Figure 1
Schematic overview of the WMDEC model. Working memory consists of four modules (shown in red in the lower part of the figure), namely the phonological buffer, the visuospatial module, the episodic buffer and the executive module. The figure also shows the sensory memory systems (on the left) and the long-term modules in the top part (in blue). Environmental information is shortly kept in sensory memory. The procedural loop (big circular arrow shown as a thick dashed green line) continuously compares condition-action rules stored in procedural long-term memory to sensory and working memory modules. One of the matching rules is selected for execution (routes 3 and 4). Sensory events are interpreted by consulting categorical long-term memory and can be instantiated in the episodic buffer and the modality-specific systems via routes 1 and 2. The episodic buffer also interacts with these modality-specific systems via routes 5 and 6 and over time the buffer contents may flow over into episodic long-term memory via route 7.
Table 1
Model parameters and their standard settings.
| NAME | EXPLANATION | VALUE | LOW | HIGH |
|---|---|---|---|---|
| EB and EM parameters | ||||
| α | Instance activation growth rate | 0.02 | 0.005 | 0.035 |
| β | Lateral inhibition rate | 0.99 | 0.985 | 0.995 |
| φ | Initial activation of new instance | 0.25 | 0.20 | 0.30 |
| τ | Inhibition rate of rejected instances | 0.75 | 0.65 | 0.85 |
| EB maximal activation capacity | 2.90 | |||
| EM maximal activation capacity | 5.0 | |||
| PL and VSM parameters | ||||
| δ | Phonological decay rate | 0.989 | ||
| ρ | Activation growth rate in rehearsal and revival | 0.10 | ||
| σ | Visual decay rate | 0.99 | ||
| LTM parameters | ||||
| η | Rule learning rate (pLTM) | 0.00008 | ||
| Κ | Consolidation rate (eLTM) | 0.001 | ||
| Attention and Motor parameters | ||||
| θ | Response threshold (neutral) | 0.50 | 0.40 | 0.60 |
| λ | Standard deviation of gaussian distribution for response production | 0.01 | ||
| ζ | Mean of gaussian noise distribution for goal-directed response production | 0.015 | 0.010 | 0.020 |
Table 2
Interaction with environment via definition and adaptation of states. Example from a task-switching context.
| NAME | COLOUR | MODALITY | POSITION | START | DURATION | END |
|---|---|---|---|---|---|---|
| CROSS | BLACK | VSP | 4,4 | 0 | 50 | 49 |
| CMAG | BLACK | VSP | 4,3 | 50 | 390 | 439 |
| D9 | BLACK | VSP | 4,5 | 140 | 300 | 439 |
| EMPTY | VSP | 4,5 | 440 | 50 | 489 | |
| Adaptations after response | ||||||
| CMAG | BLACK | VSP | 4,3 | 50 | 181 | 231 |
| D9 | BLACK | VSP | 4,5 | 140 | 91 | 231 |
| EMPTY | BLACK | VSP | 4,5 | 232 | 50 | 281 |
[i] Note. All the attributes of the environmental events are shown. The position is only applicable for events in the visuospatial modality (VSP) and gives the position in the 9 by 9 matrix used for spatial locations.
Figure 2
Illustration of events as they occur on a single task-switching trial. The figure displays the events represented in the the Episodic Buffer (EB) and in Executive Memory (EM). Over the trial, the magnitude cue (CMAG) is presented which triggers instantiation of the task goal (MAG). Later on the target (D9) is presented, which allows acivation of the task set (MAGTS) in EM. Next, the target is categorised as LARGE and in combination with the task set this leads to activation of the corresponding response (RIGHT). The goal, target, category and response are bound together (MAG-D9-LARGE-RIGHT). Finally, the response is executed.
Figure 3
Example of contents of the episodic buffer, the executive memory module and episodic long-term memory during a trial of a serial recall task. After the cue to start acquisition (CMEM) is available in the episodic buffer, the memorisation goal is instantiated (arrow 1), which triggers implementation of the memorisation task set in executive memory (arrow 2). Next, one by one the memoranda are presented and become instantiated in the episodic buffer (arrows 3, 4, 6). After a sufficient amount of refreshing, these memoranda can be represented in episodic LTM (arrows 5, 7 and 8). At the end of the learning phase, a recall cue is presented and activated in the episodic buffer; this laterally inhibits the learn cue (arrow 9), and triggers an action change in the task set including a shift from ‘Recall=OFF’ to ‘Recall=ON’ (arrow 10). After which recall proceeds and finishes.
Table 3
WMDEC predictions regarding task switching performance as tested in Studies 1 and 2 and a motivation why the model supports these predictions.
| PREDICTION | WHATa | WMDEC EXPLANATION |
|---|---|---|
| Study 1: Task preparation and switch cost (SC) | ||
| Task preparation | P+ > P– | Cue processing and goal activation may complete before the task stimulus (target) is presented |
| Task switch cost | Ptr > Pts | On switch trials but not on repetition trials, a new task set must be activated and configured in EM |
| SC reduction | Ct+ > Ct– | Preparation effect is smaller on repetition trials because less preparation is required |
| Residual SC | Ct > 0 (always) | Task set activation and configuration can only complete after the target is presented |
| Study 2: Task and dimension switching | ||
| Dimension SC | Pdr > Pds | When the task repeats, a dimension switch requires changes to the active task set |
| Task/dimension SC | Ct > Cd | A task switch requires a completely new task set including a dimension configuration, whereas a dimension switch requires only a change to a task set parameter when the task remains the same |
| Alternative | Ct = Cd = Ct+d | If it is assumed that every combination of task and dimension requires its own task set, any change (task, dimension or both) requires activation of of a new task set |
[i] a Predictions are formulated in terms of performance (P) as a function of preparation time (+ for longer, – for shorter) or transition (ts for task switch, tr for task repetition), where higer performance corresponds to faster RT and fewer errors. Some predictions are formulated as a performance difference score, namely switch cost (Ct = Pts – Ptr for task switch cost, Cd = Pds – Pdr for dimension switch cost).
Table 4
Means of observed and predicted RT (in ms) as a function of task transition (repeat vs. switch) and cue-target interval (CTI) in Experiment 2 of Logan & Bundesen (2003).
| 0 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Observed RTs | ||||||||||
| Repeat | 1132 | 976 | 929 | 850 | 820 | 790 | 760 | 764 | 769 | 750 |
| Switch | 1463 | 1330 | 1237 | 1127 | 1063 | 1013 | 995 | 964 | 918 | 917 |
| Predicted RTs | ||||||||||
| Repeat | 940 | 858 | 819 | 819 | 807 | 817 | 808 | 808 | 809 | 802 |
| Switch | 1121 | 996 | 906 | 854 | 839 | 841 | 841 | 836 | 844 | 831 |
Table 5
Means as a function of Task transition (Repetition/Switch) and Dimension transition (Repetition/Switch). Observed data in Experiments 1 and 2 of Vandierendonck et al. (2008) and the predicted means under two different sets of assumptions within the context of the WMDEC model.
| Task | CTI 0 | CTI 300 | CTI 1000 | |||
|---|---|---|---|---|---|---|
| REP | SWITCH | REP | SWITCH | REP | SWITCH | |
| Observed means | ||||||
| Rep | 1752 | 2020 | 1485 | 1739 | 1073 | 1326 |
| Switch | 2042 | 2005 | 1728 | 1673 | 1320 | 1294 |
| Prediction 1 | ||||||
| Rep | 1126 | 1174 | 974 | 978 | 982 | 976 |
| Switch | 1253 | 1255 | 1005 | 1008 | 989 | 975 |
| Prediction 2 | ||||||
| Rep | 1097 | 1314 | 974 | 1081 | 975 | 1040 |
| Switch | 1309 | 1300 | 1081 | 1068 | 1023 | 1023 |
Table 6
Overview of WMDEC predictions in a dual-task situation with execution of tasks varying in difficulty and frequency during the maintenance period in a complex span setting.
| PREDICTION | WHATa | WMDEC EXPLANATION |
|---|---|---|
| Study 3: Secondary task in maintenance interval | ||
| Task difficulty | Mdif < Measy | A more difficult task takes more time to complete than an easy task; as a consequence refreshment of to-be-remembered elements is blocked for a longer time |
| Number of tasks | Mhigh < Mlow | When more tasks have to be completed during the maintenance interval, less time is available for refreshment of to-be-remembered elements |
[i] a In dual-task context, a secondary task is present during maintenance and/or retention intervals of a serial recall task, which is scored as the number of correctly recalled elements in the correct serial position (i.e., memory span, M). This measure is observed in a difficult (Mdif) or in an easy (Measy) condition, with a high or a low number of intervening tasks (Mhigh and Mlow).
Table 7
Observed and simulated means (standard deviations between brackets) for the secondary task RTs, total processing time, and memory span in the complex span task design with memory list lengths from 1 to 7 and with tasks varying in difficulty (parity vs. location judgment) executed during the maintenance and retention periods.
| NUMBER OF STIMULI | PARITY | LOCATION | ||||
|---|---|---|---|---|---|---|
| RT | TOTAL TIME | SPAN | RT | TOTAL TIME | SPAN | |
| Observed | ||||||
| 4 | 628 (117) | 2,467 (400) | 5.16 (0.78) | 484 (61) | 1,928 (233) | 5.56 (0.75) |
| 6 | 551 (53) | 3,251 (316) | 4.58 (1.23) | 387 (41) | 2,297 (239) | 5.52 (0.62) |
| 8 | 483 (32) | 3,724 (218) | 3.69 (0.63) | 361 (39) | 2,827 (266) | 4.60 (0.82) |
| Simulated | ||||||
| 4 | 677 (46) | 2,707 (185) | 4.38 (0.69) | 607 (23) | 2,427 (93) | 4.94 (0.55) |
| 6 | 715 (49) | 4,290 (294) | 4.19 (0.81) | 624 (45) | 3,744 (270) | 4.56 (0.61) |
| 8 | 667 (27) | 5,334 (215) | 4.13 (0.60) | 606 (31) | 4,850 (247) | 4.44 (0.61) |
Table 8
Overview of WMDEC predictions regarding memory and task span in Study 4, and the impact of task switch frequency during maintenance and retention interval on serial recall performance in Study 5.
| PREDICTION | WHATa | WMDEC EXPLANATION |
|---|---|---|
| Memory and task span | M(n) ≃ T(n) | As recall of task names calls on EB, whereas task execution on EM, no interference is expected between recall and task execution |
| Memory span increases with length | M(L) > M(l), L > l | For list lengths within capacity, more items are recalled the longer the lists |
| Task span increases with length | T(L) > T(l), L > l | For list lengths within capacity, more of the named tasks will be executed correctly |
| Memory span and chunk size | MC(n) > Mc(n), C > c | The larger the chunks, the more elements can be correctly recalled |
| Task span and chunk size | TC(n) > Tc(n), C > c | When more task names are correctly recalled because of chunk size, more of the tasks will be correctly executed |
| Study 5: Memory span as function of switch frequency | ||
| Alternations and repetitions | Malt < Mrep | Because alternations last longer than repetitions, they block refreshment for a longer time |
| Few and more switches | Mmany < Mfew | As task switches take longer than repetitions, the more switches occur the longer refreshment is blocked; this is the case for tasks presented during maintenance as well as during the retention interval |
[i] a Memory span varies with the length of the to-be-remembered sequence (M(n)), where n is the number of elements, and also chunking affects the memory span (Mc(n)), where c is the size of the chunks. In Study 4, also the task span is measured (e.g., T(n)). In Study 4, the memory span is registered under task alternation (Malt) or task repetition (Mrep), and conditions with many (Mmany) or few (Mfew) switches.
Table 9
Average proportion correct recall in position as a function of Span type, List type, List length and Chunking in the WMDEC simulations applied to Experiment 2 of Logan (2004).
| LIST TYPE 2468 | LIST TYPE 2369 | |||||||
|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 6 | 8 | 2 | 3 | 6 | 9 | |
| Observed | ||||||||
| Memory | 0.93 | 0.84 | 0.57 | 0.38 | 0.95 | 0.89 | 0.61 | 0.36 |
| Task | 0.90 | 0.73 | 0.51 | 0.26 | 0.92 | 0.84 | 0.57 | 0.26 |
| No chunking | ||||||||
| Memory | 1.00 | 0.83 | 0.13 | 0.01 | 0.99 | 0.99 | 0.16 | 0.00 |
| Task | 0.98 | 0.84 | 0.23 | 0.08 | 0.98 | 0.97 | 0.26 | 0.05 |
| Chunks size 2 | ||||||||
| Memory | 0.97 | 0.97 | 0.77 | 0.50 | 0.98 | 0.95 | 0.79 | 0.29 |
| Task | 0.99 | 0.97 | 0.81 | 0.42 | 0.99 | 0.88 | 0.80 | 0.14 |
| Chunks size 3 | ||||||||
| Memory | 0.98 | 0.95 | 0.79 | 0.61 | 1.00 | 0.95 | 0.81 | 0.49 |
| Task | 0.99 | 0.84 | 0.89 | 0.46 | 0.99 | 0.99 | 0.88 | 0.62 |
Table 10
Observed and estimated memory and task spans based on a weighted combination of different degrees of chunking in the two list type conditions.
| SPAN | LIST TYPE 2468 | LIST TYPE 2369 | ||
|---|---|---|---|---|
| MEMORY | TASK | MEMORY | TASK | |
| Data | 6.58 | 6.14 | 7.25 | 6.64 |
| Average | 6.46 | 6.36 | 6.83 | 6.99 |
| Estimate | 6.52 | 6.49 | 6.80 | 6.92 |
Table 11
Average proportion correct recall in position in the three experiments of Liefooghe et al. (2008) and in the WMDEC simulations of these experiments.
| LIST LENGTH | |||||||
|---|---|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 7 | 8 | ||
| Experiment 1 | |||||||
| Observed | Single | 0.96 | 0.96 | 0.89 | 0.79 | ||
| Observed | Dual | 0.82 | 0.88 | 0.83 | 0.74 | ||
| Simulated | Single | 0.99 | 0.98 | 0.95 | 0.88 | ||
| Simulated | Dual | 0.81 | 0.81 | 0.83 | 0.70 | ||
| Experiment 2 | |||||||
| Observed | Few | 0.86 | 0.83 | 0.79 | 0.71 | ||
| Observed | Many | 0.85 | 0.79 | 0.70 | 0.68 | ||
| Simulated | Few | 1.00 | 0.92 | 0.90 | 0.85 | ||
| Simulated | Many | 0.90 | 0.88 | 0.87 | 0.80 | ||
| Experiment 3 | |||||||
| Observed | Few | 0.94 | 0.91 | 0.84 | 0.71 | 0.70 | 0.60 |
| Observed | Many | 0.90 | 0.90 | 0.81 | 0.67 | 0.72 | 0.49 |
| Simulated | Few | 0.89 | 0.74 | 0.68 | 0.63 | 0.56 | 0.49 |
| Simulated | Many | 0.87 | 0.72 | 0.67 | 0.57 | 0.54 | 0.47 |