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On costs and benefits of n−2 repetitions in task switching: towards a behavioural marker of cognitive inhibition

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Inhibition in task switching is inferred from slower reaction times returning to a recently performed task after one intervening trial (i.e. an ABA sequence) compared to returning to a task not recently performed (CBA sequence). These n−2 repetition costs are thought to reflect the persisting inhibition of a task after its disengagement. As such, the n−2 repetition cost is an attractive tool for the researcher interested in inhibitory functioning in clinical/neurological/neuroscience disciplines. In the literature, an absence of this cost is often interpreted as an absence of inhibition, an assumption with strong implications for researchers. The current paper argues that this is not necessarily an accurate interpretation, as an absence of inhibition should lead to an n−2 repetition benefit as a task’s activation level will prime performance. This argument is supported by three instances of a computational cognitive model varying the degree of inhibition present. An inhibition model fits human n−2 repetition costs well. Removal of the inhibition—the activation-only model—predicts an n−2 repetition benefit. For the model to produce a null n−2 repetition cost, small amounts of inhibition were required—the reduced-inhibition model. The authors also demonstrate that a lateral-inhibition locus of the n−2 repetition cost cannot account for observed human data. The authors conclude that a null n−2 repetition cost provides no evidence on its own for an absence of inhibition, and propose reporting of a significant n−2 repetition benefit to be the best evidence for a lack of inhibition. Implications for theories on task switching are discussed.

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  1. 1.

    There are some non-inhibitory accounts of n–2 repetition costs in the literature, but to date these have been unable to explain extant data (Mayr, 2007).

  2. 2.

    Of course, one cannot be certain of no inhibition even in the presence of an n–2 repetition benefit without explicit modelling of the latent processes.


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The authors are grateful to Katherine Arbuthnott, Bernhard Hommel, and an anonymous reviewer for their constructive feedback. We would like to thank Katherine Arbuthnott for suggesting that we discuss lateral inhibition in this context.

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Correspondence to James A. Grange.

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Appendix A

See Table 2

Table 2 A sample of studies that report n−2 repetition effects that are either not significantly different from zero, or are negative, together with a broad overview of how the authors interpreted the finding

Appendix B

See Table 3

Table 3 List of production rules—and their plain-English interpretation—that govern model behaviour

Appendix C

Implementation details of the lateral-inhibition model.

In a competitive network using LI as part of a selection mechanism, each element in the set of possible responses has inhibitory connections to all the others. The strength of this inhibitory connection, w , is usually equal for all connections and unchanging during processing. Thus any unit u i , with activation level a i will send an inhibitory signal of magnitude \( w^{ - } \times a_{i} \) to each of the others. Conversely, that unit u i will receive a combined inhibitory signal \( I = w^{ - } \sum\nolimits_{j \ne i} {a_{j} } \) from the set of units u j , j ≠ i.

To show how lateral inhibition is predicting an n−2 repetition benefit, we simulated LI in a simplified model computed in Visual Basic within Excel. In this case, each task (of 3) is represented as a single unit, with an activation level in the range [−1, 1] and a resting level of 0. A negative activation level represents a suppressed (below baseline) state and does not propagate. All three units are connected to each other via inhibitory links of equal strength. The only excitatory input to the model is an external input I ext representing the effect of a current task cue. On any trial only one task unit receives any such input, and that input builds up gradually (over 5 discrete time slices) to reach a maximum strength of 0.8. At each time t each unit u i updates its activation level a i according to

$$ a_{i} (t + 1) = \delta a_{i} (t) + I_{i}^{\text{ext}} (t) - I_{i}^{\text{inh}} (t) $$

(The activations are hard-clipped to the range [−1, 1]). In Eq. 3, \( \delta \) is a decay (or recovery) parameter, which differs depending on whether the activation a i is above or below baseline. For \( a_{i} > 0, \, \delta = 0.5 \), otherwise \( \delta = 0.95 \). The terms \( I_{i}^{\text{ext}} {\text{ and }}I_{i}^{\text{inh}} , \) respectively, represent the excitatory external input, and the (internal) lateral inhibition to unit u i . The latter is defined by

$$ I_{i}^{\text{inh}} (t) = w^{ - } \sum\nolimits_{j \ne i}^{n} {a_{j} (t - 1)} $$

where w (=0.1) is the inhibitory weight as discussed above, and the summation is over all units other than u i (recall also that sub-baseline activations do not propagate, i.e. they are treated as 0).

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Grange, J.A., Juvina, I. & Houghton, G. On costs and benefits of n−2 repetitions in task switching: towards a behavioural marker of cognitive inhibition. Psychological Research 77, 211–222 (2013).

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  • Lateral Inhibition
  • Switch Cost
  • Task Switching
  • Inhibition Model
  • Root Mean Square Deviation