Progressive acquired equivalence task

Catherine E. Myers and co-workers have developed a learning paradigm (Rutgers Acquired Equivalence Test or also known as the fish-face paradigm)(Myers et al., 2003), which can be applied to investigate a specific kind of associative learning, the visually guided equivalence learning. The acquired equivalence test is a psychophysical test, which consists of three different parts. During the first, acquisition part, subjects learn to pair different antecedents (face) to different consequents (fishes) through trial-and-error. Each pair is introduced after the subjects correctly answered two times/associations. Thus, the number of associations required to be maintained in the working memory is increased in a staircase method, where the participants learned six pairs of the possible eight pairs. (Figure 1)

Figure 1 (adopted from Puszta et al. 2020): Visual representation of the initial acquisition phase of the visual-acquired equivalence learning paradigm. (A) During each trial, the subject was instructed to select one of two possible fish by trial-and-error learning. (B) The number of pairs that had to be learned was introduced using the staircase method; therefore, the number of items that needed to be maintained increased with time.

After the associations were successfully formed, the second block (that can be divided into two different parts) starts. During this second block subjects are asked to recall the already learnt associations (retrieval part), and to form new associations based on the rule that has been learnt during the acquisition part (generalisation part). The rule is simple: two faces(antecedents) share the same fish (consequents) making thus the two antecedents equivalent (Figure 2). (This is where the acquired equivalence terminology comes from)

Figure 2: The three blocks of the acquired equivalence task. During the first part, participants learn face-fish associations through trial-and-error learning (acquisition part). In the second part the already learnt pairs are asked (retrieval part), along with the remaining two pairs (generalisation part) that can be easily solved based on the rule (the acquired equivalence of the antecedents).

Although the formal description may give the impression that the task is difficult, healthy children(Braunitzer et al., 2017) and participants with mental retardation(Bódi et al., 2009) have been shown to reliably make this kind of generalization.

The task has been widely used in various neuropsychiatric disorder(Shohamy et al., 2004; Bódi et al., 2009; Öze et al., 2017). It has been established that initial acquisition part of the task is connected to the normal function of the basal-ganglia system, and the recall-generalisation part of the task is primarily hippocampal-mediotemporal lobe dependent(Myers et al., 2003).

Clearly the first part of the task is highly basal-ganglia dependent as it requires successful problem-solving/trial-and error strategy. The associations (color-face) are randomized for each participant, but the learning of pairings is highly effected by social preconceptions. For example, if one is to be choose to decide whether the color ’red’ or ’blue’ goes to the man’s or woman’s face, the participant (especially true for children) will choose to associate the blue color over the red with the men’s face and the red one to the women’s. Even though the nowadays tendency for gender-equality, it is crucial to have preconception-free pairings and use stimuli without any higher cognitive meanings.

This is how we ended up using segmented circle as an antecedent and different shapes as a consequent. The rule is hidden in one segment of the circle, but it is unknown to the participant which one. Each segment can have two colors. The guided strategy for the participant is to concentrate their attention only one segment at the time and figure out 1.) if this segment is the basis of the rule and 2.) which color of the segment is connected to the shapes (consequents). So, let’s say we have a segmented circle as antecedent and two possible shapes like this during one trial:

First, the participant takes a guess for the segment: he/she decides to concentrate on the right segment. Then for the color he picks up the black-triangle association and give a response tapping to the triangle.

Let’s assume that is correct, but here comes the next trial which looks like this:

Following the same segment, the participant would assume that the same answer(black-triangle) is the good one. However, if he/she gets a ’fail’ feedback, her/his attention will shift to the left segment, as this segment must be the basis of the rule (i.e red -triangle and blue – square).

There are not only 2 consequents (shapes) but 2×2 resulting in a four possible associations: for example blue-square, red-triangle, blue – mixed ellipses and red – polygon .

The color-shape associations are random, and when the second two consequents come in, the participant again has to guess which color-shape pairings are the correct one, but this time he/she doesn’t have to adopt to the segments as he/she already knows which segment is the important one.

Clearly this trial-and error probabilistic learning is highly basal-ganglia dependent, and it is very similar to the Wisconsin card sorting test.

The test has also a less-commonly investigated aspect, such as the participant has to maintain more and more associations in their working memory. Thus, working memory load has a not negligible effect on the first acquisition part too.

So how could we dissociate the probabilistic learning effect from the working memory part? One possible way is to tell the participant the rule in advance, so the participant knows which segment to follow. There will be still some probabilistic learning effect when the new shapes are introduced in the course of the test, but this trial-and error learning lasts only for a negligible number of trials. Question arises, what happens if we tell the participant the color-shape pairings in advance, so no probabilistic learning would be at all. Then, the participant would learn the parings in the beginning of the task and the number of working memory items in the course of the test would be constant.

There are number of working memory tests in cognitive neuroscience, but is it really the working memory that we investigate or do we have other executive functions that shades the effect of working memory? For example, in the classical n-back tasks participants are asked to tap for the stimuli identical to the trial 2/3/nth before the current trial. However, the n-back paradigm has recently become the focus of doubts concerning its construct validity as a WM task (Kane et al., 2007; Miller et al., 2009; Jaeggi et al., 2010), mostly because it requires maintaining, continuous updating and processing of information simultaneously, making thus difficult to dissociate the working memory capacity from attention.

In the current acquired equivalence test with segmented circle we still don’t know whether failing in working memory part is primarily working memory-failure or is it affected by the consequent of failing to inhibit the processing of the different features of the stimuli (failure of attention).

In order to dissociate the two executive functions, we propose to have 4 blocks of the same acquired equivalence task with different number of segments. Therefore, the number of features that had to exclude from the periphery is alternating between the blocks. In other words, the level of (visual) attention connected to the task varies between blocks. In contrast, the working memory load does not change between the tasks, but it changes in the course of one block.

In addition, since previous studies have shown that spatial attention is a clearly lateralized process (usually the processing of visual information projected into the subdominant hemisphere is faster), the effect of lateralization can be separated by focusing spatial attention to the right and left of visual space. Thus, we can distinguish the effect of the three cognitive processes separately (working memory, spatial attention, lateralization) and the interaction of these cognitive functions on the behavioural- /EEG parameters we examine.


Bódi, N., Csibri, É., Myers, C.E., Gluck, M.A., and Kéri, S. (2009). Associative learning, acquired equivalence, and flexible generalization of knowledge in mild Alzheimer disease. Cognitive and Behavioral Neurology 22(2), 89-94.

Braunitzer, G., Őze, A., Eördegh, G., Pihokker, A., Rózsa, P., Kasik, L., et al. (2017). The development of acquired equivalence from childhood to adulthood—A cross-sectional study of 265 subjects. Plos one 12(6), e0179525.

Jaeggi, S. M., Buschkuehl, M., Perrig, W. J., and Meier, B. (2010). The concurrent validity of the N-back task as a working memory measure. Memory 18, 394–412. doi: 10.1080/09658211003702171

Kane, M. J., Conway, A. R. A., Miura, T. K., and Colflesh, G. J. H. (2007). Working memory, attention control, and the N-back task: a question of construct validity. J. Exp. Psychol. Learn. Mem. Cogn. 33, 615–622. doi: 10.1037/0278-7393.33.3.615

Myers, C.E., Shohamy, D., Gluck, M.A., Grossman, S., Kluger, A., Ferris, S., et al. (2003). Dissociating hippocampal versus basal ganglia contributions to learning and transfer. Journal of Cognitive Neuroscience 15(2), 185-193.

Miller, K. M., Price, K. K., Okun, M. S., Montijo, H., and Bowers, D. (2009). Is the N-back task a valid neurophysiological measure for assessing working memory? Arch. Clin. Neuropsychol. 24, 711–717. doi: 10.1093/arclin/acp063

Öze, A., Nagy, A., Benedek, G., Bodosi, B., Kéri, S., Pálinkás, É., et al. (2017). Acquired equivalence and related memory processes in migraine without aura. Cephalalgia 37(6), 532-540.

Shohamy, D., Myers, C., Grossman, S., Sage, J., Gluck, M., and Poldrack, R. (2004). Cortico‐striatal contributions to feedback‐based learning: Converging data from neuroimaging and neuropsychology. Brain 127(4), 851-859.


Stroop test

The Stroop Task is one of the best known psychological experiments named after John Ridley Stroop. The Stroop phenomenon demonstrates that it is difficult to name the ink color of a color word if there is a mismatch between ink color and word. For example, the word GREEN printed in red ink.

Colin MacLeod’s (1991) review article in the influential psychological journal Psychological Bulletin is frequently cited when discussing the effect.

There are many variations on the basic effect using other stimuli than colored words.

Here we present a simple application of the task implemented in mobile-phone.

Technical details:

The participant is asked to pressed a colored button at the bottom of the screen. There are three possible colors: red, green and blue. In each trial, a colored text appears at the center of the screen and the participant has maximum 1,5 s to select the color of the text. After pressing a button, a feedback of the accuracy (Correct/Incorrect/Late) is provided for 500 ms. The inter-trial interval ranges randomly between 300 and 500 ms.

There are three possible conditions: congruent, incongruent and control. In congruent trials the color of the text and the meaning of the text are equal. In the incongruent trials, there is a mismatch between the color and the meaning of the text. In the control trials, the text is a set of colored, meaningless characters (“#####”).

Given the nature of the conditions, there are three possible congruent and control trials, and six possible incongruent trials. The total number of trials is 180, equally distributed in the twelve possible trial-types. The order of the trials is constructed with two conditions: 1) two same trial-types cannot occur occur consecutively, and 2) three same conditions cannot occur consecutively.

The results collected (accuracy, reaction time) are groupped by conditions for each participant.


Cued Stop Signal task


Response inhibition is essential for navigating everyday life. Its derailment is considered integral to numerous neurological and psychiatric disorders, and more generally, to a wide range of behavioral and health problems. Response-inhibition efficiency furthermore correlates with treatment outcome in some of these conditions. The stop-signal task is an essential tool to determine how quickly response inhibition is implemented. Despite its apparent simplicity, there are many features (ranging from task design to data analysis) that vary across studies in ways that can easily compromise the validity of the obtained results.

Detailed description of the task

In this task, participants typically perform a go task (e.g. press left when an arrow pointing to the left appears, and right when an arrow pointing to the right appears), but on a minority of the trials, a stop signal (e.g. a cross replacing the arrow) appears after a variable stop-signal delay (SSD), instructing participants to suppress the imminent go response (Figure 1).

Figure 1 (Adopted from eLife 2019;8:e46323 DOI: 10.7554/eLife.46323 )


Response inhibition and impulse control are central topics in various fields of research, including neuroscience, psychiatry, psychology, neurology, pharmacology, and behavioral sciences, and the stop-signal task has become an essential tool in their study. If properly used, the task can reveal unique information about the underlying neuro-cognitive control mechanisms. By providing clear recommendations, and open-source resources, this paper aims to further increase the quality of research in the response-inhibition and impulse-control domain and to significantly accelerate its progress across the various important domains in which it is routinely applied.