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The specificity of learned parallelism in dual-memory retrieval


Retrieval of two responses from one visually presented cue occurs sequentially at the outset of dual-retrieval practice. Exclusively for subjects who adopt a mode of grouping (i.e., synchronizing) their response execution, however, reaction times after dual-retrieval practice indicate a shift to learned retrieval parallelism (e.g., Nino & Rickard, in Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 373–388, 2003). In the present study, we investigated how this learned parallelism is achieved and why it appears to occur only for subjects who group their responses. Two main accounts were considered: a task-level versus a cue-level account. The task-level account assumes that learned retrieval parallelism occurs at the level of the task as a whole and is not limited to practiced cues. Grouping response execution may thus promote a general shift to parallel retrieval following practice. The cue-level account states that learned retrieval parallelism is specific to practiced cues. This type of parallelism may result from cue-specific response chunking that occurs uniquely as a consequence of grouped response execution. The results of two experiments favored the second account and were best interpreted in terms of a structural bottleneck model.

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  1. 1.

    The success of the ES model in accounting for the performance of nongrouper subjects supports its use as a reference prediction for the evaluation of learned retrieval-stage parallelism among grouper subjects. Furthermore, the success of that model renders alternative theoretical models, and in particular capacity-sharing models, less compelling as candidate accounts. Whereas the ES model makes precise and testable claims about the lower bound for RT2 (prior to dual-retrieval practice), even in the case of response grouping, capacity-based models do not, unless the free parameters of a capacity-based system were to be independently constrained.


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Author note

This research was supported by a grant of the German Academic Exchange Service to the first author. The experiments were conducted during a research visit of the first author to the lab of T.R. at the University of California, San Diego. We thank Dorothy Nguyen and Grant Gibson for their assistance with data collection.

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Corresponding author

Correspondence to Tilo Strobach.


Appendix A

Quantitative derivation of the efficient-sequential (ES) and race model predictions

The quantitative ES and race models described here are closely related to those described by Nino and Rickard (2003). Both models assume sequential and stochastically independent (e.g., Sternberg, 1969) perceptual, memory retrieval, and motor stages of processing (p, r, and m, respectively). On a given single-retrieval trial, both models assume that

$$ RTk= Lp+ Lrk+ Lmk\kern0.36em \left(\mathrm{for}\ \mathrm{the}\ \mathrm{keypress}\ \mathrm{task}\right), $$
$$ RTv= Lp+ Lrv+ Lmv\kern0.36em \left(\mathrm{for}\ \mathrm{the}\ \mathrm{vocal}\ \mathrm{task}\right), $$

where Lp is a random variate from the latency distribution of the perceptual stage for a given cue (and subject), Lrk (or Lrv) is a random variate from the latency distribution of the keypress (or vocal-digit) retrieval stage for a given cue, and Lmk (or Lmv) is a random variate from the latency distribution for the motor stage for a given response.

The ES model of dual retrieval

The ES model assumes a bottleneck at the retrieval stage that allows for processing of only one retrieval at a time. However, it assumes that no bottleneck or capacity constraint influences the parallel execution of a retrieval stage and a motor stage, or of a keypress motor stage and a vocal motor stage. Assuming for now that the motor stage is always executed as soon as the retrieval stage is complete (i.e., the presumed case for subjects identified as nongrouper subjects), the ES model predicts that RT1 on a given dual-retrieval trial will involve that same stage sequence as does a single-retrieval trial:

$$ RT1= Lp+ Lrk+ Lmk\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{keypress}\ \mathrm{response}\ \mathrm{is}\ \mathrm{executed}\ \mathrm{first}\right), $$


$$ RT1= Lp+ Lrv+ Lmv\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{vocal}\ \mathrm{response}\ \mathrm{is}\ \mathrm{executed}\ \mathrm{first}\right). $$

The ES additive stage prediction for RT2 is either:

$$ RT2= Lp+ Lrk+ Lrv+ Lmv\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{keypress}\ \mathrm{response}\ \mathrm{is}\ \mathrm{executed}\ \mathrm{first}\right), $$


$$ RT2= Lp+ Lrv+ Lrk+ Lmk\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{vocal}\ \mathrm{response}\ \mathrm{is}\ \mathrm{executed}\ \mathrm{first}\right), $$

where RT2 includes the latency components of the perceptual stage, the retrieval stages of both tasks, and the motor stage of the second-executed task (i.e., keypress or vocal task).

Deriving the ES dual-retrieval predictions from the single-retrieval data

The ES model predicts that a random variate from the RT1 distribution on each dual-retrieval trial is estimated simply by the RT for the corresponding single-retrieval trial on the adjacent block (or more precisely, from blocks within the same triad as the target dual-retrieval trial; see pp. 14 and 24 of the text). Thus, for each dual-retrieval trial for each subject, a matched ES random variate, either RTk or RTv, can be selected.

Similarly, for each RT2 value, a matched random variate can be computed from single-retrieval trials as

$$ RT2= RTk+ RTv-200\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{keypress}\ \mathrm{response}\ \mathrm{is}\ \mathrm{completed}\ \mathrm{first}\right) $$


$$ RT2= RTk+ RTv-250\kern0.36em \left(\mathrm{if}\ \mathrm{the}\ \mathrm{vocal}\ \mathrm{response}\ \mathrm{is}\ \mathrm{completed}\ \mathrm{first}\right). $$

To understand the rationale behind Eq. 3, compare the ES additive stage equation for RT2 for the example case in which the keypress retrieval stage is executed first,

$$ RT2= Lp+ Lrk+ Lrv+ Lmv, $$

to the additive stage equation if RT2 were predicted by the simple sum of the two single-retrieval latencies:

$$ RT2= Lp+ Lrk+ Lmk+ Lp+ Lrv+ Lmv. $$

Relative to the true ES prediction for RT2 (Eq. 4), Eq. 5 has an extra Lp term and an extra Lmk term. To jointly compensate for these extra perceptual and motor terms, Nino and Rickard (2003; see also Rickard & Pashler, 2005) used empirically motivated correction factors of –200 ms, when the vocal response is executed first, and of –250 ms, when the keypress response is executed first (see Nino & Rickard, 2003, for further discussion of these correction factors), yielding Eq. 3 for RT2.

The race model of dual-retrieval

On the basis of prior results, the race model is not expected to provide a satisfactory overall account of the data. It is included, however, as a reference prediction for highly efficient parallel retrieval. In deriving this model’s predictions, we assume that a single perceptual event, Lp, runs to completion first, followed by a race between the combined retrieval and motor stages for the vocal retrieval (Lrv + Lmv) and the keypress retrieval (Lrk + Lmk). On a given dual-retrieval trials, then,

$$ RT1= Lp+ \min \left[\left( Lrv+ Lmv\right),\left( Lrk+ Lmk\right)\right], $$

where min[(Lrv + Lmv), (Lrk + Lmk)] denotes the shorter of the two retrieval plus motor stage latencies on that trial. Analogously,

$$ RT2= Lp+ \max \left[\left( Lrv+ Lmv\right),\left( Lrk+ Lmk\right)\right]. $$

Deriving the race dual-retrieval predictions from the single-retrieval data

Nino and Rickard (2003) showed that the “dangling” Lp term in Eqs. 6a and 6b has negligible influence on the statistical race dynamics (because variance in the Lp stage can be assumed to be a small fraction of the overall variance), allowing the matched race random deviates, based on the single-retrieval trials, to be simplified to

$$ RT1= \min \left[ RTk, RTv\right] $$
$$ RT2= \max \left[ RTk, RTv\right]. $$

General notes and assumptions

Using the procedures described above, each dual-retrieval trial for each subject has matched RT1 and RT2 predictions (i.e., theoretically matched random variates) corresponding to each model. Three data sets can thus be defined: (1) the observed dual-retrieval data set, (2) the trial-matched ES prediction data set based on single-retrieval trials, and (3) the trial-matched race prediction data set based on single-retrieval trials. In analyses of the mean RTs and the RT distribution quantiles, the observed dual-retrieval data sets were compared to these theoretical ES and race data sets.

The predictions for both the ES and race models should be understood as idealized predictions that correspond to best case performance, with no inefficiencies in task execution (see the main text for discussion of possible performance inefficiencies). Thus, the model predictions for mean RTs and for distribution quantiles should be understood as lower bound predictions. If either model is fundamentally on the right track in its core theoretical claims, and if dual-retrieval practice has the effect of reducing the latency impact of any initial performance inefficiencies, then dual-retrieval RTs would be expected to converge asymptotically on that model’s predictions following dual-retrieval practice. On the other hand, if in any case the observed dual-retrieval RTs fall substantially below a model’s predictions, then that model can be confidently rejected for that case in its current form.

Note that, in a departure from Nino and Rickard (2003), we excluded the 100-ms dual-retrieval trial preparation cost (Li & Wright, 2000; Pashler, 1998; Sigman & Dehaene, 2006) from the current model development. We excluded this cost because we aimed to provide idealized, lower bound RT predictions for both models. Furthermore, the inclusion of preparation costs in the Nino and Rickard derivation seem rather arbitrary because (1) no previous studies have provided evidence for a preparation cost in the case of two retrievals from a single cue, and (2) any preparation cost that may be associated with dual-retrieval in the present experiments may diminish substantially as a result of practice (e.g., Liepelt et al., 2011, for the case of choice RT dual-tasks), and it is performance after dual-retrieval practice that is of primary interest here.

Finally, two implicit assumptions in the derivation of dual-retrieval predictions based on the single-retrieval data should be noted. First, it is assumed that each subject’s mental state, with respect to factors such as motivation, speed–accuracy bias, and readiness, was the same on average for trials in adjacent single- and dual-retrieval blocks. The data appear to be consistent with this assumption. We found no evidence, for example, of speed–accuracy trade-offs between adjacent single- and dual-retrieval blocks at the end of the single–dual practice phases or in the transfer phases. A second and related assumption is that any retrieval practice effects on RTs across adjacent blocks have only a negligible biasing effect on the model predictions. Given the consistent graphical tracking that was observed over multiple blocks for the observed versus ES prediction for dual-retrieval performance, and the counterbalancing over subjects of the order of single- versus dual-retrieval blocks in Experiment 2, this assumption appears to be well justified.

Appendix B

Fig. 10

Cumulative trial proportions on single-retrieval reaction times (RTs) in the keypress task and the vocal-digit task during Experiment 2’s transfer phase. The graphs represent RTs for old and new cues in bins of 250 ms (i.e., Bin 1 = RTs of 0–250 ms, Bin 2 = RTs of 250–500 ms, …). Inclusion of all responses, regardless of accuracy, was necessary in order to maintain a valid RT ordering for each subject in these distribution analyses

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Strobach, T., Schubert, T., Pashler, H. et al. The specificity of learned parallelism in dual-memory retrieval. Mem Cogn 42, 552–569 (2014).

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  • Cued retrieval
  • Dual-retrieval practice
  • Chunked retrieval
  • Parallel retrieval