO-function with b corrected for reliability.This function thus seems to underpredict dependency. The average devia-tions for the TECO-function without corrected b show an average devia-tion of ± 0.021 (i.e. a small overprediction of dependency). The explicitsolution yielded a somewhat better ® t with an average deviation of 0.010.However, the average deviation was much smaller with the TW-function,deviating by 0.175. The average absolute deviations were 0.050, 0.055 and0.068 for the TECO-function with corrected reliability, the TECO-

FIG. 10. Cued recognition exceptions plotted according to the observed data, the TECO-function ( b = 2R/3) and the Tulving± Wiseman function. The deviations of the TECO-func-tion from the observed values are connected with lines.

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function not corrected for reliability and the explicit solution, respectively.The results for the TECO-function, TW-function and observed data areplotted in Fig. 10.

Deviations from the TECO-function

There were seven conditions which deviated more than 0.135 from theTECO-function with b corrected for reliability. Four of these were no-exceptions, one was a cued recognition exception and two were free recallexceptions (see Table 5). Three of these conditions (Begg, 1979, condi-tions 103, 133, 221; Nilsson et al., 1987; Taijka, 1978) are questionable,since they have observed values that are less than the probability ofrecognition. Conditions 133, 135 and 138 (no-exceptions) are from Begg(1979, experiment 3).

Condition 271 (Sandberg, 1990) was based on six trials only (P(Rn) =3%, n = 200). This provides very low statistical power and the deviationmay be a result of this. Conditions 133, 135, 251 and 221 may also, atleast partially, be explained in this way, since they were based on 10, 20,21 and 36 trials each.

Observed b -values

The database is divided into no-exceptions, free recall exceptions andcued recognition exceptions as speci® ed above. The b -values are calcu-lated from the observed values of P(Rn), P(Rc) and P(Rn | Rc) using theTECO-function reshown in the second column of Table 6. The e� ect oftest ± retest reliability is corrected for in column three. This is done bydividing the b -values with R (i.e. by 0.86).

The corrected result was 0.34 for P(Rn | Rc), which deviates by 0.006from the theoretical value of 1/3. In the free recall exceptions, six condi-tions where unde® ned, since their P(Rn | FRc) values were close to 1 (i.e.> 0.95) . b was 0.49 for the de® ned conditions, which deviates by0.015 from the theoretical value of 1/2. The b -value was predicted to beless than 1/2 for the unde® ned conditions, which also was found to bethe case (i.e. b = 0.39) . The b -constant was found to be 0.70 for thecued recognition exception, which deviates by 0.035 from the predictedvalue of 2/3.

The frequency distribution of b calculated on observed P(Rn | Rc) isplotted in Fig. 11, with no-exceptions, free recall exceptions and cuedrecognition exceptions shown. An idealised ® gure of predictions wouldconsist of three peaks, one around 1/3 for no-exceptions, one around 1/2for free recall exceptions, and one around 2/3 for cued recognition excep-


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tions. The peak around 0.34 can be easily seen because there are manyconditions. A close look at Fig. 11 also reveals the free recall exceptionsclustered around 0.49 and the cued recognition exceptions clusteredaround 0.70.

TABLE 6b and Phi for No-exceptions, Free Recall Exceptions, Cued Recognition Exceptions and for

the Reliability Measurementa

T ype of Data Observed Corrected Predicted Di� erence Phi

No exceptions 0.29 0.34 1/3 0.006 0.32Free recall 0.42 0.49 1/2 0.015 0.38Cued recognition 0.60 0.70 2/3 0.035 0.62Reliability 0.86 1.00 1 0.000 1.00

aFrom left to right, the columns denote the average b -values for the observed data, theobserved data corrected for reliability, the predicted data, the di� erence between the pre-dicted and observed data, and the average phi-value corrected for reliability (i.e. divided by0.81).

Note: Some conditions with free recall exceptions were omitted because of a ceiling e� ect.These conditions had P(Rn | Rc) > 0.95.

FIG. 11. The frequency distribution of b grouped in steps of 0.1 for no-exceptions, freerecall exceptions and cued recognition exceptions.


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Exceptions or General Law

Nilsson and Gardiner (1991) have formulated a law for recognitionfailure, which states that: ``Recognition is largely independent of subse-quent recall whenever the recall environment includes e� ective contextualcues that were absent in the recognition environment’ ’ . This is an empiri-cally based law. The regularity of recognition failure has been seen to besurrounded by boundaries. Inside the boundaries a regularity expressedby the TW-function has been acknowledged. The free recall and cuedrecognition conditions have been regarded as exceptions from thisregularity (Nilsson & Gardiner, 1991). Exceptions have therefore notbeen seen to be lawful and no function has been proposed.

In contrast, TECO does not view the free recall and cued recognitionconditions as exceptions from a regularity. TECO sees `̀ the exceptions’ ’as lawful and proposes a function for them. The recognition failure, freerecall and cued recognition conditions can all be described by the TECO-function with di� erent b . It is therefore possible, from the theory ofTECO, to propose a theoretically derived law for recognition failure andthe exceptions:

Recognition has a dependency (measured by b ) of 1/3 with cued recall,a dependency of 2/3 when the recognition test is cued and a depen-dency of 1/2 when the recall test lacks e� ective cues.

This law summaries the results not only for recognition failure but alsofor the exceptions. It is stated in quantitative rather than qualitativeterms, in the same way that Nilsson and Gardiner’ s law is.

CONCLUSIONS

The fundamental idea of the TECO theory may be summarised asfollows: The dependence between two memory tests is a direct measureof the degree of common connections between the two tests. Anotherbasic idea in TECO is how recall and recognition are cued by the event.The theory is rather simple but is good at predicting experimental data.One of the main advantages of TECO is that quantitative as well asqualitative predictions are possible. The Retrieval Independence Theoryand CHARM cannot predict quantitative levels of recognition failure,only simulate them. These two theories can also simulate other quantita-tive levels by changing parameters in the models. TECO predicts thequantitative levels of recognition failure by the TECO-function. It caneven predict the empirical data better than the TW-function, despite the

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fact that the TW-function was derived by minimising the least-squareerror.

Nilsson and Gardiner (1991) claimed that none of the existing theoriessuccessfully dealt with both cued recognition exceptions and free recallexceptions. No function has previously been suggested for the exceptions.It has been shown here that TECO is able to predict both exceptions. Itis also possible to apply the TECO model to the exceptions with thesame predictive power as the no-exceptions. TECO does not view the``exceptions’ ’ as deviations from a rule, but rather encapsulates them intoa larger and more general lawfulness.

The Role of the Event

``The highly stable nature of this relation indicates that it is telling ussomething important about the nature of human memory’ ’ (Metcalfe,1991). An important lesson of recognition failure is the role that theevent plays in episodic memory. There are three things regarding theevent that can be learned from the empirical phenomenon of recognitionfailure. First, the existence of an internal representation of an event thatis separate from the representation of the items. This is in contrast to theevent as the sum of items. Furthermore, and in relation to this point, thecue and target are represented in a non-overlapping manner. Second, theevent as a cue in recall. CHARM only emphasises the cue word as a cueand neglects the importance of the event as a cue. Third, the event as acue in recognition, whereas CHARM has been built on self-association ofa target with itself. The Matrix Model (Humphreys et al., 1989) andSAM (Gillund & Shi� rin, 1984) both use the event as a cue. It is claimedhere that the separate event assumption is an important psychologicalimplication that should be concluded of TECO and the phenomenon ofrecognition failure itself.

The explanation for the dependence between recognition and cuedrecall is, according to TECO, that both tests are cued by the event. Itmay be argued that a change in the cueing of an event a� ects the degreeof dependence between recognition and cued recall. More precisely,TECO predicts that elimination of the event cue in recognition or in cuedrecall gives rise to independence between recognition and cued recall.This hypothesis is testable. Cueing of the event is conducted byinstructing subjects to retrieve information from the encoded studyepisode. The event cue may be eliminated in cued recall by instructingsubjects to retrieve anything that comes to mind without explicit referenceto the study episode. This type of test may be regarded as an implicitword-fragment completion test. TECO thus predicts that implicit andexplicit tests are independent. This prediction is well documented in the


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literature (for reviews, see Gardiner & Java, 1993; Richardson-Klavehn &Bjork, 1988).

One reason why recognition failure has attracted so much attention isthe remarkable lawfulness of the phenomenon. This paper has shown thatrecognition failure and the exceptions can be captured in a generalcomprehensive theory. This shows that the phenomenon is even morelawful, and fascinating, than previously thought.

Manuscript received March 1995Revised manuscript received October 1995

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APPENDIX

An explicit derivation of the TECO model when the crosstalk terms are assumed to haverectangular distributions

Let the crosstalk term (C) be rectangularly distributed between ± 0.5 and + 0.5; P 9 (Rn) theprobability of recognition before the baseline is removed and P(Rn) the probability of recog-nition after the baseline is removed; T rn the recognition threshold and T 9rn a rescaled recogni-tion threshold. The corresponding notation is used for recall (i.e. Rc). The probabilities ofrecognition and recall may be conceived mathematically as volumes in a cube (see Fig. 12) .This cube has three dimensions which represent the crosstalk termsÐ that is, C(e ® t),C(t ® t) and C(c ® t).

T 9rn = 1/2 ± T rn/2T 9rc = 1/2 ± T rc/2P 9 (Rn) = P(1/2 [C(e ® t) + C(t ® t)] < T rn) = 1 ± T 9rn

2/2T 9rn = [2 ± 2 P 9 (Rn)]1/2

P 9 (Rc) = P(1/2 [C(e ® t) + C(t ® t)] < T rc) = 1 ± T 9rc2/2

T 9rc = [2 ± 2 P 9 (Rc)]1/2

Consider the case where P(Rn) > P(Rc):

P 9 (Rn or Rc) = 1 ± (V 1 + V 2)V 1 = T 9rn

2/2[T 9rc ± T 9rn]V 2 = T 9rn

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Fig. 12. A formal derivation of recognition given cued recall using the TECO model.


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P 9 (Rn & Rc) = P(1/2[C(e ® t) + C(c ® t)] < T rc && 1/2[C(e ® t) + C(t ® t)] < T rn)= P 9 (Rn) + P 9 (Rc) ± P 9 (Rn or Rc) = P 9 (Rn) + P 9 (Rc) ± [1 ± (V 1 + V 2)] = P9 (Rn) +P 9 (Rc) ± 1 + (2 ± 2P 9 (Rn))/2[(2 ± 2 P 9 (Rc))1/2 ± (2 ± 2P 9 (Rn))1/2] + (2 ± 2P 9 (Rc))3/2/3

Now, remove the baseline for the probabilities:

P(Rn) = 2P 9 (Rn) ± 1, P 9 (Rn) = 1/2 + P(Rn)/2P(Rc) = 2P 9 (Rc) ± 1, P 9 (Rc) = 1/2 + P(Rc)/2P(Rn | Rc) = 2P 9 (Rn | Rc) ± 1 = 2P 9 (Rn & Rc)/P 9 (Rc) ± 1 = 2(P(Rn)/2 + P(Rc)/2 + (1 ±P(Rn))[(1 ± P(Rc))1/2 ± (1 ± P(Rn))1/2]/2 + (1 ± P(Rc))3/2/3)/(P(Rc)/2 + 1/2) ± 1

Now generalise for all P(Rn):

P(Rn | Rc) = 2(P(Rn) + P(Rc) + (1 ± Max[P(Rn) , P(Rc)]) (1 ± Min[P(Rn), P(Rc)])1/2 ±2(1 ± Max[P(Rn), P(Rc)])3/2)/3)/(P(Rc) + 1) ± 1

where Min[P(Rn) , P(Rc)] is P(Rn) if P(Rn) < P(Rc) and P(Rc) otherwise, and Max[P(Rn),P(Rc)] is P(Rc) if P(Rn) < P(Rc) and P(Rn) otherwise. To avoid the problem of guessing,a preferred measurement of P(Rn), P(Rc) and P(Rn | Rc) is to remove the baseline anddivide by one minus the baseline; for example, P(Rn) = [P(Rn) ± P(baseline)] / [1 ±P(baseline)].

The conditional probability of recognition given free recall can be derived using a similartechnique. The proof of this is omitted and the result is:

P(Rn | FRc) = [P(FRc) + P(Rn) + (1 ± P(FRc)) (1 ± P(Rn))1/2 ± (1 ± P(FRc))2/4]/(P(FRc)/2 + 1/2) ± 1

for (1 ± P(Rc))2 < 2 ± P(Rn)2, which normally is the case.In the same manner, the conditional probability of cued recognition given cued recall can

be derived. The formal derivation is omitted. Here only the P(CRc) > 1/2 case is presented:

P(CRn | Rc) =

( ô (P(Rc) + P(CRn)) + ì (1 ± P(Rc))3/2 + ô [(2 ± 2P(CRn))1/3) ± (1 ± P(Rc))1/2] (1 ± P(Rc))4 Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð Ð ± 1

P(Rc) + 1

for (2 ± 2P(CRn)1/3) ± (1 ± P(Rc))1/2 > 0 and P(CRn | Rc) = 1 otherwise.

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The TECO Connectionist Theory of Recognition Failure

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