An Integrated Model of Cognitive Control in Task Switching Erik M. Altmann Michigan State University Wayne D. Gray Rensselaer Polytechnic Institute A model of cognitive control in task switching is developed in which controlled performance depends on the system maintaining access to a code in episodic memory representing the most recently cued task. The main constraint on access to the current task code is proactive interference from old task codes. This interference and the mechanisms that contend with it reproduce a wide range of behavioral phenomena when simulated, including well-known task-switching effects, such as latency and error switch costs, and effects on which other theories are silent, such as with-run slowing and within-run error increase. The model generalizes across multiple task-switching procedures, suggesting that episodic task codes play an important role in keeping the cognitive system focused under a variety of performance constraints. Keywords: cognitive control, task switching, cognitive simulation, episodic memory, executive function Questions about how people set, focus on, and switch among the short-term goals that govern everyday behavior are key issues in the domain of cognitive control.1 A number of experimental paradigms touch on this kind of control���including, at different levels, puzzle solving and the psychological refractory period���but the one most closely associated with the behavior of interest here is task switching. In a procedure of particular interest here, which we term the randomized-runs procedure, the experimental participant performs a large number of trials in sequence. Each trial involves presentation of a simple stimulus���a randomly selected digit, in the most common materials���to which the participant responds by judging whether the digit is even or odd (one task) or higher or lower than five (the other task), depending on which task is currently correct. Figure 1 shows the timeline of events in this procedure. Every few trials, a task cue is presented briefly and then withdrawn, after which the participant performs that task for the subsequent run of trials, until the next cue is presented. The cues themselves are randomly selected, such that on ���switch��� runs, the task is switched from what it was on the previous run, whereas on ���repeat��� runs, the task is the same as it was on the previous run. With the task changing frequently, accurate performance depends on maintaining some kind of mental represen- tation of the task to perform now. The idea with this procedure is to distill some of the essence of the ���what did I want now that I���m here?��� problem associated with simple errands, for example one sets out to fetch something, having fetched many similar things before, and the old things interfere���or one���s mind simply wanders. How the system responds to this mundane cognitive-control challenge is what we would like to understand in theoretical terms. At this level of everyday situations, it seems useful to distin- guish the one we sketched above from others that may be evoked by the term ���task switching.��� One such situation is task interrup- tion (Van Bergen, 1968 Zeigarnik, 1938). If someone is working on a project���a manuscript, for example���and is interrupted by a phone call, there can be a cost associated with reconstructing the mental context that was active when the interruption occurred (Altmann & Trafton, 2007 Hodgetts & Jones, 2006). Such inter- ruptions make an attractive conceptual frame for task-switching studies (e.g., Monsell, 2003), yet the costs of switching between tasks that involve some reasonable amount of cognitive state, such as working on a manuscript and talking to someone, may be driven by operations on fairly rich knowledge representations (Altmann & Trafton, 2007). In task switching, the representations that sup- port performance are much leaner, and the interruptions are much more frequent, such that behavioral measures may index rather different mechanisms. A second situation evoked by task switch- ing is multitasking, such as when someone drives a car while interacting with a navigation system or a passenger (or a caller on the phone). In an environment like this, in which one or both tasks are continuous, an important constraint is that task switches have to be scheduled such that neither task starves for attention (e.g., Salvucci & Taatgen, 2008). Thus, both task interruption and mul- titasking involve control processes beyond those that keep the system focused on a small but frequently changing unit of control information. Nonetheless, the latter would seem to be a substrate on which more complex expressions of cognitive control are built. Indeed, the computational mechanisms we describe here are adapted from a model of puzzle solving (Altmann & Trafton, 2002) in which cognitive control involves suspending and activat- ing subgoals to control search through a problem space. The 1The authors thank Gordon Logan, Nachshon Meiran, Nick Yeung, and two anonymous reviewers for their detailed and thoughtful comments on this article, and Alan Allport and Rich Carlson for formative comments on an earlier version. Erik M. Altmann, Department of Psychology, Michigan State Univer- sity Wayne D. Gray, Cognitive Science Department, Rensselaer Polytech- nic Institute. This work was supported by Office of Naval Research Grants N00014- 03-1-0063 and N00014-06-1-0077 to Erik M. Altmann and N00014-03-1- 0046 and N00014-07-1-0033 to Wayne D. Gray and by Air Force Office of Scientific Research Grants F49620-03-1-0143 and FA9550-06-1-0074 to Wayne D. Gray. Correspondence concerning this article should be addressed to Erik M. Altmann, Department of Psychology, Michigan State University, East Lansing, MI 48824. E-mail: ema@msu.edu Psychological Review Copyright 2008 by the American Psychological Association 2008, Vol. 115, No. 3, 602���639 0033-295X/08/$12.00 DOI: 10.1037/0033-295X.115.3.602 602

commonality is that accurate performance again depends on the system having access to the correct subgoal at the correct time in a situation in which the subgoal changes frequently. An active task-switching literature has grown up over the past dozen years or so, shaped by three roughly contemporaneous studies that focused on trying to explain the costs of switching between simple tasks. Allport, Styles, and Hsieh (1994) proposed that these switch costs were linked directly to carryover effects from previous performance, a construct they termed ���task-set inertia��� and likened to proactive interference. This proposal first illustrated the approach that we continue here of analyzing control processes in terms of familiar memory constructs (interference, priming, etc. Altmann, 2003). Rogers and Monsell (1995), in contrast, assumed that switch costs reflected processes dedicated specifically to cognitive control���processes that, figuratively, were the ���little signal person in the head��� (p. 217) throwing a switch that would then send the cognitive train of thought down the correct track. This has come to be known as the ���reconfigu- ration��� metaphor and remains under active consideration today (e.g., Steinhauser, Maier, & Hubner, 2007). Finally, Meiran (1996) began to bridge these two approaches, suggesting that both car- ryover effects from the previous trial and reconfiguration pro- cesses were at work. These three original studies (see also Fagot, 1994) triggered a widespread interest in trying to explain switch costs, although success with this has been limited to some extent by construct validity problems (Altmann, 2007a). One of our goals is to illuminate these problems by simulating performance in different procedures with one set of control mechanisms so as to map different switch costs to different origins. A broader goal is to show that switch costs themselves are only part of a larger empir- Figure 1. Timeline of events in the randomized-runs task-switching procedure used in Simulation Study 1, showing three consecutive runs of trials. 603 COGNITIVE CONTROL MODEL

ical landscape that, viewed as a whole, offers reasonably strong constraints on models of cognitive control in task switching. We start with the premise that each time the system is presented with a task cue, it encodes a new representation of this cue in episodic memory. We then ask what kinds of control processes the system might have to deploy to maintain access to the current code created by this process, given proactive interference from old codes created by this process in response to previous cue presen- tations. This analysis yields a blueprint that we develop into a computational model in which proactive interference builds up in the course of simulated performance. This proactive interference and the mechanisms that contend with it reproduce a variety of response-latency and error effects, some well known and widely interpreted and some less so. We constrain our theoretical approach by aiming for four types of integration. First and foremost is functional integration, mean- ing that each central mechanism in our model plays some func- tional role in the model���s performance, with some other mecha- nism(s) depending on or affected by its output. Second and related is empirical integration, meaning that we use the model to argue that empirical effects that on the surface might seem to be com- pletely unrelated are in fact related in terms of underlying mech- anisms. Third is theoretical integration, meaning that we assemble the model largely from existing cognitive constructs rather than developing new ones. Fourth is procedural integration, meaning that we show that one set of mechanisms can account for perfor- mance in multiple task-switching procedures, including the two used in the bulk of studies that make up the task-switching liter- ature. The article is organized as follows. In the first two sections, we describe our cognitive control model (CCM) at its abstract and computational levels. At the abstract level, we build on previous work (Altmann, 2002 Altmann & Gray, 2002) to make a new prediction. At the computational level, we describe a model that reproduces latency and error measures based on performance of full-length simulated experimental sessions. We then present three studies demonstrating the functional sufficiency and explanatory scope of this computational model. In Simulation Study 1, we fit data from a new experiment that integrates a suite of relevant effects in one design, some replicating previous work and some testing new questions. In Simulation Studies 2 and 3, we apply the model to published data from the two most common task- switching procedures���explicit cuing and alternating runs���to show that it generalizes beyond situations in which memory for the most recent task is an explicit performance requirement. In Sim- ulation Study 2, we also develop an account of a widely reported interaction of cue-stimulus interval (CSI) and switching, and in Simulation Study 3, we illustrate a construct-validity problem with switch cost as measured using the alternating-runs procedure. Finally, we survey task-switching phenomena that we do not yet address and examine other models that have been proposed to explain them. An Abstract Model, Basic Phenomena, and a New Prediction Here we develop CCM at an abstract level, as the basis for the computational implementation we describe later. Our basic as- sumption, as we noted earlier, is that to perform in the kind of task environment characterized in Figure 1, the system encodes a representation of every task cue in episodic memory and uses this representation to guide its behavior over subsequent trials, until the next cue is presented. We refer to this representation as a task code. We also assume that each task code lingers after its relevance expires, such that after N runs of trials, there will be N task codes in episodic memory. The significance of this is that on any given trial, when the system tries to retrieve the current task code, old ones could interfere. The core construct governing task-code processing in our model is activation. Every task code���and every other declarative mem- ory element, as we note later���has an activation level, and when the system needs to retrieve a task code, memory returns the one with the highest activation at that instant. Given this constraint, the job of the cognitive system is to ensure that the current task code is more active than any other for the duration of the current run, and to encode a new task code when the next task cue is presented, such that the new one is the most active. The job is complicated by noise in activation levels, which can temporarily make an old task code more active than the current one, or which can temporarily push all task codes below threshold, thereby making the system transiently unable to remember what it is doing. These dynamics are adapted from the ACT���R cognitive theory (Anderson, 2007 Anderson et al., 2004 Anderson & Lebiere, 1998) but bear some similarity to other formal activation constructs (e.g., Hintzman, 1988 Just & Carpenter, 1992). Figure 2 shows a representation of these principles adapted from signal-detection theory. Each curve is a probability density function for the activation of a memory code: The abscissa represents activa- tion level, increasing to the right, and the ordinate represents the probability of the code having a given activation level. The dispersion of the density function represents activation noise. Thus, when the system makes a retrieval request, the activation of a code is most likely to be at its mean level but may also be above or below, with decreasing probability the greater the distance from the mean. The bottom panel of Figure 2 shows density functions for the activation of two memory elements, which we interpret here as task codes in episodic memory (at other times, we interpret them as meaning codes in semantic memory, for which the activation dynamics are very similar). The density on the right is for the current task code, which is the retrieval target when the system needs to recall what task to perform on the current trial. The density on the left is for an old task code, which is a source of proactive interference. (In general, there are many old task codes in episodic memory, but there is no loss of generality in consid- ering this simpler scenario for now.) The activation of the current task code is higher than that of the old task code (separation 0), allowing the system to distinguish them if this separation were zero, this would represent a situation of catastrophic interference in which the current task code would be indistinguishable from its predecessor. At the intersection of the two densities is the retrieval threshold, a high-pass filter that prevents the retrieval of codes whose activation is below threshold when the retrieval is at- tempted. The mean activation of the current task code is above threshold (gain 0), and the mean activation of the old task code is below threshold (gain 0) in general, gain can be high (far from threshold) or low (close to threshold). Gain affects accessi- bility, which is the area of a density function that lies above (to the 604 ALTMANN AND GRAY

right of) threshold accessibility equals the probability that that memory element will be above threshold at a given instant. The top and middle panels of Figure 2 show supporting pro- cesses that allow the system to sustain the functional situation in the bottom panel���the current task code having positive gain and being more accessible than the old code���indefinitely across any number of task cues presented by the environment. The top panel shows encoding in response to the presentation of a task cue. Encoding, here, simply means creating a new task code and then raising its activation from some initial level (at the tail of the arrow) to a level at which the new code is accessible enough to meet performance requirements. The middle panel of Figure 2 shows the current task code decaying, or losing activation. Decay plays a functional role in our model, as an automatic architectural process that works in the background to prevent a catastrophic buildup of proactive inter- ference. To appreciate the functional role of decay, consider what would happen if it were absent. The system could perhaps respond by encoding each new task code with a higher activation level than the previous one (to make the separation quantity in Figure 2 positive) however, assuming some biological or other upper bound on activation levels, this would make shifts of cognitive control increasingly difficult and ultimately impossible. With de- cay, in contrast, flexible cognitive control is sustainable as long as each new task cue presented by the environment is encoded to an initial activation level that makes it more accessible than any old (decayed) task code in memory. Relative to inhibitory processing (e.g., Engle, Conway, Tuholski, & Shisler, 1995 Hasher & Zacks, 1988), decay can be viewed as similar in effect but more gradual and, critically, obligatory rather than controlled. An obligatory forgetting process would seem to be a useful and even necessary component of a cognitive system that must be able to update its declarative control representations frequently and con- tinually over extended periods of performance. Moreover, in forcing the system to encode new control information periodically, decay would seem to help address what Newell (1990) construed as the ���sudden death��� problem of rogue control information hijacking be- havior. For example, if the system happened to be struck by the impulse to jump in front of a bus, it would benefit if an automatic process forced it to reconsider, particularly if inhibition failed to deploy or was difficult to sustain for some reason. Thus, for a noisy system in a dynamic environment, a process that automatically trig- gers refresh of control representations seems to complement effortful inhibitory processing in important functional ways. Figure 2. Abstract representation of the cognitive control model, showing probability density functions for activation of memory elements. Top and middle: A task code is encoded in episodic memory, then decays during use. Bottom: The next task code is encoded and can govern performance because it is more active than the old one (separation 0) and is above threshold (gain 0). The bottom panel also applies to semantic memory for example, the meaning of a presented task cue is perceptually primed and therefore more accessible (right-hand density) than the meaning of the not-presented cue (left-hand density). 605 COGNITIVE CONTROL MODEL

Basic Phenomena Here we link six basic behavioral effects to the abstract model described above. To illustrate each, we refer forward to Figures 7���11, which show the data from the experiment presented in Simulation Study 1. The phenomena are summarized in Table 1, which also serves as an index to the relevant figures and analysis tables. The six basic effects fall into two classes. In the first class are effects related to the encoding process in the top panel of Figure 2. There are two such first-trial effects, each measured on the trial in serial Position 1 of a run of trials, which immediately follows presentation of the task cue for that run, making it a locus of residual effects of the encoding process. The preparation effect (see Figure 7) is the change in Position 1 response latency as a function of the CSI between onset of the task cue and onset of the Position 1 stimulus generally, the longer the CSI, the faster the Position 1 response latency, as cue-related processes have more time to complete their work before stimulus onset. Latency switch cost is the small (45 ms see Figure 7) difference in Position 1 response latencies as a function of whether the just-presented task cue was a switch cue, signifying a different task than was per- formed on the previous run, or a repeat cue, signifying the same task as was performed on the previous run. We refer to this as ���latency switch cost��� to emphasize that latency and error switch costs in CCM arise from different underlying mechanisms. The second class consists of four within-run effects related to the decay process in the middle panel of Figure 2. Within-run slowing (see Figure 8) is a gradual increase in latencies across trials starting with Position 2, an effect we attribute to decay of the current task code. Within-run error increase (see Figure 9) is a corresponding trend in error rates, which is often noisier but is crucial to the interpretation of within-run slowing because it rules out a speed���accuracy tradeoff account of the two effects together. A runlength effect that we have partially documented before (Altmann & Gray, 2002) is the finding that the slopes of within-run slowing and error increase vary inversely with the average number of trials between task cues���that is, the shorter the average run- length in a condition, the steeper the slope (see Figures 8 and 9). We describe this effect and develop a new runlength prediction in the next subsection. Finally, full-run error-switch cost, as distinct from the latency switch cost we noted above, is evident on all trials of a run, rather than just Position 1, and manifests in terms of errors (see Figure 10) but not response latencies (see Figure 11). In our model, this effect is caused primarily by memory errors in which old task codes intrude on the current task code, which are more likely to cause performance errors on switch runs than on repeat runs. We touch on these effects again in describing the computational implementation of CCM and describe them in more detail in Simulation Study 1, which is the context for the figures to which we have been referring. Table 1 also identifies two ���other effects��� that CCM reproduces and that we describe later but that do not directly flow from the abstract model. Extending CCM: A Second Runlength Effect A prediction of the model in Figure 2 concerns the effect of varying the activation of the most active old code, which general- izes the left-hand density function in Figure 2 (bottom panel). Earlier we took this density to represent one old task code, but in the general case, it represents the activation of the most active of all old codes. If the system tries to retrieve the current task code and retrieves an incorrect task code instead, the intruder will have been the most active old code. The activation of the most active old code is the interference level (Altmann & Trafton, 2002). Table 1 Summary of Behavioral Effects Reproduced by the Computational Implementation of the Cognitive Control Model Effects Descriptions Relevant figures Relevant tables and contrasts First-trial effects Preparation effect Position 1 latency faster with longer cue-stimulus interval 7 B1: Cue-stimulus interval Latency switch cost Position 1 latency faster on repeat runs than switch runs 7 B1: Switching Within-run effects Within-run slowing Latencies increase gradually across positions within a run, starting with Position 2 8 B2: Position, main effects and linear trends Within-run error increase Errors increase gradually across positions within a run, starting with Position 1 9 B3: Position, main effects and linear trends Runlength effects Effect of average runlength on slopes of within- run slowing and error increase main effect of average runlength on errors 8 9 B2: R P B3: R P, Runlength Full-run error switch cost Main effect of switching on errors, driven by incongruent trials, on all positions in a run 10 B3: Switching, S G Other effects Congruency Fewer errors and faster latencies when the stimulus has the same response under both tasks 10 13 13 B3: Congruency B1: Congruency B2: Congruency Failure-to-engage effects Position 1 latency distributions shift and change shape with cue-stimulus interval 19 Note. R runlength P position S switching G congruency. 606 ALTMANN AND GRAY