Short- and long-term recency in the temporal context model: Commenton Davelaar et al. 2005

Per B. SederbergDepartment of Psychology and

Center for the Study of Brain, Mind, and BehaviorPrinceton University

Princeton, NJ 08540, USA

Marc W. HowardDepartment of Psychology

Syracuse UniversitySyracuse, NY 13244, USA

Michael J. KahanaDepartment of PsychologyUniversity of Pennsylvania

Philadelphia, PA 19104, USA

Manuscript in review. DO NOT CITE!

Countering claims that recency effects observed at different time scales arise from a commonforgetting process, Davelaar et al. (2005) presented a number of experimental dissociations be-tween short- and long-term recency. They used these dissociations to argue that separate mech-anisms underlie short- and long-term recency. Here we show that the temporal context model(TCM), which assumes that both short- and long-term recency arise from the same contextualdrift process, can account for the major recency dissociations at different time scales. Ourversion of TCM, which includes the Usher and McClelland (2001) leaky-accumulator modelas a retrieval rule, captures the dynamics of immediate, delayed, and continual distractor freerecall, and shows that dissociations between short- and long-term recency naturally arise froma model that uses an internal contextual state as the sole cue for retrieval across time scales.

Davelaar, Goshen-Gottstein, Ashkenazi, Haarmann, andUsher (2005) recently argued that separate short-term andlong-term memory mechanisms underlie the recall advantagefor recently experienced items (i.e., the recency effect) whenit is observed at shorter versus longer time scales. Specifi-cally, they highlight several striking differences between therecency effects observed in immediate free recall (IFR) andcontinual-distractor free recall (CDFR). In IFR, participantsare asked to recall the list items, in any order, immediatelyfollowing the last item presentation. In CDFR, participantsare given a demanding distractor task following each listitem. After the last period of distraction they are asked torecall the items in any order (see Figure 1 for a graphical de-scription of the free recall tasks). The presence of a recencyeffect in both IFR and CDFR led a number of theorists to pro-pose that recency represents a general forgetting process anddoes not require the distinction between short-term and long-term storage (Crowder, 1982; Greene, 1986). Davelaar etal. (2005) challenged this view by pointing out several strik-ing dissociations between recency in IFR and CDFR. These

The authors acknowledge support from National Institutes ofHealth research grants MH061975 to MJK and MH072138 andMH080526 to PBS. Correspondence concerning this article may beaddressed to Per B. Sederberg (persed@princeton.edu).

dissociations, they argue, rule out models that hypothesizea general forgetting process underlying recency phenomenaobserved at different time scales.

Davelaar and colleagues specifically call into questionmodels that have used a time-varying internal context sig-nal to model recency across time scales (e.g., Howard &Kahana, 2002; Brown, Neath, & Chater, 2007). Prior totheir paper, these context models had enjoyed considerablesuccess in explaining data from a number of episodic mem-ory paradigms, including free recall (see Kahana, Howard,& Polyn, in press, for a review). Davelaar and colleaguesinstead propose a model of free recall in which an activation-based short-term store (STS) produces recency in IFR, and atime-varying context signal produces recency via a weight-based long-term store (LTS) in CDFR.

As one of the groups that has advocated a context-basedaccount of the free recall task, we sought to examine whetherour temporal context model (TCM) was, in fact, unable toproduce the dissociations identified by Davelaar and col-leagues. Although prior work on TCM had highlighted theprominent parallels between short- and long-term recencyeffects, the model does not predict identical behavior underthese conditions. Here we show that TCM predicts severalmajor dissociations between recency in IFR and CDFR. Inorder to fit TCM to the more varied findings studied by Dave-laar et al. (2005), we used a more sophisticated retrieval rulebased on the information accumulation and decision model

2 SEDERBERG, HOWARD, & KAHANA

of Usher and McClelland (2001).We next review some the major empirical phenomena ob-

served in free recall and their relevance for single- and dual-store theories of episodic memory. We conclude the intro-duction with a discussion of the dissociations between im-mediate and long-term recency effects that Davelaar et al.(2005) claim necessitate both an activation-based STS and aweight-based LTS.

Single- versus dual-store accounts of free recall

In delayed free recall (DFR), a filled distractor intervalintervenes between the last item and the test, resulting in adramatic reduction in the short-term recency effect observedin IFR (Glanzer & Cunitz, 1966; Postman & Phillips, 1965).According to dual-store models (e.g., Atkinson & Shiffrin,1968; Davelaar et al., 2005; Raaijmakers & Shiffrin, 1980),the recency effect in IFR is due to a direct read-out from aSTS, which has a capacity of approximately 2 to 5 items.When no additional items can be retrieved from STS, recallcontinues with retrieval from the LTS. Although easily acces-sible, items in the STS are extremely sensitive to retroactiveinterference from incoming information. Consequently, thedistractor interval clears items from STS and retrieval in DFRis based only upon LTS.

Because in free recall the order of recall reflects the or-der in which items come to mind, recall transitions from oneitem to the next presumably reflect the organization of mem-ory for the list items. To examine the effects of the tempo-ral organization of the list on free recall transitions, Kahana(1996) measured the conditional response probability as afunction of lag (lag-CRP). Given that the participant has justrecalled the item from serial position i, the lag-CRP indicatesthe probability that the next item recalled comes from serialposition i + lag. Lag-CRP analyses have shown that the con-tiguity effect, a tendency for participants to recall items fromnearby in the list to the just-recalled item, and the asymmetryeffect, a tendency for participants to recall items in the for-ward direction, are extremely robust properties of free recall(see Kahana et al., in press, for a review).

In much the same way that dual-store models provide anatural account of recency effects in immediate and delayedrecall, they also provide a natural explanation of the conti-guity effect in immediate and delayed recall. The search ofassociative memory model (SAM, Raaijmakers & Shiffrin,1980, 1981; Mensink & Raaijmakers, 1988, 1989; Sirotin,Kimball, & Kahana, 2005; Kimball, Smith, & Kahana, inpress), a detailed implementation of a dual-store model, pos-tulates that connections in long-term memory between itemsthat are simultaneously active in STS are strengthened. Acontiguity effect arises because items from nearby positionsin the list are likely to be co-active in STS. The inter-itemassociations then provide a boost in the probability of transi-tioning to a nearby item during retrieval from LTS (Kahana,1996).

The ease with which the dual-store model addresses re-cency and contiguity effects in IFR and DFR would give riseto an almost unquestioned adoption of dual-store models of

memory were it not for the discovery of the long-term re-cency effect (Bjork & Whitten, 1974) in continual-distractorfree recall (see Figure 1). In CDFR, there is a filled distrac-tor interval not only after the last item and before the recalltest, as in DFR, but also in the interstimulus interval betweenthe study of each list item. Buffer models of STS cannotaccount for recency in CDFR; if the end-of-list distractor inDFR is sufficient to clear STS, then it should also be suffi-cient to clear STS in CDFR. Nonetheless, long-term recencyeffects are robustly observed in CDFR (Bjork & Whitten,1974; Tzeng, 1973; Glenberg et al., 1980; Glenberg, Bradley,Kraus, & Renzaglia, 1983; Howard & Kahana, 1999; Thapar& Greene, 1993; Watkins, Neath, & Sechler, 1989; Neath,1993).

The discovery of long-term recency effects in free re-call and other similar tasks led Crowder (1982) and Greene(1986) to conclude that STS is not a sufficient explanationof recency effects in free recall. While it is easy enough topostulate an additional source of recency in retrieval fromLTS to account for the long-term recency effect—for instanceAtkinson and Shiffrin (1968) postulated that there was slowdecay of information from LTS (see also Davelaar et al.,2005; Mensink & Raaijmakers, 1988, 1989; Raaijmakers,1993; Sirotin et al., 2005)—similarities between immediateand long-term recency made it appealing to develop single-store models of memory that account for recency across timescales with a common mechanism.

Temporal distinctiveness models (Murdock, 1960; Neath& Crowder, 1990; Glenberg & Swanson, 1986; Brown etal., 2007; Nairne, Neath, Serra, & Byun, 1997; Neath &Crowder, 1996) assume that recall of an item depends noton its absolute recency but on its relative recency to otherlist items. According to this view, CDFR results in largerrecency than DFR because the last item in the list is moredistinctive in CDFR due to the fact that the delay in the inter-stimulus interval has placed the other items further into thepast.1 Because the relative spacing of the list is similar in IFRand CDFR, temporal distinctiveness models can account forthe existence of both immediate and long-term recency usingthe same mechanism. Temporal distinctiveness models oftenleave the mechanism by which a temporally-varying signalis implemented as an abstract concept; time tags (Yntema &Trask, 1963) or a randomly-varying temporal context (Estes,1955; Bower, 1972; Murdock, 1997) are two hypothesizedcandidates. The idea of a time varying context representa-tion has also been used to explain a wide range of interfer-ence phenomena (e.g., Ceraso & Henderson, 1966; Mensink& Raaijmakers, 1988).

Like the recency effect, the contiguity effect also persistswhen items are separated by an interval of distracting ac-tivity (Howard & Kahana, 1999, see also Howard, Youker,& Venkatadass, in press). Following similar logic to thatemployed in our discussion of the long-term recency effect,STS cannot simultaneously account for the contiguity ef-

1 Put another way, the last item in the list in CDFR is subjectto less proactive interference from its predecessors due to the inter-item delay.

RECENCY AND TCM 3

ImmediateFree Recall

+

Dragon

Flower

xx

Chicken

Room

*****

Time

DelayedFree Recall

+

Dragon

Flower

xx

Chicken

Room

3+4+2=?

xx

9+1+3=?

*****

Cont. Dist.Free Recall

+

5+2+6=?

Dragon

4+1+1=?

Flower

xxxxx

Chicken

4+3+9=?

Room

8+1+3=?

*****

Figure 1. Graphical illustration of immediate, delayed, and continual distractor free recall. Each trial beginswith a fixation cross. A row of asterisks signals participants to recall the items in any order.

4 SEDERBERG, HOWARD, & KAHANA

fect observed in CDFR and the effect of a delay on the re-cency effect—if the inter-item distractor is effective at clear-ing items from STS then adjacent items would never be inthe STS at the same time in CDFR.

Howard and Kahana (2002) proposed a model of temporalcontext (TCM) to account for the pattern of results observedfor recency and contiguity effects in free recall across pre-sentation schedules. During study, items are associated withthe current state of a gradually-changing representation oftemporal context. The recency effect follows because itemsthat were studied more recently are more similar to the time-of-test (TOT) context. TCM employed a probabilistic rule forselecting which item to recall that was sensitive to the relativeactivation of the items in the list. The contextual coding pro-cess along with the probabilistic choice rule enabled TCM toaccount for immediate and long-term recency using the samelogic as distinctiveness models of long-term recency.

According to Howard and Kahana (2002), temporal con-text is not independent of the items being presented. Ratherthan drifting randomly, context changes from moment to mo-ment in TCM because the items, themselves, drive the evolu-tion of context. This property provides a natural account ofcontiguity effects—when an item is recovered at test, it rein-states the temporal context active when that item was stud-ied. Because this context overlaps with the encoding contextof the items’ neighbors, a contiguity effect results. Becausethe retrieval rule was sensitive to the relative activation of thelist items, TCM predicts a long-term contiguity effect for thesame reason as it predicts the long-term recency effect.

Howard and Kahana (2002) focused on modeling thecontextual evolution and retrieval process, noting that TCMlacked much of the machinery needed to provide a compre-hensive account of the major phenomena observed in freerecall. To account for these phenomena, additional mech-anisms would be needed. For instance, TCM lacked a stop-ping rule that would determine when recall terminates. It alsolacked mechanisms to account for recall latency, as well asrules to avoid repetition of already-recalled items. However,the simplicity of their approach allowed Howard and Kahana(2002) to focus on fundamental explanations of recency andcontiguity across distractor schedules.

Davelaar et al. (2005) questioned the assertion, made byboth TCM and the distinctiveness models, that short- andlong-term recency could share a common source. They iden-tified a number of experimental dissociations between short-and long-term recency that they argued could not be ac-counted for by single-store models in general, and TCM inparticular. Moreover, they argued on theoretical grounds thatthe computational requirements of short- and long-term re-cency demand activation-based and weight-based learningmechanisms, respectively. We address both these empiricaland theoretical claims in the present manuscript. Briefly, al-though several of the experimental dissociations describedby Davelaar et al. (2005) reflect important and robust differ-ences between short- and long-term recency, we show thatthey can be addressed within the framework of TCM withoutchanging any of the basic assumptions about context or itsrole in cuing recency effects. To capture these dissociations

we augmented TCM with a more elaborate retrieval rule that,while retaining the property that probability of recall dependson the relative activation of items, is also sensitive to changesin the overall level of activation. We accept the merit of thetheoretical argument about activation-based vs weight-basedmemory, but argue that this criticism does not apply to TCM,in which the maintenance of the current state of temporalcontext can be seen as an activation-based memory.

We start by reviewing the empirical dissociations betweenshort- and long-term recency. We then present TCM-A, anelaboration of TCM that uses competing accumulators to re-trieve particular items given a contextual cue (Usher & Mc-Clelland, 2001). A series of simulations demonstrate thatTCM-A can address the key dissociations between short- andlong-term recency despite the fact that temporal context is thesole cue for recall in both short- and long-term recency ex-periments. More theoretical concerns about activation-basedand weight-based memory are postponed until the GeneralDiscussion.

Dissociations between short- and long-term re-cency

Although there are many commonalities between short-and long-term recency in free recall (e.g. Greene, 1986),there are also a number of empirical dissociations betweenrecency in these tasks. Two dissociations between recencyin IFR and CDFR can be seen by examining the timing andorder of participants’ recalls. Although participants exhibit asimilar tendency to begin recall at the end of the list in bothtasks, they take longer to initiate recall in CDFR. Second,participants tend to recall several end-of-list items in succes-sion in IFR whereas in CDFR they tend to jump to earlierlist items after recalling one or two items from the end ofthe list. This dissociation can be seen in the lag-CRP func-tions: In IFR, the lag-CRP exhibits much stronger contiguityin early than in late output positions (Kahana, 1996). Thisis not the case in DFR or CDFR where the contiguity effectis approximately constant across output positions (Howard& Kahana, 1999). Whereas these first two dissociations canbe seen in the standard IFR and CDFR paradigms, Davelaaret al. (2005) identified four other dissociations which can beobserved through specific experimental manipulations. Thefirst of these additional dissociations is that the recency effectis more sensitive to proactive interference in CDFR than inIFR. Second, the long-term recency effect, but not the imme-diate recency effect, is disrupted in patients with anterogradeamnesia. Third, negative recency is observed in final freerecall following a series of IFR lists, but not after a seriesof CDFR lists. Fourth, the long-term, but not short-term,recency effect survives instructions to start recall from thebeginning of the list. Below we discuss each of these disso-ciations.

Dissociation: Time to first recall. A prominent and robustdissociation between IFR and CDFR can be seen in the timeparticipants take to initiate recall. In IFR, recall starts quicklywith a burst of several items, typically from the end of the

RECENCY AND TCM 5

list (Kahana, 1996; Nilsson, Wright, & Murdock, 1975). Asrecall proceeds, interresponse times (IRTs) increase (expo-nentially) with output position (Murdock & Okada, 1970).CDFR does not start with a quick burst of items, but startsslowly (unpublished observations) in a way that appears torequire an effortful search for the participants. Analysis ofresponse times from Howard and Kahana (1999) shows thatthe mean time to initiate recall was 1.04 s in IFR and 2.15 sin CDFR.

Dissociation: Changes in the contiguity effect with out-put position. Davelaar et al. (2005) noted that in IFR thecontiguity effect measured for the first few recalls is muchmore pronounced than the contiguity effect observed at lateroutput positions (Kahana, 1996; Howard & Kahana, 1999;Kahana, Howard, Zaromb, & Wingfield, 2002), but that thisdecrease in the contiguity effect with output position is notobserved in DFR nor CDFR (Kahana et al., 2002; Howard &Kahana, 1999). According to buffer models, the change inthe contiguity effect with output position occurs because par-ticipants begin recall by reporting all of the items availablein STS (Kahana, 1996; Davelaar et al., 2005). The items inthe STS at the time of test tend to be from the end of thelist. In IFR, these adjacent items are recalled first. Later inrecall, responses depend on retrieval from the LTS, resultingin a reduced contiguity effect. According to two-store mod-els, retrieval in CDFR takes place entirely from LTS, so therewould be no reason for the contiguity effect to change withoutput position (Davelaar et al., 2005).

Dissociation: Proactive interference. The short-term re-cency effect observed in IFR is remarkably insensitive toproactive interference. This point can be illustrated simplyby noting the observation of Murdock (1962) that the short-term recency effect is not affected by changing list length; theitems at the end of a list of, say 40 items, should be subject tomore proactive interference from the other list items than anitem at the end of a 20 item list would be. In fact, the robust-ness of short-term recency to proactive interference may bethe single most compelling rationale for a short-term mem-ory buffer—no matter how much information a participanthas been exposed to over the course of their lives, informa-tion presented in the last couple of seconds remains accessi-ble2.

Davelaar et al. (2005) presented an experiment in whichthey observed a reduction in the magnitude of the recencyeffect in CDFR, but not in IFR, due to proactive interferencefrom semantically similar items on a previous list. Althoughthe large primacy effect seen in their data suggests that thedistractor and presentation rate they employed did not pre-vent the potential confound of rehearsing earlier list itemsduring study, it is reasonable to assume that presenting twolists of semantically similar items effectively increases thelist length of the second list, and thus increases proactive in-terference, due to the semantic associations with the prior listitems.

Dissociation: Anterograde amnesia. Carlesimo, Marfia,Loasses, and Caltagirone (1996) reported a dissociation be-

tween short- and long-term recency, as measured by twotasks given to matched amnesic and control participants.They tested immediate recency by means of a standard IFRprocedure with each of 10 list items presented for 5 seconds.The test for long-term recency was quite different; they hadparticipants solve lists of 10 anagrams with 30 seconds foreach anagram. Each anagram was preceded by a 10 seconddistractor of backwards counting and the last item was fol-lowed by 30 seconds of backwards counting. The behavioralresults revealed no difference in recall for the last serial posi-tion in IFR, but a decrease in recall at all positions in theirvariant of CDFR. These results were taken as support fordual-store models of free recall because the amnesics’ pre-sumably intact STS supports recall of recency items in IFRwhereas their damaged LTS impairs recall of recency itemsin CDFR.

Because the critical comparison of Carlesimo et al. (1996)is between two very different tasks, it is difficult to makestrong inferences from their reported dissociation. Further-more, their use of a very long presentation rate would al-low participants to engage in extensive rehearsal thus furtherconfounding the relationship between the items’ nominal andfunctional serial positions (Brodie & Murdock, 1977; Tan &Ward, 2000; Ward, Woodward, Stevens, & Stinson, 2003).

Dissociation: Negative recency. As reported by Craik(1970), negative recency manifests as a decreased probabil-ity of recalling items from the last few serial positions of eachstudy-listduring a surprise test for recall of items from any ofthe previously studied lists (termed final free recall (FFR)).Davelaar et al. (2005) cite the dual-store interpretation of thisresult, which claims that items in the last few serial positionsspend less time in the buffer and, consequently, are not en-coded as well as earlier list items. By this same account, neg-ative recency is often absent in FFR following CDFR study-lists because each item spends the same amount of time inthe short-term store (Davelaar et al., 2005).

A number of results suggest that a contextual theory canprovide an equally parsimonious interpretation of negativerecency. Greene (1986) suggested that participants know thatTOT context provides a strong cue for the immediate recall ofend-of-list items and, consequently, spend less time rehears-ing those items. Less rehearsal gives rise to decreased acces-sibility during FFR because TOT context no longer providesa strong cue for recency items and retrieved context is thesole source for recalls. In fact, when participants do not knowwhen the list will end, and can not change their encodingstrategy, the negative recency effect is diminished (Watkins& Watkins, 1974). Other results suggest that the negativerecency effect is due to retrieval processes, not differencesin the encoding task. For example, Marmurek (1983) failedto find negative recency in IFR lists that were not tested im-mediately following study. This led Greene (1986) to state

2 Unlike the recency effect in IFR, which does not appear to besensitive to proactive interference, proactive interference does effectrecognition memory for recently experienced items (e.g., Monsell,1978).

6 SEDERBERG, HOWARD, & KAHANA

that negative recency can not dissociate dual- and single-store memory theories because any theory that claims thatinitial recall of recency items “is based on information thatis less useful at final free recall would predict this pattern ofresults” (p. 225). In light of the fact that negative recencyin IFR can be eliminated (Marmurek, 1983), we believe thatnegative recency does not place strong constraints on modelsof short- and long-term recency.

Dissociation: Directed output order. The directed outputorder recency dissociation refers to the finding that the re-cency effect is greatly attenuated in IFR when the partici-pant is instructed to initiate recall from the beginning of thelist (Dalezman, 1976), whereas the long-term recency effectis intact when participants in CDFR are instructed to beginrecall with the beginning of the list (Whitten, 1978). Dav-elaar et al. (2005) claim these results lend further supportfor an activation-based STS explanation of the dissociationsbetween short- and long-term recency. If the output fromthe activation buffer is responsible for the recency effect inIFR, beginning recall with non-recency items would flush thebuffer and eliminate the recency effect. Since the buffer is notresponsible for recency in CDFR, it would be unharmed byoutput order.

The directed output order recency dissociation is difficultto interpret for several reasons. First, the dissociation iden-tified by Davelaar et al. (2005) compares IFR in one study(Dalezman, 1976) with CDFR from another (Whitten, 1978).It is not clear whether the different results are a consequenceof a genuine empirical dissociation or one of the several ma-jor methodological differences between the two studies (e.g.,the list length in the IFR study was 15 items, whereas it was15 items in the CDFR study). Second, it is easy to manipu-late, even unintentionally, participants’ encoding strategiesin CDFR experiments and obtain “long-term recency” ef-fects that are a consequence of different levels of rehearsalfor end-of-list items. For instance, Koppenaal and Glanzer(1990) and Poltrock and MacLeod (1977) observed “long-term recency effects” that were eliminated when participantswere given a novel distractor in the retention interval. Thissuggested that the recency effect they had observed was de-pendent on habituation to the distractor such that it was lesseffective at preventing rehearsal for end-of-list items (but seeThapar & Greene, 1993; Neath, 1993). Recency effects ob-served in, for instance, free recall of US presidents (e.g.,Healy & Parker, 2001) are also likely to be attributable tosimilar encoding effects. The large primacy effect seen inthe Whitten (1978) data suggest that their participants wereable to rehearse items across the distractor interval in CDFR.As with the negative recency effect, we conclude that theempirical evidence regarding directed output order does notcurrently place strong constraints on models of the recencyeffect in free recall.

OverviewThe original implementation of TCM lacked the mecha-

nisms needed to account for a number of free recall phe-nomenon, including the key short- versus long-term recency

dissociations outlined above: namely, differences in recallonset latency, the contiguity effect across output positions,proactive interference, and anterograde amnesia. These dis-sociations all refer to a similar phenomenon—robust rapidrecall of multiple items with the end-of-list cue in immedi-ate recency in contrast to the slower more fragile long-termrecency effect.

We present a new model that combines the associativeframework of TCM with a dynamical decision component.The new model, called TCM-A, replaces the old retrieval rulein TCM with a set of leaky, competitive accumulators rep-resenting the words in the list (Usher & McClelland, 2001).The Usher and McClelland (2001) decision model has gainedconsiderable currency in both psychology and neuroscience,providing realistic accounts of behavioral reaction times andneural activity during a wide variety of tasks (McMillen &Holmes, In press; Bogacz, 2007; Bogacz, Usher, Zhang, &McClelland, 2007).

The novel property of TCM-A that enables it to accountfor the key differences between short- and long-term recencyis that the accumulator retrieval rule, which, while retainingsensitivity to the relative activation of items in selecting acandidate item to recall, behaves differently in response tochanges in the absolute levels of activation. This, coupledwith the gradual change of temporal context across outputpositions, ensures that the recency effect in immediate freerecall extends over several output positions, whereas the re-cency effect in CDFR falls offmore steeply, affecting primar-ily the last item.

The next sections describe the implementation of TCM-A in detail, followed by the results of simulations comparedto data from Howard and Kahana (1999). These simulationsshow that our elaborated version of TCM can account for thefour critical dissociations described above without the needto posit a separate buffer mechanism. We conclude that whileworking memory may serve other useful cognitive functions,a rehearsal-based STS does not appear necessary to explainthe recency and contiguity effects observed in free recall.

TCM with accumulating retrievaldynamics

TCM provides a formal computational model of how con-text evolves as a consequence of item encoding and retrieval.It also describes an associative architecture, implemented asa simple neural network, that links both items to contextand context to items. This section describes our implemen-tation of TCM with the addition of a retrieval rule basedon the Usher and McClelland (2001) competitive leaky-accumulator model of decision-making and reaction time.We refer to this expanded model as TCM-A. We now stepthrough the basic components of TCM-A and show how theyinteract to create a system that can be used to flexibly storeand retrieve episodic memories. In our description of TCM-Abelow, we will note aspects of the model that differ from theoriginal TCM (Howard & Kahana, 2002; Howard, Kahana,& Wingfield, 2006).

RECENCY AND TCM 7

Item Layer (F)

Context Layer (T)

MFT MT F

AccumulatorsStimuli

Figure 2. TCM-A: Temporal context model with accumulator retrieval rule.

Components of TCMThe evolution of context is driven by the studied items. In

TCM-A, ti, the state of context at time i, evolves due to theinformation that is currently being processed by the memorysystem. Mathematically, TCM models the context vector asevolving according to the equation:

ti = ρiti−1 + βtINi , (1)

where β is a parameter that determines the rate of contextualdrift during encoding, ρi is a scaling parameter, chosen ateach time step such that ti is always of unit length, and tIN

iis the input at timestep i (throughout this article we use boldface letters to denote vectors and matrices). t0 is the stateof context prevailing when the first item, f1, is presented forstudy. In TCM-A, as in prior work on TCM, we assume thatthe vectors representing the studied items, denoted as fi, areorthonormal. As we will explain below, the input pattern tIN

1is the contextual information retrieved by item f1. Thus, afterf1 has been studied, t1 = ρ1t0 + βtIN

1 . This is the context thatprevails when the subsequent item, f2, is presented.

Hebbian associative memory. TCM-A uses matrices torepresent item to context and context to item associations(see Figure 2). The context-to-item associations are stored ina matrix, MT F , which allows contextual states to cue items.The item to context matrix, MFT , allows items to recoverprevious states of context. In TCM-A we distinguish be-tween pre-experimental and experimentally-learned item-to-context associations, which we denote as MFT

pre and MFTexp,

respectively. We also distinguish between pre-experimentaland experimentally-learned context-to-item associations viaMT F

pre and MT Fexp. This distinction between new (episodic)

learning and longstanding (semantic) knowledge enablesTCM-A to simulate performance in situations where themechanisms responsible for new associative learning havebeen damaged (Carlesimo et al., 1996). A similar assump-tion made in the eSAM and fSAM models proved crucial

for simulating the interacting effects of pre-experimentaland new learning in categorized free recall (Sirotin et al.,2005) and in the Deese-Roediger-McDermott false memoryparadigm (Kimball et al., in press).

For simplicity, we fix MFTpre and MT F

pre as identity matri-ces that do not change during the encoding and recall of asimulated list. Clearly, these pre-experimental weight ma-trices must change over time, but at a much slower timescale than the course of a single simulated list. Finally, thematrices representing experimental item-to-context associa-tions, MFT

exp and MT Fexp, are set to zero at the beginning of each

simulated list3 and updated to learn the associations betweenitems and context during list presentation.

Encoding new associations between items and context.TCM-A assumes that items become associated with context.We update a Hebbian outer-product matrix, MT F

exp, that asso-ciates the prevailing context with the presented item’s repre-sentation. This follows the equation:

∆MT Fexp = φifit>i−1, (2)

where > denotes the transpose operator 4. As described inthe Modeling primacy section below, φi biases learning de-pending on the item’s serial position in the list such that itemsfrom early serial positions are more strongly encoded. Simi-lar assumptions have been used by computational models todescribe primacy effects in serial recall (e.g., Brown, Preece,& Hulme, 2000; Burgess & Hitch, 1999).

Prior to updating context, we also increment the Hebbianouter-product matrix, MFT

exp, that associates the active item to

3 Resetting the experimental association matrices between listsis a simplification to allow us to focus on intra- rather than inter-listeffects.

4 In this implementation we are assuming that the dimensionalityof the f vectors is the same as the dimensionality of the t vectors.This is not a necessary feature of the model.

8 SEDERBERG, HOWARD, & KAHANA

the state of context:

∆MFTexp = ti−1f>i . (3)

As a consequence of this learning in MFTexp, recalling an item

recovers the state of context prevailing just prior to its initialpresentation.

After storing the newly-learned associations between t0and f1, we update the current state of temporal context ac-cording to Equation 1. Specifically, t1 = ρ1t0 + βtIN

1 . Thefirst time an item is presented, only MFT

pre contributes to theretrieved context. For instance, tIN

1 will be given by the equa-tion:

tIN1 =MFT

pref1. (4)

Because MFTpre is an identity matrix and the fis are orthonor-

mal, this means that the input patterns caused by a list ofunique items will also be orthonormal. Thus, the state ofcontext following the presentation of f1 is simply a weightedsum of the prior state of context, t0, and the representa-tion of f1. Following the presentation of f2 we would havet2 = ρ2t1 + βtIN

2 = ρ2ρ1t0 + ρ2βtIN1 + βt

IN2 . Note that tIN

2 willhave a larger weight than tIN

1 because ρi < 1.As each item is presented for study, TCM-A first stores the

association between the item and the current state of contextand then updates context based on Equation 1. As describedin the next subsection, many of the same processes operateduring retrieval, except that context is used as a cue to re-trieve items.

Contextual states are used to retrieve item representa-tions. According to dual-store models of free recall, re-trieval begins by first reporting the items in the STS, or thoseitems whose activations exceed a threshold (Raaijmakers &Shiffrin, 1981; Sirotin et al., 2005; Davelaar et al., 2005). Itis this buffer mechanism that is responsible for the recencyeffect in IFR and the recency dissociations between IFR andCDFR. Unlike these models, TCM-A assumes that recall be-gins by using the time of test (TOT) context as a retrieval cue.TOT context serves as a cue for recall of items via MT F .

Multiplying MT F by the context vector, tTOT , retrieves asuperposition of the items fi, each activated to the extent thatthe TOT context overlaps with both their encoding and pre-experimental contexts stored in MT F :

f = (1 − γT F)(MT FpretTOT ) + γT F(MT F

exptTOT ), (5)

where γT F controls the relative contribution of the pre-experimental and experimental context in driving item re-trieval and the activation of each item fi is

fi = (1 − γT F)(tINi · tTOT ) + γT F(ti−1 · tTOT ). (6)

Thus, items that were originally seen in a study context (ti−1)that is similar to the TOT context will be more strongly ac-tivated than those that were originally seen in a completelydissimilar context. Similarly, recently-studied items will bemore strongly activated because they will have greater rep-resentation (via tIN

i ) than early list items in the TOT context

vector.We fixed γT F at 0.8 (except for the amnesia simula-

tions), which indicates that the item activations derivedfrom the TOT context are based more on the newly-learnedexperimental context-to-item associations than on the pre-experimental associations. Although one could imaginethat participants might dynamically bias retrieval to fa-vor pre-experimental/semantic or newly-learned experimen-tal/temporal associations, which would be equivalent tochanging γT F during the recall period, we do not considersuch biasing effects in this manuscript.

Accumulator-based retrieval mechanism. In TCM-A, wereplaced the Luce choice retrieval rule used in TCM witha set of competitive, leaky accumulators as described inthe Usher-McClelland model of perceptual decision mak-ing (Usher & McClelland, 2001). The Usher-McClelland ac-cumulator model has a number of desirable properties, in-cluding the ability to model competitive choice processeswith realistic reaction times.

The accumulators are easily integrated with TCM, actingas a drop-in replacement for the Luce choice rule. The itemactivations f derived from the current state of context (Equa-tion 5) provide the input I to the accumulators:

I = CV f (7)

where CV is the coefficient of variation of the item activa-tions, defined as the standard deviation divided by the mean,which serves as a measure of the signal to noise ratio in theaccumulators. To ensure that only relevant inputs are con-sidered in the determination of the input noise, items whoseactivations are below a minimum activation ( fi < αmin) arenot included in the calculation of the CV . If the CV is greaterthan one, then the input is of high variance relative to itsmean (i.e., the input is noisy) and is scaled up to help dis-criminate between items. Conversely, if the CV is less than 1,then the input’s variance is low relative to its mean (i.e. theinput is less noisy) and item activations are scaled down withrespect the accumulator noise, making the inputs more sim-ilar to one another. Such gain modulation has been reportedto occur in the cortex to scale neuronal activity to respondoptimally to a wide variety of inputs (Abbott, Varela, Sen,& Nelson, 1997; Chance, Abbott, & Reyes, 2002). Finally,if the CV is undefined or zero, as is the case when the stan-dard deviation or mean across item activations is zero, the CVremains unchanged from the previous recall or is set to 1 ifthere have been no previous responses.

At the start of recall, the accumulators x are initialized tozero and they grow due to the input from each list item:

∆x = [I − (κ + λL)x]∆tτ+ ε

√∆tτ, (8)

where, x is the state of the vector of accumulators across alllist items, I is the vector of inputs to these accumulators (pro-vided by TCM-A from the current state of context), κ is aconstant controlling the strength of recurrent inhibition, L is

RECENCY AND TCM 9

a lateral inhibition matrix with components Li j = (1 − δi j),where δi j is the Kronecker delta, which equals 1 if i = jand 0 otherwise, ε is a normally-distributed random variablewith mean zero and standard deviation σ, ∆t is the size ofthe timestep, and τ is the time constant. x is rectified ateach timestep to prevent negative activations. The four termson the right hand side of Equation 8 correspond to a drivingforce from the input from TCM-A, a recurrent inhibition termthat keeps the magnitude of x from growing without bound,a lateral inhibition term that penalizes an accumulator to theextent that the other accumulators are activated, and a noiseterm. The equations for the accumulators are exactly as pre-sented in Usher and McClelland (2001) with the exceptionthat rather than a two-choice response, we have l accumula-tors corresponding to the l items in the list.

The accumulators grow according to Equation 8 until anaccumulator crosses a threshold Θ. Although all accumula-tors continue to compete across the course of recall, if an ac-cumulator for a recalled item crosses threshold it is ignoredand reset to zero, thus precluding it from being repeated.5This accumulator framework improves on the Luce choicerule used in previous simulations (Howard & Kahana, 2002;Howard, Fotedar, Datey, & Hasselmo, 2005; Howard et al.,2006) by providing a much richer set of retrieval dynamicsthat is able to generate a measure of response latency.

The retrieval process for subsequent recalls. When anitem is recalled, TCM-A retrieves a combination of thatitem’s pre-experimental contexts via MFT

pre, as well as theitem’s experimental context (the state of context when theitem was presented at time i) via MFT

exp. These two contextualrepresentations combine to form the input that contributes tothe new state of context:

ti = ρiti−1 + β((1 − γFT )MFT

prefi + γFT MFTexpfi

)(9)

Depending on the value γFT , the change in t can be biased to-wards the newly-learned experimental cue, which provides abidirectional cue to items from a similar temporal context, ortowards the pre-experimental cue, which provides a forward-asymmetric cue for words that were studied after the recalleditem. Before updating context, the retrieved context is scaledto unit length. Once updated, the new context then serves asthe cue for the next recall in the same way that TOT contextserved as the cue for the first recall.

Stopping rule. The criterion for terminating recall is anessential ingredient for modeling serial position effects thatwas absent from the original TCM implementation. In TCM-A, the accumulators provide a natural stopping rule that isanalogous to the time-limits imposed on participants in freerecall experiments. Specifically, we assume that recall endsafter a fixed number of accumulator timesteps. In the subse-quent simulations, this value is set at 1000 timesteps.

Modeling distractors. In TCM-A, the arithmetic distrac-tors employed in delayed and continual-distractor free recallare modeled as orthogonal vectors that cause context to driftat a rate βdist. Although distractor items drive context, we

assume that they do not give rise to any modification of theMFT

exp and MT Fexp weight matrices. This assumption seems rea-

sonable as participants have no reason to learn the distractors.

Modeling primacy. Numerous studies have demonstratedthat the two main sources of primacy effects in free recall arean increased tendency to rehearse items from early serial po-sitions throughout the list presentation (Rundus, 1971; Mur-dock & Metcalfe, 1978; Tan & Ward, 2000) and increased at-tention or decreased competition during the study of early listitems giving rise to better encoding (Sederberg et al., 2006).Howard and Kahana (1999) employed fast presentation ratesand orienting tasks during encoding, which presumably at-tenuated rehearsal and, in turn, the primacy effect. Still,small primacy effects remained, which often manifested asan increase in the probability of initiating recall with the firstitem in the list and a higher probability of recalling itemsfrom early serial positions, both with respect to middle listitems. Not wanting to complicate TCM-A by including a re-hearsal mechanism during encoding, we chose to model pri-macy as an exponentially decaying boost in the learning ratefor early serial positions. This encoding boost, is folded intothe learning rate φi in Equation 2:

φi = φse−φd(i−1) + 1, (10)

where φs + 1 determines the size of the primacy effect at thefirst serial position and φd controls the rate of decay of theprimacy effect with each additional list item.6

Simulations of experimental data

Table 1 provides a summary of the free and fixed param-eters in TCM-A, organized into three categories. The TCMBase category contains the parameters relevant to the theo-retical foundation of TCM. The Primacy category lists theparameters specific to our implementation of primacy in themodel. Finally, the Accumulator category lists the parame-ters from the Usher and McClelland (2001) decision modelthat determines which item is recalled given a set of activa-tions. Allowed parameter ranges are specified for the freeparameters.

As in Davelaar et al. (2005), our goal was to producereasonable qualitative fits of the key dissociations. This ap-proach has several advantages over attempting to find excel-lent quantitative fits by separately estimating parameters foreach experimental condition being studied. First, it avoidsthe tendency to overfit the model to certain phenomena atthe expense of enabling the model to simultaneously capturethe trends observed across multiple experiments. Second, it

5 In free recall of randomly chosen common words, healthyyoung participants very rarely make repetitions (Zaromb et al.,2006), however a more complete model of recall would need toaccount for the occasional repetitions that participants do commit.

6 The parameters used in the actual simulations produced asharply-decaying exponential function such that Eq. 10 provideda substantial recall advantage only for the first list item.

10 SEDERBERG, HOWARD, & KAHANA

leads to more easily interpretable parameter values and pre-vents one from having to explain differences in parametersacross different conditions. Finally, it ensures that the modeland not the parameters are doing the work in producing thepattern of dissociations observed across multiple experimen-tal conditions. Consequently, by enforcing a fixed set ofparameters across experimental conditions we were able tocompare unambiguously simulation results across free recallconditions at the expense of accurate and quantitative fits tothe data.

We employed a genetic algorithm (GA) to ensure themodel was working in the correct parameter space to providefits to the IFR, DFR, and CDFR conditions across Experi-ments 1 and 2 in Howard and Kahana (1999). The geneticalgorithm starts with a large population of candidate modelparameter sets (that span the entire free parameter space ina multidimensional grid), and, thus, is largely immune to lo-cal minima. At each generation, the GA simulates the indi-vidual parameter sets and calculates the root mean squareddeviation (RMSD) from the behavioral data. To ensure anapproximate fit across conditions, we calculated the RMSDto a combination of the serial position curve, the probabilityof first recall, and the contiguity effect as seen in the lag-CRPfunctions from both the IFR and DFR conditions of Experi-ment 1 and from both the DFR and CDFR conditions fromExperiment 2. The best fitting parameter sets from each gen-eration evolve to form the next generation until reaching astable state. We evolved a population made up of 8000 indi-viduals, which we culled to 1000 individuals after 50 gener-ations. These 1000 runs typically took 50 additional gener-ations to stabilize at a single set of parameters that providedapproximate fits to all critical conditions.

Modeling short-term andlong-term recency

Our simulation results are organized as follows. First, wefit TCM-A to serial position curves, recency effects, and con-tiguity effects from IFR, DFR and CDFR tasks reported inExperiments 1 and 2 of Howard and Kahana (1999). Usinga single parameterization to fit data from all three tasks andfrom both experiments, we show that TCM-A also accountsfor dissociations between immediate and long-term recency,including the dissociation in the contiguity effect (See Dav-elaar et al. (2005)). Further simulations using the same pa-rameterization account for the differential effect of proactiveinterference on immediate and long-term recency (Davelaaret al., 2005). By turning off weight-based learning, whileleaving all other parameters unchanged, we show that TCM-A produces a dissociation between the effect of amnesia onimmediate and long-term recency (Carlesimo et al., 1996).

Simulating recency and contiguity in immediate,delayed and continual distractor free recall

Our first goal was to assess whether TCM-A could repro-duce the basic features of the serial position curve acrossIFR, DFR, and CDFR. Figure 3 shows the probability of re-call as a function of serial position for the behavioral data

and model simulation. TCM-A reproduces the major featuresof the serial position curve in IFR (top row, Figure 3 solidline), illustrating a strong recency effect and a modest pri-mary effect. By simulating a distractor following the studylist, TCM-A was able to capture the attenuated recency ob-served in DFR (Figure 3 dashed line). Notably, the differ-ence between IFR and DFR is much greater at the end thanat the beginning of the serial position curve. Although themodel parameters were fixed between experiments, we plotthe delayed condition (dashed line) to provide a point of ref-erence between experiments (top and bottom). In fitting datafrom Experiment 2, TCM-A captured the relative behavior ofthe serial position curve in both DFR (Figure 3, bottom row,dashed line) and CDFR (Figure 3, bottom row, dotted line).TCM-A illustrates both the reduced overall level of recall atearly serial positions in CDFR and the increased recency ef-fect.

Whereas the serial position curve collapses data over thedynamics of the retrieval process, one can separately exam-ine the way participants initiate recall and the way they maketransitions. The probability of first recall (PFR Hogan, 1975;Laming, 1999), a serial position curve calculated only forthe first item recalled, illustrates participants’ tendency toinitiate recall with one of the terminal list items. As firstshown by Deese and Kaufman (1957) the recency effect isclosely related to participants’ tendency to begin recall at theend of the list (see, also, (Kahana, 1996; Howard & Kahana,1999)). Figure 4 shows PFR curves generated by the samesimulations used to generate the serial position curves in Fig-ure 3. These curves illustrate that participants’ tendency toinitiate recall at the end of the list was very strong in both IFRand CDFR, but much weaker in DFR. As the PFR functionsare strikingly similar in both IFR and CDFR, this analysisillustrates the approximate time-scale invariance of recency.TCM-A provides a good qualitative fit to both to the overallform of the PFR and to the changes in the PFR across dis-tractor schedules.

The foregoing analyses show that TCM-A successfully ac-counts for the qualitative form of both the serial position andPFR functions across IFR and DFR. TCM-A was also able topredict the recovery of recency (both in relative and absolutelevels) in CDFR.

Another striking feature of free recall is the contiguityeffect as seen in the lag-CRP analysis of Kahana (1996).Whereas dual store models account for contiguity based onthe co-occurrence of items in STS, contiguity in TCM arisesbecause recall of an item recovers its associated temporalcontext, which is similar to neighboring list items. Becauseretrieval is competitive, TCM predicts contiguity across timescales so long as the distractors separating the list items areunrelated to the list items (Howard & Kahana, 2002). Asshown in Figure 5, the lag-CRP curves generated from thesame simulations depicted in Figures 3 and 4 account forsimilar levels of contiguity and asymmetry seen in both DFRand CDFR.

Thus, using accumulator dynamics to model the retrievalprocess, TCM-A reflects a much richer set of recall dynamicsthan previous implementations of TCM. Nonetheless it still

RECENCY AND TCM 11

Data Model

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Figure 3. Serial position curves. Behavioral data (left) from Howard & Kahana (1999) and model simulations (right) ofthe corresponding free recall conditions. Top: Immediate (solid line) and delayed (dashed line) free recall from Exp. 1.Bottom: Delayed (dashed line) and continual distractor (dotted line) free recall from Exp. 2. Note that the simulated fits to thedelayed condition (dashed line) are repeated in the top and bottom because we did not allow parameters to change betweenexperiments.

12 SEDERBERG, HOWARD, & KAHANA

Table 1Summary of free and fixed parameters in TCM-A. Fixed parameters have only a single value denoted in the Range column.

Category Parameter Description RangeTCM Base β Rate of contextual drift at item encoding and retrieval. 0.0–1.0

βdist Rate of contextual drift due to a distractor. 0.1–1.0γFT Relative weight of pre-exp. to exp. context (item to context). 0.0–1.0γT F Relative weight of pre-exp. to exp. context (context to item). 0.8

Primacy φs Primacy scale factor. 0.0–5.0φd Primacy decay rate. 0.0–5.0

Accumulator κ Strength of recurrent inhibition. 0.0–0.9λ Strength of lateral inhibition 0.0–0.9σ Standard deviation of accumulator noise. 0.0–0.8Θ Recall threshold. 1.0∆t/τ Ratio of the time step to the time constant. 0.1αmin Minimum item activation for inclusion in CV scaling. .0001

retains the ability to describe the long-term recency effectand long-term contiguity effects that the Howard and Kahana(2002) version of the model was developed to explain.

Summary of parameters

Table 2 reports the model parameters (eight free) that pro-duced the fits shown in Figures 3, 4, and 5. Though of sim-ilar magnitude, the contextual drift rate during item presen-tations and retrievals (β) is moderately fast, which gives riseto the sharp contiguity effect observed in Figure 5. Simi-larly, the contextual drift due to a distractor period (βdist) isquite large, effectively replacing the current state of contextwith the orthogonal distractor context. The value of γFT indi-cates that the relative contributions of pre-experimental andexperimental item-to-context associations are nearly equiv-alent (there is a slight bias towards pre-experimental con-text.) The scale and decay of primacy (φs and φd) providea strong boost for the first item in the list, but this boost de-cays quite quickly for subsequent serial positions, droppingfrom ∼ 2.26 for the first item to ∼ 1.17 for the second item,which is close to the asymptotic value of 1. For the accu-mulator, we required the lateral inhibition λ to be equal tothe leak (decay) rate κ resulting in accumulators that followa drift diffusion process, which has been shown to be desir-able when fitting reaction times of decision processes (Bo-gacz, Brown, Moehlis, Holmes, & Cohen, 2006; McMillen& Holmes, In press; Smith & Ratcliff, 2004). Finally, therelatively high variance of the accumulator’s noise parame-ter enables remote transitions during recall as this is the onlystochastic component of TCM-A.

Dissociations between short- and long-term re-cency

The preceding simulations demonstrate that TCM-A canexplain the basic recency and contiguity phenomena acrossconditions with a single set of parameters. In particular,TCM-A, like the original treatment of TCM, is able to de-scribe the commonalities between short- and long-term re-

Table 2Best fitting parameters for TCM-A simulations. Parametersmarked with an ∗ were fixed.

Category Parameter ValueTCM Base β 0.62676

βdist 0.97607γFT 0.44542γT F 0.8∗

Primacy φs 1.26554φd 1.98112

Accumulator κ 0.28000λ 0.28000σ 0.36233Θ 1.0∗

∆t/τ 0.1∗

αmin .0001∗

cency, and the analogous similarity between contiguity ef-fects observed in DFR and CDFR. Using the same model,and the same set of parameters, we now demonstrate thatTCM-A is also able to account for the major dissociationsbetween short- and long-term recency. Davelaar et al. (2005)argued that these dissociations necessitate separate mecha-nisms underlying recency in IFR and CDFR. The follow-ing sections demonstrate TCM-A’s ability to capture thesedissociations using gradually-changing temporal context asthe sole retrieval cue to initiate recall across conditions. Infact, temporal context, governed by the equations describedabove, is the sole retrieval cue at all recall attempts.

Time to first recall. Although it has not been explicitlyreported before, it is well-known to investigators examiningIFR and CDFR that the recall latency to the first response dif-fers across these conditions. Figure 6 illustrates the model’sability to capture this dissociation with the latencies to ini-tiate recall in the IFR, DFR, and CDFR conditions for boththe behavioral data from Howard and Kahana (1999) and the

RECENCY AND TCM 13

Data Model

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(Fir

st

Recall)

Figure 4. Probability of first recall. Behavioral data (left) from Howard & Kahana (1999) and model simulations (right)of the corresponding free recall conditions. Top: Immediate (solid line) and delayed (dashed line) free recall from Exp. 1.Bottom: Delayed (dashed line) and continual distractor (dotted line) free recall from Exp. 2.

simulations.7 This finding reflects a key advantage of TCM-A. The accumulators are sensitive to both the relative activa-tions of the list items and to their absolute level of activation.In particular, the greater overall level of activation for end-of-list items in IFR causes the accumulators to reach thresholdmore quickly than in CDFR.

Contiguity effects in early output positions. The contigu-ity effect in IFR is much stronger at the first couple of out-

put positions than it is later in recall (Kahana, 1996). Thischange in the shape of the lag-CRP with output position isnot observed in either DFR or CDFR (Howard & Kahana,

7 Although the IFR data and CDFR data are taken from differ-ent experiments, the DFR conditions from Experiments 1 and 2 ofHoward and Kahana (1999) show comparable response times, sug-gesting that there is a meaningful difference between latencies inthe IFR and CDFR conditions.

14 SEDERBERG, HOWARD, & KAHANA

Data Model

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.Figure 5. Conditional response probability. Behavioral data (left) from Howard & Kahana (1999) and model simulations(right) of delayed (dashed line) and continual distractor (dotted line) free recall from Exp. 2.

Data Model0

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4

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6

Tim

e t

o 1

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Recall (

s) IFR - Exp. 1

DFR - Exp. 1DFR - Exp. 2CDFR - Exp. 2

Figure 6. Time to first recall. Data and model fits of the time, inseconds, until the first recalled item. White bars indicate the time tothe first recall in continual distractor free recall (CDFR), while darkgrey bars provide the time to the first recall in IFR. The intermedi-ate grey bars show the time to first recall in the delayed conditionsof Exps. 1 and 2 from Howard & Kahana (1999) as a reference.Note, model output is in timesteps ∆t, scaled by 15 to match thebehavioral data. Error bars are 95% confidence intervals.

1999). Figure 7 demonstrates that TCM-A can account forthe decline in the contiguity effect across output positionsseen in IFR and the lack of such a change in the contiguityeffect across output positions in CDFR. The top row of Fig-ure 7 shows that TCM-A captures the reduction in the conti-guity effect between the first output position (solid line) andlater output positions (dashed line) in IFR. Figure 7 (bot-tom) shows that TCM-A correctly predicts the absence ofany change in the contiguity effect across output positionsin CDFR. The dissociation was observed in the same sim-ulations that generated the serial position curves, PFRs andlag-CRPs above.

Proactive interference. Davelaar et al. (2005) showed thatalthough the short-term recency effect was not sensitive toproactive interference, the long-term recency effect was. Weexamined whether TCM-A can account for the dissociationbetween the effect of proactive interference on short- andlong-term recency by re-running the simulations reportedabove with increasing list lengths. The items at the end of thelonger lists are subject to more proactive interference frompreceding list items than items at the end of shorter lists. Ourgoal here is not to fit any particular data set that manipulateslist length, but simply to demonstrate that the model accountsfor this qualitative dissociation between short- and long-termrecency. As illustrated in Figure 8, TCM-A correctly predictsthat the recency effect, as illustrated by the serial positioncurve, remains relatively constant in IFR (left) but declineswith list length in CDFR (right).

RECENCY AND TCM 15

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Figure 7. Conditional response probability by output position. Lag-CRPs of the first (solid line) and then remaining (dashedline) output transitions for behavioral data (left) from Howard & Kahana (1999) and model simulations (right) in the immediatefree recall condition of Exp. 1 (top) and the continual distractor free recall condition of Exp. 2.

Anterograde amnesia. Carlesimo et al. (1996) studiedIFR and CDFR in control participants and in patients suf-fering from anterograde amnesia. Notably, the amnesic pa-tients showed robust recency effects in both IFR and CDFR.Carlesimo et al. (1996) found that in IFR patients with an-terograde amnesia showed a smaller decrease in their overalllevel of recall in the recency portion of the serial positioncurve than at the beginning or middle of the list. In CDFR thedecrease in recall performance across groups was consistent

across all serial positions.

Insofar as amnesic participants have difficulty recallingwords from all serial positions in CDFR, there is still anincreased probability of recalling items from recency serialpositions. As has been illustrated in both normal and olderparticipants (Howard & Kahana, 1999; Kahana et al., 2002),the shape of the serial position curve corresponds to a simi-lar shape of the PFR curve, wherein the relative differencein probability of recall between recency and non-recency

16 SEDERBERG, HOWARD, & KAHANA

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Figure 8. Proactive interference effect. Model simulations of serial position curves illustrating the effect of increasing thelist length in immediate free recall (left) versus continual distractor free recall (right).

items correlates with the magnitude of the recency effect inthe PFR. Consequently, Carlesimo et al’s (1996) findings areconsistent with a situation in which the recency effect ob-served in the PFR is consistent across groups and conditions.

We hypothesize that the effect of anterograde amnesia,similar to the effect of aging (Kahana et al., 2002), is re-stricted to a disruption in the ability to encode an item inits temporal context and for the item to recover its temporalcontext when repeated. If amnesics are unable to recall sub-sequent items after the recency effect appropriate for eachcondition, then we will have accounted for Carlesimo et al.’s(1996) qualitative findings. Because the methods of the Car-lesimo et al. (1996) study differ considerably from those em-ployed in the Howard and Kahana (1999) data from the fore-going simulations, and in fact the methods in the immedi-ate and continual-distractor conditions of the Carlesimo et al.(1996) study differed dramatically from each other, we willnot attempt a direct fit to their published results (i.e. serialposition curves). Rather, we will examine the PFR curvesand changes in the CRP with output position across groups.

To simulate the effect of anterograde amnesia, we as-sumed that no learning took place at MFT

exp and MT Fexp, i.e.

γT F = γFT = 0. All other aspects of the model—the grad-ual change of temporal context from moment-to-moment,the pre-experimental weights (i.e. MFT

pre and MT Fpre), and the

retrieval dynamics of the accumulators, —were left intact.With the exception of the change in learning rates acrossgroups, the parameters used in this simulation are identicalto those used in the previous model fits.

As can be seen from the top panel of Figure 9, TCM-A pre-dicts nearly identical PFR curves for controls and amnesics

in both IFR or CDFR. As outlined above, TCM-A’s pre-diction of a long-term recency effect that persists in CDFRis consistent with previous studies (Carlesimo et al., 1996;Marks & Cermak, 1998). In contrast with the PFR predic-tions, TCM-A produced dramatic differences in the lag-CRP,and in the effect of amnesia across distractor conditions. Thesimulated amnesics showed a peaked lag-CRP at the first out-put position in IFR but a flat lag-CRP at later output positions(Figure 9, lower left). In contrast, the contiguity effect per-sisted across output positions in the simulated control par-ticipants (see Figure 7, top right). In CDFR, the simulatedamnesics showed a flat lag-CRP both early and late in output.

The fact that amnesia resulted in a peaked lag-CRP earlyin IFR, but not in CDFR reflects an important dissociationbetween short- and long-term recency. The strong activationresulting from end-of-list context in IFR is sufficient to per-sist across multiple output positions. In contrast, the abso-lute difference in the activation due to end-of-list context inCDFR is relatively weaker, such that it cannot affect multipleretrieval attempts in CDFR.

Essential properties of the retrieval rule

TCM-A’s ability to capture the dissociations betweenshort- and long-term recency results from the retrieval rulegenerating several fast recalls from the end of the list in re-sponse to the strong end-of-list cue in IFR. Here we describehow our parameterization of TCM-A produce the dissocia-tions described above.

Figure 10, left, displays the input to the accumulators (I)derived from the TOT context (see Equations 6 and 7) for

RECENCY AND TCM 17

0 2 4 6 8 10 12Serial Pos.

0.0

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irst

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IFR - AmnesicIFR - Control

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-6 -4 -2 0 2 4 6Lag

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-6 -4 -2 0 2 4 6Lag

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Figure 9. Effects of amnesia. Probability of first recall (top) and conditional response probability by output position (bottom)curves showing simulated effects of amnesia in immediate free recall (left) and continual distractor free recall (right). Notethat while the top panels compare controls to amnesics, the bottom panels compare the CRP from the first output position toall other serial positions, as in Figure 7, for just the amnesics.

each item as a function of serial position. These inputs showa strong recency effect in both IFR and CDFR, however,the absolute magnitude of the inputs is smaller in CDFR.This difference in magnitude is due to the distractor delayin CDFR, which gives rise to a smaller overlap between theTOT context and the encoding context (Howard, 2004).8 Theoverall scale of the accumulator growth due to the input islargely determined by the standard deviation of the noise

term, σ, which took on a value of .36 in our simulations(see Table 1). Given that the only sources of accumulator

8 The inclusion of the coefficient of variation in Eq. 7 counter-acts this difference in the absolute level of activation. However, theinclusion of the threshold αmin causes the coefficient of variation inCDFR to be larger than it would be without the threshold, allowingthe model to preserve the difference in overall activation betweenIFR and CDFR.

18 SEDERBERG, HOWARD, & KAHANA

1st Recall 2nd Recall

0 2 4 6 8 10 12Serial Pos.

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Accu

m.

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ut

IFRCDFR

Figure 10. Accumulator input as a function of serial position for first and second output positions. Accumulator input forIFR and CDFR conditions for the first (left) and second (right) output positions. To illustrate the tendency to remain at the endof the list following the first response, the data for the second output condition were included only when the first output wasthe last item in the list.

growth are the input and the noise (see Equation 8), if thenoise is much larger than the input it will mask the effectof the input. Inspection of Figure 10 shows that while theactivation of several items is above, or at least near, σ whenimmediate recall is initiated, only the last item in the list hasan activation on the order of σ in CDFR.

The absolute difference in the level of activation in theinitiation of IFR compared to CDFR leads to the differencesbetween the short- and long-term recency effects observed inthe simulations. For instance, the greater magnitude of theactivations in IFR means that the accumulators reach thresh-old more quickly, accounting for the difference in time toinitiate recall. Critically, the greater absolute level of acti-vation of several end-of-list items enables TCM-A to recallseveral end-of-list items in IFR. In TCM, context is assumedto evolve during retrieval as well as during list presentation.The right panel of Figure 10 shows the activation of eachitem as a function of serial position on the second recallattempt, given that the last item in the list was recalled inthe first output position.9 The strong end-of-list cue that ispresent when immediate recall is initiated persists, weightedby ρ, as part of the cue for the second recall. In IFR, thestrong residual activation from the end-of-the list items com-bines with the reinstated context to provide a stronger cuefor recall than retrieved context would alone. Consequently,the average input to the accumulators for the second outputis still higher for items from the end of the list than for otheritems (Figure 10 right, solid line). Moreover, the activationof several end-of-list items is on the order of, or even greater

than σ in IFR. In CDFR, the accumulator input for subse-quent responses is more evenly distributed throughout thelist, with the largest input less than one-third the standarddeviation of the accumulator noise, resulting in a CRP that isnearly flat with output position.

It should be noted that for the parameters used in thesesimulations, residual activation in the accumulators betweenresponses is not contributing to the recency dissociations.The original motivation for using the accumulators in TCM-A was the expectation that non-recalled recency items in IFRwould be close to the recall threshold when another item isrecalled, thus increasing their chance of being recalled next.However, for the parameters used in these simulations, reset-ting all the accumulators to zero following each recall had noeffect on the simulated results.10 The dissociations betweenshort- and long-term recency observed in the simulations donot apparently depend on persistent activation of items acrossretrieval attempts, but rather reflect properties inherited fromthe rules for contextual evolution and recovery provided byTCM.

9 Although the last item still receives input from the accumulator,it can not be recalled so that point is removed from the graph.

10 It is also possible that allowing the accumulator for the just-recalled item to evolve during retrieval, and thus provide lateralinhibition to the other items, is also affecting the behavior of themodel here.

RECENCY AND TCM 19

General Discussion

Davelaar et al. (2005) claimed that empirical dissociationsbetween immediate and long-term recency made a commonexplanation of both phenomena untenable. In this paper, weprovide an existence proof that counters that assertion. TheTCM-A model assumes that a gradually-changing contextrepresentation serves as the sole retrieval cue throughout im-mediate (IFR), delayed (DFR) and continual distractor freerecall (CDFR). We have shown how TCM-A not only cap-tures the standard serial position, recency, and contiguity ef-fects (Figures 3 to 5), but also accounts for several key disso-ciations between short- and long-term recency. These disso-ciations include the findings of faster recall initiation in IFRas compared with CDFR (Figure 6), more local recall transi-tions among recently studied items in IFR than CDFR (Fig-ure 7), significantly greater proactive interference in CDFRthan in IFR (Figure 8), and differing effects of anterogradeamnesia on IFR and CDFR (Figure 9).

The gradually-changing context representation in TCM-Acues recall of items using a combination of pre-existing (e.g.MT F

pre) and newly-learned (e.g. MT Fexp) weight-based memo-

ries. Due to the temporal evolution of this context representa-tion, and its associations with the studied items, recent itemsare activated more than remote items when cued with time-of-test context. This relative advantage for recent items givesrise to the recency effect observed both in IFR and CDFRtasks. Although the relative activations of recent as comparedwith remote items depends primarily on the relative timing ofitem presentations (which is constant across IFR and CDFR)the absolute magnitude of the activations is much greater inIFR than in CDFR. It is this difference in absolute activationsthat enables TCM-A to account for the dissociations betweenimmediate and long-term recency.

The associative framework of TCM-A

Following study or recall of an item, the retrieval of pre-experimentally learned and newly-learned associations com-bine to update the current state of context, and during recallthe current state of context acts as the sole cue for retrieval ofits associated associated item representations. As items arepresented for study, TCM-A stores new experimental associ-ations between items and context, but pre-experimental as-sociations are not updated. Although these encoding and re-trieval processes have separate components, it is overly sim-plistic to think of any piece in isolation as a store that holdsmemory traces.

Consider what would happen if we were to follow the pro-cess of learning far beyond the time scale of a single list?In this case, learning of item-to-context and context-to-itemassociations would build up over time to describe the set ofcontexts in which an item has been presented. However, atsome point, it would seem necessary for the labile “experi-mental” component of these associative matrices to becomethe fixed “pre-experimental” component of the associativematrices. This would allow the model to account for the find-ing that in amnesics some “long-term memories” are intact,

although the formation of new “long-term memories” is im-paired.

In this sense, the associative framework of TCM-A mayfit well with the theory of complementary learning systems,which posits that there are fast and slow learning mechanismsin the brain, working in concert to learn and store informa-tion (McClelland, McNaughton, & O’Reilly, 1995). The fastsystem, which is comprised of the hippocampus and othermedial temporal lobe structures, is able to learn associationsquickly, but is unable to store these representations for longperiods of time. Over time, learned associations are trans-ferred to the cortical system, which learns slowly, but holdslasting representations of our experience. This type of model(see also Alvarez & Squire, 1994) has often been proposed toaccount for the standard model of consolidation in amnesia(Eichenbaum, Otto, & Cohen, 1994; Squire, 1992, but seeNadel & Moscovitch, 1997, 2001).

Short-term memory and temporal context

The equation describing the change of context frommoment-to-moment in TCM-A (Eq. 1) is reminiscent of thecorrelated contextual fluctuations of variable context models(Anderson & Bower, 1972; Mensink & Raaijmakers, 1988;Murdock, 1997). These correlated vector states can be seenas an activation-based memory in the sense Davelaar et al.(2005) used the term. Indeed, Howard et al. (2005) noted thata very close analogue of Eq. 1, with persistent neural activ-ity representing the current state of context, could be imple-mented in a neurally realistic simulation that relied on knownproperties of cells in the entorhinal cortex (Egorov, Hamam,Fransen, Hasselmo, & Alonso, 2002; Fransen, Tahvildari,Egorov, Hasselmo, & Alonso, 2006) and cortical networks(Chance et al., 2002; Chance & Abbott, 2000). In TCM-A,the “fluctuations” are not random, but are caused by the itempresented at each time step. As a consequence, one mightview the state of context after the presentation of item i, ti,as conceptually analogous to the contents of a short-termbuffer. To see why this is so, consider what would happenif contextual retrieval were turned off (mathematically, sup-pose γFT = 0). Under these circumstances, each time anitem is presented it causes a particular pattern to be input tothe temporal context vector. Insofar as there is a one-to-onecorrespondence between this input pattern and the item beingpresented, we can think of these patterns as a representationof the item itself. In this case, the temporal context vectorcontains the patterns of recently presented items—much likestandard ideas about STS.

There are two salient differences between ti and tradi-tional buffer models. One difference is that in TCM-A, theinput patterns do not drop out in an all-or-none fashion, butdecay gradually as more information comes in. This prop-erty makes it considerably easier for TCM-A to describe re-cency and contiguity effects over different time scales (seealso Howard & Kahana, 2002). The other salient differenceis that in TCM-A, the patterns caused by an item do not, ingeneral, stay constant over multiple repetitions of the item,but rather change to reflect the changing contexts in which

20 SEDERBERG, HOWARD, & KAHANA

the item has been presented. It is this latter property that en-ables TCM-A to describe contiguity effects (see also Howardet al., 2006), including those in short-term recency (Howard,Venkatadass, Norman, & Kahana, in press).

The functionality of the TCM framework

In this paper, we have shown how appending an elaboratedretrieval rule to the TCM cuing framework enabled TCM-Ato describe dissociations between short- and long-term re-cency. It is important to note, however, that the modelingdescribed in the paper did not have to significantly alter thefundamental mechanisms of TCM. Indeed, recent behavioraland neurophysiological evidence has supported the centralmechanisms of TCM.

Howard, Venkatadass, et al. (in press) compared behav-ioral predictions of TCM with those of buffer models in de-scribing associative effects in the early stages of the immedi-ate recency effect. In this study, some lists contained an itemfrom the middle of the list that was repeated just before thetest. Howard, Venkatadass, et al. (in press) observed a boostfor neighbors of the original presentation of the repeated itemin early recall transitions, and even the initiation of immedi-ate recall. While TCM predicts these associative effects as anatural outcome of using temporal context as the cue to ini-tiate immediate recall, buffer models of immediate recencywould predict no such effect. One would not expect the pre-dictions of TCM about immediate recency to be borne outover those of a buffer model if gradually-changing temporalcontext was not the cue for the initiation of IFR.

Whereas Howard, Venkatadass, et al. (in press) confirmedpredictions of TCM over a few seconds, Howard, Youker,and Venkatadass (in press) evaluated predictions over a muchlonger time scale. Participants were presented with forty-eight lists one at a time for immediate free recall. At theend of the session, they were given a surprise final free re-call test in which they were instructed to recall as manyitems as possible from all the lists in any order they cameto mind. In examining the final free recall data, Howard,Youker, and Venkatadass (in press) observed a recency ef-fect that extended six to eight lists into the past. More-over, Howard, Youker, and Venkatadass (in press) observeda contiguity effect across lists in the final free recall data thatextended about ten lists in either direction. A particularlystriking feature of these data was the similar functional formobserved for the recency and contiguity effects across timescales, suggesting that a similar cuing mechanism operatesover short and long time scales, as predicted by TCM.

TCM naturally explains the findings of Howard, Youker,and Venkatadass (in press) if the temporal context vector isallowed to change gradually across lists in addition to chang-ing gradually within each list. If the temporal context vectoris an activation-based memory in the medial temporal lobe,as hypothesized by Howard et al. (2005), this means thatthere should be neural activity in the medial temporal lobethat persists across the lists. Manns, Howard, and Eichen-baum (submitted) examined the ensemble firing patterns ofcells in the hippocampus while rats performed a judgment of

recency task on lists of odors. In their experiment, rats weregiven “lists” of five odors. At the end of each list, the animalswere presented with two odors from the list and rewardedfor approaching the one that was presented earlier in the list.The rats were implanted with electrodes in the hippocampusthat were able to record from multiple, as many as severaldozen, hippocampal neurons at one time. Manns et al. (sub-mitted) treated these ensembles as vectors of neural activityand examined the way the ensemble firing pattern changedacross time periods when the animal was “studying” the listodors. Manns et al. (submitted) showed that the neural ac-tivity vector was more similar for study events that occurredcloser together in time than for events that occurred furtherapart in time (see Eq. 1). That is, all other things beingequal, the ensemble patterns for study events correspondingto nearby serial positions within a particular list were moresimilar to each other than ensemble patterns correspondingto study events from serial positions further apart in the list.Remarkably, (Manns et al., submitted) also observed a con-tiguity across lists as well, with robust changes in the neuralactivity vector extending over essentially the entire record-ing session. The change in the neural activity vector acrosslists in the rat hippocampus parallels the predicted change inthe temporal context vector across lists of words in behav-ioral studies with humans (Howard, Youker, & Venkatadass,in press).

In summary, these recent findings have confirmed both be-havioral and neurophysiological predictions of TCM at bothshort and longer time scales. This suggests that the TCMframework captures some basic insights about how episodicmemory is encoded and retrieved. Future behavioral, theoret-ical and neurophysiological work will be necessary to fleshout a more detailed picture of how episodic memory is im-plemented, but the present study indicates that the findingsof recency dissociations in free recall do not rule out TCM asa description of either short- or long-term recency.

Conclusions

Davelaar et al. (2005) identified a number of empiricaldissociations between short- and long-term recency. They ar-gued that these findings required that distinct memory storessupport the recency effect observed using different distrac-tor schedules. We evaluated an extension of the temporalcontext model, TCM-A, with an elaborated retrieval rule us-ing competitive, leaky accumulators Usher and McClelland(2001). TCM-A was able to account for these dissociationseven though the current state of temporal context was the solecue for recall at all times. The key feature of the retrieval ruleis that it be able to respond to changes in the absolute levelof activation in addition to relative changes in activation inselecting an item to be recalled.

References

Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synap-tic depression and cortical gain control. Science, 275(5297),220–224.

RECENCY AND TCM 21

Alvarez, P., & Squire, L. R. (1994). Memory consolidation and themedial temporal lobe: a simple network model. Proceedings ofthe National Academy of Sciences U S A, 91(15), 7041–7045.

Anderson, J. R., & Bower, G. H. (1972). Recognition and retrievalprocesses in free recall. Psychological Review, 79(2), 97-123.

Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: Aproposed system and its control processes. In K. W. Spence &J. T. Spence (Eds.), The psychology of learning and motivation(Vol. 2, p. 89-105). New York: Academic Press.

Bjork, R. A., & Whitten, W. B. (1974). Recency-sensitive retrievalprocesses in long-term free recall. Cognitive Psychology, 6, 173-189.

Bogacz, R. (2007). Optimal decision-making theories: linking neu-robiology with behaviour. Trends in Cognitive Sciences, 11(3),118–125.

Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D.(2006). The physics of optimal decision making: a formal anal-ysis of models of performance in two-alternative forced-choicetasks. Psychological Review, 113(4), 700–765.

Bogacz, R., Usher, M., Zhang, J., & McClelland, J. L. (2007,Apr). Extending a biologically inspired model of choice:multi-alternatives, nonlinearity and value-based multidimen-sional choice. Philosophical Transactions of the Royal Societyof London B Biological Sciences.

Bower, G. H. (1972). Stimulus-sampling theory of encoding vari-ability. In A. W. Melton & E. Martin (Eds.), Coding processesin human memory (p. 85-121). New York: John Wiley and Sons.

Brodie, D. A., & Murdock, B. B. (1977). Effects of presentationtime on nominal and functional serial position curves in free re-call. Journal of Verbal Learning and Verbal Behavior, 16, 185-200.

Brown, G. D. A., Neath, I., & Chater, N. (2007). A temporal ratiomodel of memory. Psychological Review, 114(3), 539–576.

Brown, G. D. A., Preece, T., & Hulme, C. (2000). Oscillator-basedmemory for serial order. Psychological Review, 107(1), 127–181.

Burgess, N., & Hitch, G. J. (1999). Memory for serial order: Anetwork model of the phonological loop and its timing. Psycho-logical Review, 106(3), 551–581.

Carlesimo, G. A., Marfia, G. A., Loasses, A., & Caltagirone, C.(1996). Recency effect in anterograde amnesia: Evidence fordistinct memory stores underlying enhanced retrieval of termi-nal items in immediate and delayed recall paradigms. Neuropsy-chologia, 34, 177-184.

Ceraso, J., & Henderson, A. (1966). Unavailability and associativeloss in RI and PI: second try. Journal of Experimental Psychol-ogy, 72(2), 314-316.

Chance, F. S., & Abbott, L. F. (2000). Divisive inhibition in recur-rent networks. Network, 11(2), 119–129.

Chance, F. S., Abbott, L. F., & Reyes, A. D. (2002). Gain modula-tion from background synaptic input. Neuron, 35(4), 773–782.

Craik, F. I. M. (1970). The fate of primary memory items in freerecall. Journal of Verbal Learning and Verbal Behavior, 9, 658-664.

Crowder, R. G. (1982). The demise of short-term memory. ActaPsychologica, 50, 291-323.

Dalezman, J. (1976). Effects of output order on immediate, de-layed, and final recall performance. Journal of ExperimentalPsychology: Human Learning and Memory, 2(5), 597–608.

Davelaar, E. J., Goshen-Gottstein, Y., Ashkenazi, A., Haarmann,H. J., & Usher, M. (2005). The demise of short-term memoryrevisited: Empirical and computational investigations of recencyeffects. Psychological Review, 112, 3–42.

Deese, J., & Kaufman, R. A. (1957). Serial effects in recall of unor-ganized and sequentially organized verbal material. Journal ofExperimental Psychology, 54, 180-187.

Egorov, A., Hamam, B., Fransen, E., Hasselmo, M., & Alonso, A.(2002). Graded persistent activity in entorhinal cortex neurons.Nature, 420(6912), 173–8.

Eichenbaum, H., Otto, T., & Cohen, N. J. (1994). Two functionalcomponents of the hippocampal memory system. Behavioraland Brain Sciences, 17, 449-518.

Estes, W. K. (1955). Statistical theory of distributional phenomenain learning. Psychological Review, 62, 369-377.

Fransen, E., Tahvildari, B., Egorov, A. V., Hasselmo, M. E., &Alonso, A. A. (2006). Mechanism of graded persistent cellu-lar activity of entorhinal cortex layer V neurons. Neuron, 49(5),735–746.

Glanzer, M., & Cunitz, A. R. (1966). Two storage mechanisms infree recall. Journal of Verbal Learning and Verbal Behavior, 5,351-360.

Glenberg, A. M., Bradley, M. M., Kraus, T. A., & Renzaglia, G. J.(1983). Studies of the long-term recency effect: Support for acontextually guided retrieval theory. Journal of ExperimentalPsychology: Learning, Memory & Cognition, 12, 413-418.

Glenberg, A. M., Bradley, M. M., Stevenson, J. A., Kraus, T. A.,Tkachuk, M. J., & Gretz, A. L. (1980). A two-process account oflong-term serial position effects. Journal of Experimental Psy-chology: Human Learning and Memory, 6, 355-369.

Glenberg, A. M., & Swanson, N. G. (1986). A temporal distinctive-ness theory of recency and modality effects. Journal of Experi-mental Psychology: Learning, Memory & Cognition, 12, 3-15.

Greene, R. L. (1986). Sources of recency effects in free recall.Psychological Bulletin, 99, 221-228.

Healy, A. F., & Parker, J. T. (2001). Serial position effects in se-mantic memory: Reconstructing the order of U. S. presidentsand vice presidents. In H. L. Roediger & J. S. Nairne (Eds.), Thenature of remembering: Essays in honor of Robert G. Crowder(p. 171-188). Washington, DC: American Psychological Asso-ciation.

Hogan, R. M. (1975). Interitem encoding and directed search infree recall. Memory & Cognition, 3, 197-209.

Howard, M. W. (2004). Scaling behavior in the temporal contextmodel. Journal of Mathematical Psychology, 48, 230–238.

Howard, M. W., Fotedar, M. S., Datey, A. V., & Hasselmo, M. E.(2005). The temporal context model in spatial navigation andrelational learning: Toward a common explanation of medialtemporal lobe function across domains. Psychological Review,112(1), 75–116.

Howard, M. W., & Kahana, M. J. (1999). Contextual variabilityand serial position effects in free recall. Journal of ExperimentalPsychology: Learning, Memory, and Cognition, 25, 923–941.

Howard, M. W., & Kahana, M. J. (2002). A distributed representa-tion of temporal context. Journal of Mathematical Psychology,46, 269-299.

Howard, M. W., Kahana, M. J., & Wingfield, A. (2006). Agingand contextual binding: Modeling recency and lag-recency ef-fects with the temporal context model. Psychonomic Bulletin &Review, 13(3), 439–445.

Howard, M. W., Venkatadass, V., Norman, K. A., & Kahana, M. J.(in press). Associative processes in immediate recency. Memory& Cognition.

Howard, M. W., Youker, T. E., & Venkatadass, V. (in press). Thepersistence of memory: Contiguity effects across several min-utes. Psychonomic Bulletin & Review.

22 SEDERBERG, HOWARD, & KAHANA

Kahana, M. J. (1996). Associative retrieval processes in free recall.Memory & Cognition, 24, 103–109.

Kahana, M. J., Howard, M. W., & Polyn, S. M. (in press). As-sociative processes in episodic memory. In H. L. Roediger III(Ed.), Cognitive psychology of memory. Vol. 2 of Learning andmemory: A comprehensive reference, 4 vols. (J. Byrne, Editor).Oxford: Elsevier.

Kahana, M. J., Howard, M. W., Zaromb, F., & Wingfield, A. (2002).Age dissociates recency and lag recency effects in free recall.Journal of Experimental Psychology: Learning, Memory, andCognition, 28, 530–540.

Kimball, D. R., Smith, T. A., & Kahana, M. J. (in press). The fSAMmodel of false recall. Psychological Review.

Koppenaal, L., & Glanzer, M. (1990). An examination of the con-tinuous distractor task and the long-term recency effect. Memory& Cognition, 18, 183-195.

Laming, D. (1999). Testing the idea of distinct storage mechanismsin memory. International Journal of Psychology, 34, 419-426.

Manns, J. R., Howard, M. W., & Eichenbaum, H. (submitted). Thehippocampus and episodic memory: Neural representations oftemporal context support remembering the order of events inunique experiences.

Marks, A. R., & Cermak, L. S. (1998). Intact temporal memory inamnesic patients. Neuropsychologia, 36(9), 935–943.

Marmurek, H. H. (1983). Negative recency in final free recall:Encoding or retrieval. American Journal of Psychology, 96(1),17–35.

McClelland, J. L., McNaughton, B. L., & O’Reilly, R. C. (1995).Why there are complementary learning systems in the hip-pocampus and neocortex: insights from the successes and fail-ures of connectionist models of learning and memory. Psycho-logical Review, 102(3), 419–57.

McMillen, T., & Holmes, P. (In press). The dynamics of choiceamong multiple alternatives. Journal of Mathematical Psychol-ogy.

Mensink, G.-J. M., & Raaijmakers, J. G. W. (1988). A model forinterference and forgetting. Psychological Review, 95, 434-455.

Mensink, G.-J. M., & Raaijmakers, J. G. W. (1989). A model forcontextual fluctuation. Journal of Mathematical Psychology, 33,172-186.

Monsell, S. (1978). Recency, immediate recognition memory, andreaction time. Cognitive Psychology, 10, 465-501.

Murdock, B. B. (1960). The distinctiveness of stimuli. Psycholog-ical Review, 67, 16-31.

Murdock, B. B. (1962). The serial position effect of free recall.Journal of Experimental Psychology, 64, 482-488.

Murdock, B. B. (1997). Context and mediators in a theory ofdistributed associative memory (TODAM2). Psychological Re-view, 104, 839-862.

Murdock, B. B., & Metcalfe, J. (1978). Controlled rehearsal insingle- trial free recall. Journal of Verbal Learning and VerbalBehavior, 17, 309-324.

Murdock, B. B., & Okada, R. (1970). Interresponse times in single-trial free recall. Journal of Verbal Learning and Verbal Behav-ior, 86, 263-267.

Nadel, L., & Moscovitch, M. (1997). Memory consolidation, retro-grade amnesia and the hippocampal complex. Current Opinionin Neurobiology, 7(2), 217–227.

Nadel, L., & Moscovitch, M. (2001). The hippocampal complexand long-term memory revisited. Trends in Cognitive Sciences,5(6), 228–230.

Nairne, J. S., Neath, I., Serra, M., & Byun, E. (1997). Positional

distinctiveness and the ratio rule in free recall. Journal of Mem-ory and Language, 37, 155-166.

Neath, I. (1993). Contextual and distinctive processes and the serialposition function. Journal of Memory and Language, 32, 820-840.

Neath, I., & Crowder, R. G. (1990). Schedules of presentationand temporal distinctiveness in human memory. Journal of Ex-perimental Psychology: Learning, Memory and Cognition, 16,316-327.

Neath, I., & Crowder, R. G. (1996). Distinctiveness and very short-term serial position effects. Memory, 4, 225-242.

Nilsson, L. G., Wright, E., & Murdock, B. B. (1975). The effects ofvisual presentation method on single-trial free recall. Memory&Cognition, 3, 427-433.

Poltrock, S. E., & MacLeod, C. M. (1977). Primacy and recencyin the continuous distractor paradigm. Journal of ExperimentalPsychology: Human Learning and Memory, 3, 560-571.

Postman, L., & Phillips, L. W. (1965). Short-term temporal changesin free recall. Quarterly Journal of Experimental Psychology,17, 132-138.

Raaijmakers, J. G. W. (1993). The story of the two-store model ofmemory: Past criticisms, current status, and future directions. InD. Meyer & S. Kornblum (Eds.), Attention and performance xiv(p. 467-488). Cambridge, MA: MIT Press.

Raaijmakers, J. G. W., & Shiffrin, R. M. (1980). SAM: A theoryof probabilistic search of associative memory. In G. H. Bower(Ed.), The psychology of learning and motivation: Advances inresearch and theory (Vol. 14, p. 207-262). New York: AcademicPress.

Raaijmakers, J. G. W., & Shiffrin, R. M. (1981). Search of associa-tive memory. Psychological Review, 88, 93-134.

Rundus, D. (1971). An analysis of rehearsal processes in free recall.Journal of Experimental Psychology, 89, 63-77.

Sederberg, P. B., Gauthier, L. V., Terushkin, V., Miller, J. F., Bar-nathan, J. A., & Kahana, M. J. (2006). Oscillatory correlatesof the primacy effect in episodic memory. NeuroImage, 32(3),1422–1431.

Sirotin, Y. B., Kimball, D. R., & Kahana, M. J. (2005). Goingbeyond a single list: Modeling the effects of prior experienceon episodic free recall. Psychonomic Bulletin & Review, 12(5),787-805.

Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiologyof simple decisions. Trends in Neurosciences, 27(3), 161–168.

Squire, L. R. (1992). Memory and the hippocampus: A synthesisfrom findings with rats, monkeys, and humans. PsychologicalReview, 99, 195-231.

Tan, L., & Ward, G. (2000). A recency-based account of the pri-macy effect in free recall. Journal of Experimental Psychology:Learning, Memory, and Cognition, 26, 1589-1626.

Thapar, A., & Greene, R. L. (1993). Evidence against a short-term-store account of long-term recency effects. Memory & Cogni-tion, 21, 329-337.

Tzeng, O. J. L. (1973). Positive recency in delayed free recall.Journal of Verbal Learning and Verbal Behavior, 12, 436-439.

Usher, M., & McClelland, J. L. (2001). The time course of percep-tual choice: The leaky, competing accumulator model. Psycho-logical Review, 108(3), 550-592.

Ward, G., Woodward, G., Stevens, A., & Stinson, C. (2003). Usingovert rehearsals to explain word frequency effects in free recall.Journal of Experimental Psychology: Learning, Memory, andCognition, 29, 186-210.

Watkins, M. J., Neath, I., & Sechler, E. S. (1989). Recency ef-fect in recall of a word list when an immediate memory task is

RECENCY AND TCM 23

performed after each word presentation. American Journal ofPsychology, 102, 265-270.

Watkins, M. J., & Watkins, O. C. (1974). Processing of recencyitems for free recall. Jornal of Experimental Psychology, 102(3),488–493.

Whitten, W. (1978). Output interference and long-term serial po-sition effects. Journal of Experimental Psychology: HumanLearning and Memory, 4, 685–692.

Yntema, D. B., & Trask, F. P. (1963). Recall as a search process.Journal of Verbal Learning and Verbal Behavior, 2, 65-74.

Zaromb, F. M., Howard, M. W., Dolan, E. D., Sirotin, Y. B., Tully,M., Wingfield, A., et al. (2006). Temporal associations andprior-list intrusions in free recall. Journal of Experimental Psy-chology: Learning, Memory, and Cognition, 32(4), 792–804.