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Acta Psychologica 141 (2012) 133–139

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Increasing set size breaks down sequential congruency: Evidence for an associative locus of cognitive control☆ Chris Blais a, 1, Tom Verguts b,⁎, 1 a b

University of California, Davis, United States Ghent University, Belgium

a r t i c l e

i n f o

Article history: Received 27 October 2011 Received in revised form 6 June 2012 Accepted 7 July 2012 Available online xxxx PsycINFO codes: 2300 2340 4160

a b s t r a c t In recent years, a number of studies have revealed that cognitive control is strongly context-dependent (e.g., Crump et al., 2006). Inspired by this, computational models have been formulated based on the idea that cognitive control processes are based on associative learning (Blais et al., 2007; Verguts & Notebaert, 2008). Here, we test a natural consequence of this idea, namely, that sequential congruency effects (Gratton et al., 1992) should gradually decrease with an increasing number of task-relevant features (e.g., stimuli). The effect is empirically observed and simulated in a computational model. Implications of our findings are discussed. © 2012 Elsevier B.V. All rights reserved.

Keywords: Cognitive control Associative learning Computational modeling

1. Introduction In order to be useful, cognitive control must act fast. Consider the situation in which roadwork forces you to avoid construction workers on your habitual route to work. If your control system worked only at slow time scales, you would not be able to avoid them, leading to great danger for all persons involved. Consistent with this example, recent studies have emphasized that control is flexible and fast. A key phenomenon motivating this dynamic view of control is the sequential congruency effect (SCE; Gratton, Coles, & Donchin, 1992). Consider for example the Stroop task, where the task is to name the ink color of words. Stimuli can be either congruent (e.g., RED written in red) or incongruent (e.g., RED written in blue). The congruency effect is the difference in performance (e.g., reaction time) to incongruent versus congruent stimuli (see MacLeod, 1991 for a review). The SCE refers to the observation that the congruency effect is reduced following an incongruent trial compared to a congruent trial. This effect demonstrates that control does not operate (only) at ☆ CB was supported by a postdoctoral fellowship from the Natural Sciences and Engineering Research Council of Canada (NSERC). TV was supported by Ghent University BOF/GOA, BOF08/GOA/011. ⁎ Corresponding author at: Department of Psychology, H. Dunantlaan 2, 9000 Ghent, Belgium. Tel.: +32 9 264 64 08; fax: +32 9 264 64 96. E-mail addresses: [email protected] (C. Blais), [email protected] (T. Verguts). 1 Both authors contributed equally to this paper. 0001-6918/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.actpsy.2012.07.009

slow time scales, but on a trial-by-trial basis. In the present paper, we investigate the nature of cognitive control as pertains to the SCE in an experiment and a computational modeling study. A central construct to explain how a cognitive system can deploy fast control is response conflict. Botvinick, Braver, Barch, Carter, and Cohen (2001) introduced this concept to their conflict monitoring model to account for the SCE (in addition to explaining traditionally “slower” cognitive control manifestations such as listwise proportion congruency effects; Tzelgov, Henik, & Berger, 1992). Response conflict occurs when two or more competing responses are simultaneously active (see Appendix and Botvinick et al. for formal definition). They assumed that when response conflict is detected on a given trial, the current task (e.g., color naming) is given extra attention. Formally, this was implemented by increasing activation of a task demand unit (Cohen, Dunbar, & McClelland, 1990) that codes for the current task (e.g., “name ink color”) and that biases processing of the input dimension (e.g., color). Because there is more response conflict on an incongruent trial than on a congruent trial, there is also more attention to the relevant input dimension (e.g., color) after an incongruent trial, leading to the SCE. Despite its success, the conflict monitoring model has difficulty dealing with a number of recent findings (Blais, Robidoux, Risko, & Besner, 2007). Consider again the Stroop task. Suppose that colors red and green are presented mostly congruently and colors blue and yellow mostly incongruently. Jacoby, Lindsay, and Hessels (2003) showed that the congruency effect is then larger for red and green.

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This is called the item-specific proportion congruency effect. Similarly, if one location (e.g., upper) is associated with a higher congruency proportion than a second location (e.g., lower), the congruency effect will be larger for the first location than for the second one (Crump, Gong, & Milliken, 2006). This is called the location-specific proportion congruency effect (LSPC). In a similar way, it has been shown that text font (Bugg, Jacoby, & Toth, 2008) or color (Vietze & Wendt, 2009) can serve as a cue for cognitive control. Together, these findings indicate that cognitive control operates in a context-dependent manner. To remedy the problem that the conflict monitoring model cannot deal with the associative effects just mentioned, Blais et al. (2007) formulated an associative version of it. They retained the idea that response conflict determines when control is exerted, but assumed that control operates more locally by strengthening relevant connections. For example, suppose again that the colors red and green are presented congruently on most trials and colors blue and yellow presented incongruently on most trials. The association from the current task representation (i.e., task demand unit “name ink color”) to the “blue ink color” representation is then increased more often than the association of the current task representation to the “red ink color” representation, because the former is more often coupled with conflict. As a result, the congruency effect for blue stimuli will be smaller than the congruency effect for red stimuli. In a similar way, the model can account for other context-specific control effects. Verguts and Notebaert (2008, 2009) noted that the conflict monitoring model and the Blais et al. (2007) version of it clearly specify when extra control should be exerted, but not where. In particular, response conflict warns the cognitive system that it should be attentive, thus specifying when it should be activated. The conflict monitoring model further postulates that this is done by increasing activation of the currently relevant task representation (task demand unit). However, how the control system knows which task is currently relevant (i.e., where to intervene) is left unspecified. Similarly, Blais et al. assumed that cognitive control operates by increasing the weights attached to the currently relevant stimulus (e.g., color) representations. This again begs the question how the system knows which stimulus representations are relevant at the current trial. As a solution to this conceptual “homunculus” problem, Verguts and Notebaert argued that adaptive responding in this situation could be implemented as associative (Hebbian) learning boosted by response conflict. During high conflict situations (e.g., an incongruent trial), continuously ongoing associative learning is increased and thus active units are bound together even more strongly than when there is less conflict. Because active units tend to be task-relevant, task-relevant representations are typically strengthened, leading to enhanced cognitive control. This solves the homunculus problem, because the system does not need to be told which connections to increase: It simply increases the connections attached to active representations.

Verguts and Notebaert (2008) also provided an alternative interpretation of the SCE than in the original conflict monitoring hypothesis. In this model, if a stimulus is incongruent, the features of this stimulus (e.g., color, location, etc.) become coupled to the current task representation. However, since all features are always at least slightly activated, even the connections for features that are not present on the current trial are able to be modified, albeit slightly, by the Hebbian learning rule. As a consequence, if some of these features (e.g., the complete stimulus) repeat on the next trial, their connections to the current task representation will be slightly increased leading to a smaller congruency effect on the next trial. Overall then, there is a strong SCE for stimuli (or some of its features) that are repeated, and a weaker SCE for a different stimulus presented on the next trial. This is consistent with empirical findings that show a reduction in the size of the SCE as the various complete and partial feature repetition trials are excluded from the analysis (Notebaert & Verguts, 2006; Ullsperger, Bylsma, & Botvinick, 2005). Despite these differences, the models of Blais et al. (2007) and Verguts and Notebaert (2008) share the view that cognitive control operates by modifying (usually task-relevant) associations. In general, our framework posits that any feature in the environment can become strongly associated to the current task representation if that feature is correlated with conflict. Thus, when this feature repeats on a later trial (e.g., the next trial), there will be increased top-down activation from the current task representation resulting in increased cognitive control on such trials. In the current paper, we test an implication of this “adaptation by binding” idea. For this purpose, we apply the Verguts and Notebaert (2008) model. However, in the earlier version, it was assumed that “all” features (although with different strengths) are activated whenever any stimulus is presented. This is not very realistic: A more realistic interpretation is that only stimulus-relevant features are activated on every trial, but because activation gradually decays back to zero, residual activation remains in the representations of features that were presented on earlier trials. In this way, features that are not present on the current trial can still be slightly active nevertheless. This idea was implemented in the current version of the model (see below). An illustrative example of this process with four features across three trials is shown in Fig. 1A. With this improved version, we can then outline the following prediction. If there is conflict on a given trial, all stimuli will enhance their connections to the task demand units, but proportionally to their activation. The amount of conflict adaptation will be a direct, and inverse, function of the number of stimuli, even when stimulus repetitions are removed from the analysis. Indeed, if there are more stimuli, the activation of a currently-not-presented stimulus will typically be lower, because the delay since that stimulus was last presented will typically be longer. As consequence, the adaptation of any currently-not-presented stimulus will be smaller, leading to a

Fig. 1. Panel A: illustration of feature node activation when features 2, 3, and 1 are presented sequentially. Panel B: sketch of the flanker task model used in the simulations for set size 4.

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larger congruency effect if that stimulus happens to be presented on the next trial. To test this prediction, we use the numerical flanker task because the number of stimulus repetitions across trials is easy to control parametrically. The numerical flanker task consists of making a response to the central digit (target) that is flanked on either side by other digits (flanker). Similar to the task demand representations in the Stroop task, an attentional module (Botvinick et al., 2001; see Fig. 1B) biases processing toward the target rather than the flanker stimuli. However, because such attention is not absolute, participants are faster when the flanker and target are congruent (e.g., with two flankers on each side, 11111) than when the target and flanker are incongruent (e.g., 11211). This difference in RT is the flanker effect. Like the Stroop task, the flanker task exhibits an SCE (e.g., Gratton et al., 1992). A central tenet of the model is that the SCE is strongest for target repetitions because the corresponding target unit is active and hence is associated most strongly to the attention module (via the Hebbian learning rule, described in Appendix). However, the other stimuli can also enhance their associations with the attention module if there is residual activation within their input unit from earlier trials. Hence, decreasing the frequency of stimulus repetitions across trials should decrease the magnitude of the SCE. In a typical 3-choice flanker task there are nine unique stimulus combinations. In a 9-choice flanker experiment there are eighty-one unique stimulus combinations. Thus, even when the ratio of congruent to incongruent trials is held constant, increasing the number of stimuli should decrease the size of the SCE. In general, our model predicts that if a stimulus repeats exactly, adaptation should be maximal, because adaptation occurs exactly at the level of individual stimulus features. However, because such repetitions do not distinguish our theory from a main alternative (feature binding theory; Mayr, Awh, & Laurey, 2003), we will treat them as confounding factors (Mayr et al., 2003; i.e., target repetitions: tT; distractor repetitions: dD; target-becomes-distractor: tD, distractor-becomes-target: dT). Rather than remove large amounts of data (and different amounts across the different conditions), we use the regression analysis proposed by Notebaert and Verguts (2007) in which these possible confounds are added as covariates in a regression along with congruency, previous congruency, and their interaction (i.e., factor coding for the Gratton effect). We first report a Simulation demonstrating that the model described above does indeed produce a smaller Gratton effect when fewer stimuli repeat across trials, even when immediate repetitions (i.e., from trial n − 1 to n) are accounted for using separate regressors. This simulation is followed by an experiment that provides an empirical test of this hypothesis. 2. Simulation At the input level, targets and flankers are implemented using localist representations. Fig. 1b shows the model for a 4-choice version in which there are 4 target units and 4 flanker units. Similar models are used for the 3-, 6- and 9-choice versions of the task. There is one attention unit for the target stimulus and one for the flanker stimulus (cf. Botvinick et al., 2001). Through conflict-modulated Hebbian learning, the attention units become associated to the input dimensions. In general, we envision that all associations can be affected by conflict-modulated associative learning, but here only the attention-to-input associations are updated. A main reason for limiting associative learning in this way is to replicate our earlier work (Blais et al., 2007; Verguts & Notebaert, 2008). Secondly, it provides the clearest interpretation of what the model does; it assigns more attention to elements that were incongruent on earlier trials. 2.1. Method A typical interactive activation network, with activation between layers, and inhibition within the response layer, was used to model

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the task. One input layer was implemented for the targets, and one input layer for the flankers. Each layer had n units for conditions with set size n. There were also n response units. Each target input unit has a weight of 1 to its corresponding response, each flanker input unit a weight of 1.1. The flanker weight is higher than the target weight to simulate the idea that there are typically multiple flankers and that without the input from the attention module, the irrelevant dimension would dominate. On every trial, targets, flankers, and the attention units are activated. Stimuli were presented until response. Throughout a trial, the attention unit for the relevant dimension (target) has an activation value of 1, the attention unit for the irrelevant dimension (flanker) an activation of 0.3, reflecting the fact that attention cannot be perfectly allocated to the relevant dimension. Each response unit received input from its two input layer units (target and flanker) and inhibition from the other n − 1 response units. Response units were updated until one of them reached a threshold of 0.6. The time needed to reach this threshold is the model response time. Then, conflict is calculated in the response layer. The control signal is a weighted average of current and previous conflict, with more weight given to current conflict (exactly as in Botvinick et al., 2001; see Eq. (A3)). This control signal is used to update the attention-to-input connections via conflict-modulated Hebbian learning. After every trial, all input dimension activations decay to 40% of its value (= residual activation). No noise was added to the model, but model runs differ because the initial weights are randomly assigned and trial sequence is random. Response units are set to zero after each trial. Model performance was robust to changes in parameter values. All model equations can be found in the Appendix. Thirty-six simulated subjects were run through 1296 trials for each of the four conditions (3, 4, 6, and 9 stimuli). The data from each “subject” was analyzed using the approach suggested by Notebaert and Verguts (2007). As noted above, this approach is favored because, as the number of stimuli increases, the relative frequency of combinations of repetitions changes considerably within the four cells of the Gratton analysis. Rather than restrict the analysis to the small subset of trials for which nothing repeats, vectors coding for the various repetitions (tT, dD, tD, and dT) were entered into a regression analysis along with the vectors which coded for congruency, previous congruency, and previous congruency by congruency as predictors of RT. Given our focus on the SCE, the β estimate (regression coefficient) for the previous congruency × congruency interaction is of most interest. The first trial from each block was not included in the analyses. 2.2. Results and discussion There were no errors on congruent trials and the overall error rate on incongruent trials was between 1.01 and 8.07% for each of the eight cells (set size× previous congruency). A detailed report of means and standard deviations of errors is shown in Table 1. Before assessing whether the SCE decreases as a function of set size, it is important to establish a flanker effect is observed at each set size. For this purpose, a paired-sample t-test was performed on the latencies for correct trials comparing congruent to incongruent at each set size. All flanker effects were significant (ts > 200, ps b .001). The means at set size three were 10.45 cycles vs. 17.62 cycles; at set size four, 10.62 vs. 18.40; at set size six 10.78 vs. 19.05; at set size nine 10.90 vs. 19.46. The SCE was significant for all conditions (ts > 15, ps b .001) and decreased monotonically from 2.61 to 2.08 to 1.49 to 1.01 as set size increased from 3 to 9 (all ts > 5, ps b .001). Means and standard deviations are reported in Table 2. To control for the various repetitions (i.e., tT, dT, tD, and dD) in measuring the flanker effect and the SCE, we now turn to the repeated-measures regression approach (Notebaert & Verguts, 2007). For clarity we plot the absolute beta values, so that a positive value corresponds to a regular Gratton effect. As shown in Fig. 2A, and confirmed by a linear regression analysis, the parameter estimates for the Gratton

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Table 1 Mean error rates and difference scores. Standard deviations are in [square brackets] and standard deviation of the differences is in (parentheses). Set size

Previous trial

Flanker effect

Compatible Current trial

Model

Group 369

Group 469

3 4 6 9 3 6 9 4 6 9

SCE

Incompatible Previous trial

Compatible

Incompatible

Compatible

Incompatible

Compatible

Incompatible

.00 .00 .00 .00 3.2 2.9 2.5 2.7 2.8 2.9

8.07 [2.81] 6.35 [2.33] 3.86 [2.01] 2.54 [1.36] 6.2 [4.5] 4.0 [4.1] 2.1 [2.4] 3.9 [4.7] 2.8 [2.1] 2.9 [3.1]

.00 .00 .00 .00 2.8 2.9 2.5 3.3 2.8 3.3

1.73 [.63] 1.73 [.58] 1.25 [.67] 1.01 [.51] 4.5 [3.3] 3.2 [3.3] 3.0 [2.8] 3.9 [4.9] 2.8 [3.1] 2.6 [2.6]

8.07 (2.81) 6.35 (2.33) 3.86 (2.01) 2.54 (1.36) 2.9 (4.4) 1.2 (2.3) −0.4 (2.1) 1.2 (2.5) 0.0 (2.7) 0.0 (2.3)

1.73 (.63) 1.73 (.58) 1.25 (.67) 1.01 (.51) 1.7 (2.4) 0.3 (2.7) 0.5 (2.2) 0.5 (3.5) 0.0 (2.2) −0.7 (1.8)

[.00] [.00] [.00] [.00] [3.9] [2.8] [2.4] [3.4] [3.4] [2.4]

[.00] [.00] [.00] [.00] [3.0] [3.9] [2.8] [4.7] [2.2] [3.2]

effect decrease (in absolute value) as the number of stimuli increases (β = .859, t142 = 20.0, p b .001). Conceptually, this translates to a reduction in the size of the Gratton effect as the probability of becoming associated to the task demand unit decreases. These results are consistent with the predictions outlined above. 3. Experiment Participants were tested using a task design similar to the one implemented in the simulation. Two groups of eighteen participants performed a numerical flanker task across three blocks of trials. One group of participants received set sizes of 3, 6, and 9 and the other group received set sizes of 4, 6, and 9. 3.1. Method 3.1.1. Participants Thirty-six undergraduates from the University of California, Berkeley (UCB) were tested individually and received course credit or $8 for their participation. They were treated in accordance with the guidelines set forth by the UCB's Internal Review Board. 3.1.2. Apparatus The experiment was programmed in E-Prime (www.pstnet.com) running on a Pentium computer with a color monitor. 3.1.3. Stimuli and design Digits were displayed in white 24 pt Arial font (1.1° tall when viewed at approximately 60 cm) 4.1° degrees to the right or left of fixation. The stimulus consisted of a central target flanked by two

6.34 (2.50) 4.61 (2.18) 2.61 (2.01) 1.53 (1.52) 1.3 (3.5) 0.9 (3.8) −0.9 (2.8) 0.7 (3.0) 0.0 (3.6) 0.7 (2.9)

digits on either side (e.g., 77377). The 369 group used the digits 123, 123456, or 123456789 for the three conditions, respectively. The 469 group used the digits 1379, 134679, or 123456789 for the three conditions, respectively. In each block, half of the trials were congruent and half incongruent. Whenever the program called for an (in)congruent trial, one was randomly selected with replacement from all possible (in)congruent trials for that set size. The number of stimuli (e.g., 3, 6, or 9 in the 369 group) was blocked and the order of blocks counterbalanced across subjects. 3.1.4. Procedure Each trial began with a fixation marker at the center of the screen for 500 ms. The stimulus was then presented and participants were asked to respond to the central digit by pressing the appropriate key on a standard keyboard number pad. The fixation marker appeared immediately following the response. Each participant saw a different randomized set of 1200 trials (divided into 3 blocks of 400 trials). The first trial of each block was excluded from the analyses. 3.2. Results and discussion The overall error rate was between 2.5 and 6.2% for each of the 24 set size × congruency × previous congruency × group cells and the pattern was similar to the RT data (see Table 1). Correct RTs less than 200 ms and greater than 2000 ms were removed (0.22%). Different trimming procedures on RTs led to very similar results as those reported here. Before assessing whether the SCE decreases as a function of set size, it is important to establish that a flanker effect is observed at each set size. For this purpose, a paired-sample t-test was performed comparing congruent to incongruent at each set

Table 2 Mean RTs and difference scores. Standard deviations are in [square brackets] and standard deviation of the differences is in (parentheses). Set size

Previous trial

Flanker effect

Compatible Current trial

Model

Group 369

Group 469

3 4 6 9 3 6 9 4 6 9

SCE

Incompatible Previous trial

Compatible

Incompatible

Compatible

Incompatible

Compatible

Incompatible

10.57 10.69 10.82 10.90 466 612 678 638 663 660

20.22 20.39 20.37 20.28 490 644 703 658 685 678

9.98 10.32 10.66 10.88 474 616 678 648 673 664

17.01 17.93 18.73 19.26 486 642 702 653 682 685

9.65 (.41) 9.69 (.32) 9.56 (.32) 9.38 (.25) 24 (13) 32 (19) 25 (25) 20 (25) 22 (25) 18 (25)

7.03 (.26) 7.62 (.21) 8.07 (.20) 8.37 (.17) 11 (17) 27 (21) 24 (16) 4 (26) 10 (21) 21 (34)

[.06] [.06] [.04] [.03] [54] [112] [109] [122] [113] [118]

[.43] [.33] [.33] [.25] [53] [105] [104] [121] [109] [115]

[.10] [.14] [.10] [.10] [52] [105] [105] [123] [106] [122]

[.24] [.18] [.16] [.14] [51] [100] [106] [119] [107] [126]

2.61 2.08 1.49 1.01 13 5 1 15 12 −3

(.46) (.37) (.36) (.31) (20) (22) (22) (42) (35) (26)

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Fig. 2. Panel A: regression coefficients (in absolute value) of Gratton predictor for simulated data. Panel B: regression coefficients (in absolute value) of Gratton predictor for empirical data. Panel C: same as panel b, but for first block only. Error bars represent the standard error of the mean.

size. In the 369 group, set size three, 471 ms vs, 488 ms, t17 =6.76, p b .001; set size six, 614 ms vs. 643 ms, t17 =7.24, p b .001; set size nine, 678 ms vs. 703 ms, t17 =5.62, pb .001. In the 469 group, set size four, 643 ms vs. 656 ms, t17 =3.71, pb .005; set size six, 668 ms vs. 684 ms, t17 = 4.49, p b .001; set size nine, 662 ms vs. 682 ms, t17 = 3.06, pb .01. The SCEs for the 369 group were 13 ± 5 ms (t17 = 2.82, p b .01), 5 ± 5 ms (t17 = 1.01, p > .20), and 1 ± 5 ms (t17 = 0.13, p > .50) respectively. The SCEs for the 469 group were 15 ± 10 ms (t17 = 0.36, p > .50), 12± 8 ms (t17 = 1.52, p = .15), and −3 ±6 ms (t17 = −0.52, p > .50) respectively. See Table 2 for RT means in every cell of the design. The correct RTs for each subject and each block were submitted to the same regression analysis described above with tT, dD, tD, dT, previous congruency, congruency, and previous congruency × congruency (i.e., the SCE) as regressors. The regression coefficients for the SCE in the empirical data as a function of the number of stimuli are shown in Fig. 2B. A linear mixed model analysis on the standardized beta coefficients was performed with set size as a fixed factor, and subject and block order as random effects. This corresponds to the linear regression used on the simulated data, except that a mixed model needs to be used here because set size (and hence block order) was a repeated variable. This analysis confirms that the parameter estimates for the Gratton effect decrease in absolute magnitude as the number of stimuli (set size) increases, t71.1 = 2.76, p b .01. The astute reader will notice that some digits (e.g., 1, 3, 7, and 9 in the 469 group) appear in all three blocks while others (e.g., 2, 5, and 8) appear in only a single block. This could be problematic because the increased practice occurring for the stimuli that occur in each block may contribute to smaller repetition effects. Although it is impossible to completely rule this out in our design, 2 we can eliminate any block-to-block carryover effects by examining only the first block from each subject. Thus, we performed the same linear regression we used for the simulation on a dataset restricted to the first block, effectively creating a between-subjects manipulation of set size with sample sizes equal to 6, 6, 12, and 12 for set sizes 3, 4, 6, and 9 respectively. These means are shown in Fig. 2C, and the regression analysis yields, β = .300, t34 = 1.83, p = .076. Finally, we report the analysis where only complete-alternation trials are included (i.e., all numbers have to change between

2 That is, even if our design used four characters in one block and a new set of nine characters in a different block, the fact that the two blocks are of equal length means that each participant will see each stimulus in the set size 4 block more frequently than the set size 9 block.

consecutive trials). This is not possible for the set size 3 data; for the other set sizes, we included data of all participants. This yielded a pattern consistent with the more powerful analysis reported above (Gratton effects of 5, 4, and − 6 for set sizes 4, 6, and 9, respectively), although the differences did not reach statistical significance (t = 1.13). 4. General discussion Based on an associative perspective on cognitive control, we predicted that the SCE would decrease as the number of unique features (i.e., stimuli) increases, even when controlling for the number of immediate repetitions. The empirical test confirms this prediction; the size of the SCE decreased as the number of unique stimuli increased in a numerical flanker task. Based on earlier reports of associative effects in cognitive control, some theorists have challenged the standard interpretation of cognitive control effects and have suggested that they result entirely from feature binding (e.g., Hommel, 2004; Hommel, Proctor, & Vu, 2004; Mayr et al., 2003; Schmidt & Besner, 2008; Schmidt & De Houwer, 2011; Schmidt, Crump, Cheesman, & Besner, 2007) and hence are not related to cognitive control at all. This view is not supported by the current data. These accounts predict that the Gratton effect is entirely due to immediate target or flanker repetitions, which have been included as covariates in the current analysis. Hence, according to the pure feature binding theory, the previous congruency × current congruency interaction should have a zero regression weight in the regression for all set sizes. We predicted, and confirmed, that it should only approach zero for larger set sizes. As we have pointed out earlier, however, cognitive control can be thought of as modulating associative processes. In this sense, feature binding theory and cognitive control are not contradictory (a position called “adaptation by binding” in Verguts & Notebaert, 2009). In particular, we assume that situations that lead to arousal (such as incongruency: see Kobayashi et al., 2007) increase Hebbian learning. Such a modulated learning mechanism readily explains single trial learning in which a strong stimulus–response pair is formed after a single occurrence. For example, few people need to learn the association between a hand on a burning stove and its consequences more than once. More generally, it is consistent with the well-established finding from learning theory that associations are formed better if they are accompanied by arousal (e.g., McGaugh, 1990). It remains to be determined, however, exactly which “features” are relevant. In the current experiment, both the number of unique stimuli and the number of response options increased with increasing set size. Future research must determine which is more critical. In

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addition, other features that were not addressed in the paper have been suggested to be relevant as well (see Schmidt & De Houwer, 2011, for discussion). Finally, whether the current results apply to other conflicts tasks is an open question. However, the standard selective attention tasks tend to exhibit similar effects. For example, Simon, Stroop, and Eriksen flanker tasks all exhibit congruency effects, proportion effects, and SCE (e.g., Stroop: Kerns et al., 2004; Simon: Kerns, 2006; Eriksen flanker: Gratton et al., 1992). The SCE has even been observed across transitions in a sequential learning task (Jiménez, Lupiáñez, & Vaquero, 2009). Thus, we see no reason why these results would fail to generalize. Fast cognitive control is difficult to reconcile with the traditional view of control acting slowly and with effort (e.g., Posner & Synder, 1975). It does, however, follow naturally from the view that cognitive control operates by the online modulation of associative learning. Such learning can be fast and, in principle, proceed without much effort. More generally, a slow cognitive control system would not be very useful given that its aim is to adapt to ever changing circumstances. It is thus no coincidence that the brain relies on associative learning to implement cognitive control.

where xcon denotes the mean activity of the control unit up to trial n. When both difference terms in (A5) are negative, the equation is set to zero. Weights w ti are only adapted between task representations and their corresponding input layer units and are restricted to be nonnegative. Parameters were chosen as follows: τ=0.1, winh =−0.5, C=0.7, λcon =0.8, βcon =1, λw =0.2, α=20, βw =0.5. The activation of the target attention unit was set at 1, that of the flanker attention unit at 0.3. The initial strength of each attention unit to its corresponding input units (i.e., initial entries in matrix wti) was 0.5. The strength of input-response connections for the target layer equals 1 (e.g., from number 1 to response “1”; matrix wir); the strength of input-response connections for the flanker layer equals 1.1. In each trial, activation of the input and response units was updated according to Eqs. (A1) and (A2) until one of the response units reached a threshold value of 0.6. The corresponding response was taken to be the model's response choice and the time needed to reach that unit was taken to be the model's RT. The qualitative pattern of results was robust to changes in these parameters.

Appendix A

References

Most specifications here are taken from Verguts and Notebaert (2008). Time in a trial is indexed by t; the cascade rate of activation in a trial is denoted by τ. The activation equation for an arbitrary input unit i (either in the target or flanker layer, see Fig. 1) is as follows:

Blais, C., Robidoux, S., Risko, E. F., & Besner, D. (2007). Item-specific adaptation and the conflict monitoring hypothesis: A computational model. Psychological Review, 114, 1076–1086. Botvinick, M., Braver, T. S., Barch, D. M., Carter, C. S., & Cohen, J. D. (2001). Conflict monitoring and cognitive control. Psychological Review, 108, 624–652. Bugg, J. M., Jacoby, L. L., & Toth, J. P. (2008). Multiple levels of control in the Stroop task. Memory & Cognition, 36, 1484–1494. Cohen, J. D., Dunbar, K., & McClelland, J. L. (1990). On the control of automatic processes: A parallel distributed processing account of the Stroop effect. Psychological Review, 97, 332–361. Crump, M. J., Gong, Z., & Milliken, B. (2006). The context-specific proportion congruent Stroop effect: Location as a contextual cue. Psychonomic Bulletin & Review, 13, 316–321. Gratton, G., Coles, M. G., & Donchin, E. (1992). Optimizing the use of information: strategic control of activation of responses. Journal of Experimental Psychology. General, 121, 480–506. Hommel, B. (2004). Event files: Feature binding in and across perception and action. Trends in Cognitive Sciences, 8, 494–500. Hommel, B., Proctor, R. W., & Vu, K. P. L. (2004). A feature-integration account of sequential effects in the Simon task. Psychological Research, 68, 1–17. Jacoby, L. L., Lindsay, D. S., & Hessels, S. (2003). Item-specific control of automatic processes: Stroop process dissociations. Psychonomic Bulletin & Review, 10, 638–644. Jiménez, L., Lupiáñez, J., & Vaquero, J. M. M. (2009). Sequential congruency effects in implicit sequence learning. Consciousness and Cognition, 18, 690–700. Kerns, J. G. (2006). Anterior cingulate and prefrontal cortex activity in an FMRI study of trial-to-trial adjustments on the Simon task. NeuroImage, 33, 399–405. Kerns, J. G., Cohen, J. D., MacDonald, A. W., III, Cho, R. Y., Stenger, V. A., & Carter, C. S. (2004). Anterior cingulate, conflict monitoring, and adjustments in control. Science, 303, 1023–1026. Kobayashi, N., Yoshino, A., Takahasi, Y., & Nomura, S. (2007). Autonomic arousal in cognitive conflict resolution. Autonomic Neuroscience-Basic & Clinical, 132, 70–75. Mayr, U., Awh, E., & Laurey, P. (2003). Conflict adaptation effects in the absence of executive control. Nature Neuroscience, 6, 450–452. McGaugh, J. L. (1990). Significance and remembrance: The role of neuromodulatory systems. Psychological Science, 1, 15–25. MacLeod, C. M. (1991). Half a century of research on the Stroop effect: An integrative review. Psychological Bulletin, 109, 163–203. Notebaert, W., & Verguts, T. (2006). Stimulus conflict predicts conflict adaptation in a numerical flanker task. Psychonomic Bulletin & Review, 13, 1078–1084. Notebaert, W., & Verguts, T. (2007). Dissociating conflict adaptation from feature integration: A multiple regression approach. Journal of Experimental Psychology. Human Perception and Performance, 33, 1256–1260. Posner, M. I., & Synder, C. R. (1975). Facilitation and inhibition in the processing of signals. In P. M. Rabbitt, & S. Dornic (Eds.), Attention and performance V (pp. 669–682). San Diego, CA: Academic Press. Schmidt, J. R., & Besner, D. (2008). The Stroop effect: why proportion congruent has nothing to do with congruency and everything to do with contingency. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34, 514–523. Schmidt, J. R., Crump, M. J., Cheesman, J., & Besner, D. (2007). Contingency learning without awareness: Evidence for implicit control. Consciousness and Cognition, 16, 421–435. Schmidt, J. R., & De Houwer, J. (2011). Now you see it, now you don't: Controlling for contingencies and stimulus repetitions eliminates the Gratton effect. Acta Psychologica, 138, 176–186. Tzelgov, J., Henik, A., & Berger, J. (1992). Controlling Stroop effects by manipulating expectations for color words. Memory & Cognition, 20, 727–735.

in

in

xi ðt þ 1Þ ¼ ð1−τÞxi ðt Þ þ τ Ii ðt Þ:

ðA1Þ

Ii(t) is an indicator function which is 1 if the stimulus corresponding to that unit i is presented at time t, and zero otherwise. To implement residual activation from earlier trials, activation of input units at the start of trial n was set to 40% of the value at the end of trial n − 1. The activation equation for a response unit j is: res

res

ir in

xj ðt þ 1Þ ¼ ð1−τ Þxj ðt Þ þ τ ∑ wi xi ðt Þ C þ i

2 X k¼1

ti

td

!

wki ðnÞxk ðnÞ

inh

þw

res

!

∑ xk ð t Þ : k≠j

ðA2Þ

The matrix w ir contains bottom-up weights from ! the input layers 2 P ti td wki ðnÞxk ðnÞ incorporates the to the response layer. The term C þ k¼1

top-down attentional weighting from the two task demand units (flanker, target) to the input layers by weight matrix w ti which is adaptively changed over trials n. The term winh ∑ xres k ðt Þreflects response k≠j

res competition. The summation −winh ∑ ∑ xres j ðt Þxk ðt Þ over response j

k≠j

units represents the total amount of response conflict (response conflict unit in Fig. 1). The activation equation for the control unit equals: x

con

ðn þ 1Þ ¼ λcon x

con

inh

ðnÞ þ ð1−λcon Þ −w

res res ∑ ∑ xj xk j k≠j

!

þ βcon : ðA3Þ

This equation is applied at the end of each trial n. Finally, weights are adapted according to a conflict-modulated Hebbian learning rule: ti

ti

wki ðn þ 1Þ ¼ λw wki ðnÞ þ ð1−λw Þðα % f þ βw Þ:

ðA4Þ

The term f reflects the conflict-modulated Hebbian term: ! " ! " con in ti f ¼ x ðnÞ−xcon xi ðt Þ xk ðnÞ−1=2 ;

ðA5Þ

C. Blais, T. Verguts / Acta Psychologica 141 (2012) 133–139 Ullsperger, M., Bylsma, L. M., & Botvinick, M. M. (2005). The conflict adaptation effect: It's not just priming. Cognitive, Affective, & Behavioral Neuroscience, 5, 467–472. Verguts, T., & Notebaert, W. (2008). Hebbian learning of cognitive control: Dealing with specific and nonspecific adaptation. Psychological Review, 115, 518–525.

139

Verguts, T., & Notebaert, W. (2009). Adaptation by binding: A learning account of cognitive control. Trends in Cognitive Sciences, 13, 252–257. Vietze, I., & Wendt, M. (2009). Context specificity of conflict frequency-dependent control. Quarterly Journal of Experimental Psychology, 62, 1391–1400.