Forward and backward blocking in statistical learning

İlayda Nazlı; Ambra Ferrari; Christoph Huber-Huber; Floris P. de Lange

doi:10.1371/journal.pone.0306797

Abstract

Prediction errors have a prominent role in many forms of learning. For example, in reinforcement learning, agents learn by updating the association between states and outcomes as a function of the prediction error elicited by the event. One paradigm often used to study error-driven learning is blocking. In forward blocking, participants are first presented with stimulus A, followed by outcome X (A→X). In the second phase, A and B are presented together, followed by X (AB→X). Here, A→X blocks the formation of B→X, given that X is already fully predicted by A. In backward blocking, the order of phases is reversed. Here, the association between B and X that is formed during the first learning phase of AB→X is weakened when participants learn exclusively A→X in the second phase. The present study asked the question whether forward and backward blocking occur during visual statistical learning, i.e., the incidental learning of the statistical structure of the environment. In a series of studies, using both forward and backward blocking, we observed statistical learning of temporal associations among pairs of images. While we found no forward blocking, we observed backward blocking, thereby suggesting a retrospective revaluation process in statistical learning and supporting a functional similarity between statistical learning and reinforcement learning.

Citation: Nazlı İ, Ferrari A, Huber-Huber C, de Lange FP (2024) Forward and backward blocking in statistical learning. PLoS ONE 19(8): e0306797. https://doi.org/10.1371/journal.pone.0306797

Editor: Fernando Blanco, University of Granada: Universidad de Granada, SPAIN

Received: November 24, 2023; Accepted: June 24, 2024; Published: August 5, 2024

Copyright: © 2024 Nazlı et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The minimal underlying data are freely available on the Donders Repository (https://doi.org/10.34973/pwza-qh43). To access the data, ensure you are logged in by clicking the “Login” button at the top left corner of the page. You can optionally log in using your ORCID account. Once registered and logged in, you can request access by confirming your compliance with all regulations imposed by the ethics committee and acknowledging that you will use the data responsibly and credit it when publicly presenting any results derived from it.

Funding: This work was supported by a personal scholarship provided to İ.N. by the Ministry of National Education of the Republic of Türkiye, and by a personal grant provided to F.P.d.L. by the European Union (ERC Consolidator Grant 101000942, “Surprise”). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Learning is an essential feat of animal cognition. It allows us to build and refine our internal models of the world, so that we predict and flexibly adapt to our dynamic environment. A key feature of learning is the ability to form associations between events that take place in a systematic relationship across space or time [1]. For example, in a typical classical conditioning experiment [2], a dog automatically salivates (i.e., unconditioned response) in response to food (i.e., outcome or unconditioned stimulus). During conditioning, the sound of a bell (i.e., cue or conditioned stimulus) is repeatedly paired with the food. Once conditioning is accomplished, the bell itself elicits salivation (i.e., conditioned response).

Cue competition is a crucial category of phenomena in associative learning. It refers to the observation that learning which cues predict an outcome not only depends on the presence of the cues before the outcome. Rather, cues compete with each other to gain predictive power over the outcome, and this moderates the learning process [3–6].

One key example of cue competition is Kamin blocking, also known as forward blocking [7]. In a typical forward blocking paradigm (see Table 1), observers first learn the association between cue A and outcome X (A→X), and later they are trained with the association between cues A + B and outcome X (AB→X). As a result of forward blocking, observers learn the association between cue B and outcome X less strongly, because X is already completely predicted by cue A. In other words, the previously learned A-X association blocks learning the association between cue B and outcome X. Forward blocking cannot be explained by simple contiguity-dependent Hebbian associative learning [8]. Thereby, it suggests that the simple temporal co-occurrence of different stimuli is not sufficient for learning to occur. Instead, the model developed by Rescorla and Wagner [9] provides an explanation for blocking (though see [10] for a modification of the traditional model). According to the Rescorla-Wagner model, changes in associative strength are determined by the amount of discrepancy between the expected and the observed outcome, i.e. the prediction error. In the forward blocking procedure, the previously learned A→X association prevents the formation of an associative link between the second cue B and the outcome X, because the cue A already minimizes the prediction error during the exposure to the A→X pairs in the first training phase.

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Table 1. General experimental design.

https://doi.org/10.1371/journal.pone.0306797.t001

A similar, but distinct form of cue competition is backward blocking, which is an example of retrospective revaluation: a change in the associative strength occurs because the association between the companion cue (i.e., the cue that is previously associated with the target cue and outcome) and the outcome is revaluated. In the backward blocking paradigm [11], observers are first trained with AB→X association, and subsequently with A→X association. In spite of the reversed order of training phases compared to forward blocking, backward blocking leads to a similar outcome as forward blocking: a lack of association between blocked cue B and outcome X. Here, in the first training phase, both A-X and B-X associations are formed equally (i.e., depending on the saliency of cues). However, in the second training phase, as observers are trained with A→X association, the associative strength between cue A and outcome X becomes stronger, which in turn weakens the association between cue B and outcome X. While this form of retrospective revaluation cannot be explained by the traditional Rescorla–Wagner model, as this model assumes that the relevant cue must be present in order to change the associative strength [9,12,13], backward blocking can be successfully modeled by a slightly revised version of the traditional model. For example, backward blocking can be explained by a Rescorla-Wagner learning model that assigns non-zero salience to non-presented blocked stimuli whose memories or representations are retrieved by competing stimuli that had previously been paired with those blocked stimuli [14] or by a Bayesian generalization of the Rescorla–Wagner model, the Kalman filter [12,15], where the weights of all possible cues are updated simultaneously, and the sum of all possible weights equals to 1.

In typical blocking experiments, associations are learned either when the outcome is a reward [16–19] or when performance-related feedback is provided [5,20–25]. This provides support that reinforcement learning (i.e., learning associations between events via trial and error) relies on an error-driven learning algorithm [26]. Another powerful form of learning is known as statistical learning, often defined as the incidental extraction of regularities from the environment without intention [27–31]. In the context of statistical learning, we have limited information about how the learning process itself occurs. Several studies suggest that statistical learning may indeed similarly rely on prediction errors. In rats, dopaminergic activity in the ventral tegmental area is important for the formation of an association between two non-rewarding stimuli [18,32]. In humans, statistical learning involves the ventral striatum [33], which has been hypothesized to signal prediction errors [33–35]. However, other researchers, using variants of forward blocking, did not find clear-cut evidence for error-driven statistical learning. Beesley and Shanks [36] did not observe any forward blocking in contextual cueing experiments, where participants incidentally learnt the spatial relationship among distractors and targets in a visual search task. This procedure however deviates from classic forward blocking paradigms, which rely on a temporal prediction between a cue and a future outcome [4,5,16,17,19–23,25,37,38]. Two subsequent experiments [6,39] observed forward blocking of temporal associations only for material that was intentionally learnt, but not for incidentally learnt stimulus associations. Such learning conditions substantially deviate from a typical statistical learning scenario, where observers extract regularities without intention [27,28,30,31]. While few studies investigated forward blocking in incidental learning [6,20,36,39], less is known about backward blocking in incidental learning. Importantly, there is evidence of retrospective revaluation (of which backward blocking is an instance) not only in adults and children [40–43] but also in 8-month-old infants [44,45], who clearly did not follow any explicit task instructions. This suggests that backward blocking may be present even in incidental learning, where observers attune themselves to statistical regularities by simple passive exposure.

According to the attentional account model [46], forward blocking occurs as a result of less attention devoted to the blocked cue. Namely, in the first training phase observers learn that cue A predicts outcome X and cue A therefore becomes a relevant and attended cue. Therefore, in the second training phase where novel cue B is presented together with cue A, more attention is paid to the relevant and predictive cue A, compared to the novel predictive cue B. The lower attention to cue B leads to the failure to associate cue B with outcome X. This attentional explanation would however not be able to explain backward blocking, given that equal attention is paid to cues A and B in the first phase. Hence, the use of backward blocking enables us to examine more closely the attentional account of blocking and, crucially, test for retrospective revaluation in statistical learning. Therefore, we set out to examine forward and backward blocking during statistical learning in a series of experiments. In some statistical learning experiments, participants are exposed to a continuous stream of stimuli containing statistical regularities [27,29,47–50]. Other studies have instead presented two successive stimuli on each trial, with conditional probabilities controlling their pairing [51,52]. In terms of neural processing, both continuous streams [53] and pairs [54] show identical modulations of sensory responses after statistical learning, suggesting that both paradigms elicit similar learning processes. We opted for pairs of stimuli in order to connect our study to the classic forward and backward blocking paradigms [7,11]. On every trial, we presented participants with two consecutive visual object stimuli and asked them to categorize the trailing object as either electronic or non-electronic. Unbeknownst to participants, we manipulated the conditional probabilities between the leading and trailing stimuli, such that each trailing image could be predicted on the basis of its preceding, leading image. After learning, we evaluated statistical learning by presenting participants with expected and unexpected image pairs and measuring their reaction time for categorization judgments of the trailing image. Successful learning was indexed by faster reaction times to expected relative to unexpected trailing stimuli [49,52,55].

Experiment 1

Method

Preregistration and data availability.

All experiments were preregistered on the Open Science Framework (https://osf.io/r243e for Experiment 1; https://osf.io/7kmtv for Experiment 2). All data and code used for the analyses are freely available on the Donders Repository (https://doi.org/10.34973/pwza-qh43). Deviations from the preregistration are mentioned as such and justified in the corresponding sections below.

Participants.

The experiment was performed online by using the Gorilla platform [56], and participants were recruited through the Prolific platform (https://www.prolific.co/). 92 participants performed the experiment. 42 of them were excluded based on a priori exclusion criteria (see section ‘Exclusion and inclusion criteria’ below) before they started the second training phase (i.e. before the relevant data for the analysis was collected). Importantly, our selection criteria applied to a very simple task where the general population is expected to score at ceiling [51,52,57]. Thus, our criteria (i.e. accuracy below 80%) allowed us to exclude outliers who clearly underperformed either because they did not read the instructions carefully, or did not understand the requirements of the task, or did not pay enough attention to stimuli; accordingly, it is common in online experiments that approximately half of the participants shows careless and inattentive behavior [58,59]. Consequently, we carried out our analyses on a subset of the population who showed high motivation and adequate attention to the stimuli, as required to support statistical learning (Richter & de Lange, 2019). 50 participants (18 females; mean age 25.80, range 18–40 years) were included in the final data analysis. In Supplementary Forward Blocking Experiment 1 with 100 participants (see Supplementary information 2), we found successful learning of stimulus transition probabilities (b = 11.23, CI = [6.80, 15.59], Cohen’s d_z = 0.54). From this observation, we concluded that 50 participants was an adequate sample size for Experiment 1.

All participants had normal or corrected to normal vision, normal hearing and no history of neurological or psychiatric conditions. They provided written informed consent and received financial reimbursement (8 euro per hour) for their participation in the experiment. The study followed the guidelines for ethical treatment of research participants by CMO 2014/288 region Arnhem-Nijmegen, The Netherlands.

Experimental design.

In each experimental trial, participants were exposed to two images presented on the left or right side of the central fixation point in quick succession: a leading stimulus was followed by a trailing stimulus. For each participant, there were 4 leading objects and 4 trailing stimuli objects. Everyday objects were randomly chosen from a pool of 64 stimuli derived from Brady et al. (2008) per participant, thereby eliminating potential effects induced by individual image features at the group level. In each stimulus set, 50% of objects were electronic (consisting of electronic components and/or requiring electricity to function) and 50% were non-electronic. The expectation manipulation consisted of a repeated pairing of objects in which the leading object predicted the identity of the trailing object, thus over time making the trailing object expected given the leading object. Importantly, each trailing object was only (un)expected depending on which leading object it was preceded by. Thus, each trailing object served both as an expected and unexpected object depending on the leading object at test phase. In addition, trial order was pseudo-randomized, with the pairs distributed equally over time. In sum, any difference between expected and unexpected occurrences cannot be explained in terms of familiarity, adaptation, or trial history. In addition, object position (left / right) was counterbalanced with respect to Expectation (expected / unexpected) and Condition (antedating / blocked / control). In other words, leading and trailing objects appeared equally often on the left or right side of the central fixation point across trials. As a result, the expectation manipulation did not depend on spatial position. Also, both hemi-fields were equally task-relevant, which fostered participants’ attention to both sides. Throughout the experiment, participants needed to categorize the trailing object as electronic or non-electronic as fast as possible. This task was aimed at assessing any implicit reaction time (RT) benefits due to incidental learning of the temporal statistical regularities: upon learning, leading object could be used to predict the correct categorization response before the trailing object appeared. In addition to the main object categorization task, there was an oddball detection task involving the leading stimuli in the training phases (16% of all trials per participant): participants were required to press a specific button as soon as they saw an animate leading stimulus. The aim of the animate detection task was to ensure that participants also paid attention to the leading stimuli, such that the association would be better learnt. For each participant, 4 animate leading stimuli (i.e., 2 for antedating leading stimulus and 2 for blocked leading stimulus) were randomly chosen from a pool of 8 stimuli [60]. Finally, there were attention check trials where participants were simply asked to press a specific key based on a message on screen (e.g., "Press left-arrow key"). The aim of these trials (7% of all trials per participant) was to monitor participants’ vigilance (see ‘Exclusion and inclusion criteria’). A fixation bull’s-eye was presented in the center of the screen throughout the experiment.

The blocking paradigm comprised two consecutive training phases, followed by one test phase (see Fig 1A). During the two training phases, leading objects were perfectly predictive of their respective trailing objects (i.e. P(trailing | leading = 1); see Fig 1B). Participants were not informed about this deterministic association, nor were they instructed to learn this association at the beginning of the experiment. Therefore, the pair associations were likely learned incidentally. Note that the participants may, however, still develop explicit knowledge of the associations over the course of the experiment, which we tested in a final recognition task. In training phase 1, the leading object (A) was always followed by the same trailing object (X). In training phase 2, a novel leading object (blocked [B] leading object) was presented along with the leading object presented in training phase 1 (antedating [A] leading stimulus), hence creating a compound stimulus (AB). This was followed by the same trailing object (X) as in training phase 1. In addition, two novel leading (object + object [CD]) and a trailing (object [Y]) objects were presented as a control condition. In the test phase, the leading stimulus of each condition (antedating [A] / blocked [B] / control [D]) was presented alone, followed by either the expected trailing object (based on the training phases), or an unexpected trailing object. Expected and unexpected object pairs were presented equally often to prevent any learning at this final test stage (see Fig 1C). In the test phase, control (D) trials were compared to blocked (B) trials to assess blocking while controlling for the amount of exposure. It should be noted that the amount of exposure to trailing object X and trailing object Y are not the same, given that trailing object Y was only introduced in the second learning phase. This difference is an inevitable feature in classic blocking paradigms. If we would have presented trailing object Y in isolation in an additional experimental phase or if we would have paired Y with another leading stimulus in training phase 1, this could have elicited latent inhibition (i.e., difficulty in learning associations as a result of pre-exposure, [61]). Thus, we opted for the classic blocking paradigm. Furthermore, the control trials in the test phase allowed us to assess whether new associations were learned during training phase 2.

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Fig 1. Experimental procedure and results of Experiment 1.

Note. (A) Experiment 1 comprised two training phases (training phase 1 and training phase 2) and a test phase. On every trial throughout the experiment, participants saw a pair of consecutively presented stimuli, i.e., a leading object followed by a trailing object. In training phase 1, the antedating leading object (i.e., A) was followed by a specific trailing object. In training phase 2, a novel blocked leading object (i.e., B) was presented in compound, along with the antedating (A) leading object (i.e., AB), and followed by the same trailing object from the antedating stimulus in training phase 1. In addition, we introduced novel control compound leading (i.e., CD) and trailing (i.e., Y) objects. In the test phase, antedating, blocked or control leading stimuli were followed by the associated (expected) or not associated (unexpected) trailing object. There were four different object pairs for AB→X and CD→Y. Throughout the experiment, participants performed a categorization task on the trailing object. They reported, as fast as possible, whether the trailing object was electronic or non-electronic. (B) Statistical regularities depicted as image transition matrix with stimuli pairs in training phase 1 and training phase 2. Ls represent leading stimuli, and Ts represent trailing stimuli. There were 16 different leading objects and 8 different trailing objects coming from four different AB→X and CD→Y pairs. (C) Statistical regularities depicted as image transition matrix with stimuli pairs in test phase. Green cells represent expected pairs, and red cells represent unexpected pairs. (D) Across participants’ mean reaction times as a function of Expectation (expected / unexpected) and Condition (antedating / blocked / control). Reaction times were faster to expected than unexpected trailing objects in each condition. The reaction time difference between expected and unexpected trials was greater in blocked than control trials, providing evidence for the absence of blocking effect and the augmentation of learning. (E) Across participants’ mean reaction time difference between expected and unexpected trials as a function of time. Please note that we split data into successive runs for visualization purposes only; data analysis was performed with number of trials as a continuous fixed factor (Exposure). The decrease in reaction time difference between expected and unexpected trials over exposure showed rapid extinction in learning antedating condition. (F) Posterior coefficient estimates of effects of the model jointly analyzing blocked and control conditions with error bars representing 95% confidence intervals. Estimates indicate significant results when they do not overlap with zero. (G) Across participants’ proportion correct responses in pair recognition test. Participants showed slightly above chance-level performance in all conditions indicating whether the trailing object was likely or unlikely given the leading object.

https://doi.org/10.1371/journal.pone.0306797.g001

Data was collected during one single session per participant. Firstly, participants familiarized themselves with all trailing objects (both X and Y). In each trial, an object image was presented for 3500 ms, and participants had 1500 ms to categorize the object image as electronic or non-electronic (via a keyboard key press, keys counterbalanced across participants). Then, written feedback indicated the true category and the name of the object for 2000 ms (8 pairs × 2 trials / pairs = 16 trials in total). Afterwards, participants performed the experiment (i.e., training phase 1, training phase 2 and test phase). In each trial, the leading and trailing objects were presented for 500 ms successively with no inter-stimulus interval, followed by a 1500 ms inter-trial interval. Participants categorized the trailing object as electronic or non-electronic as fast as possible (via keyboard key press, keys counterbalanced across participants). Training phase 1 and training phase 2 started with a short practice period (practice training phase 1: 4 pairs × 4 trials / pairs = 16 trials in total; practice training phase 2: 8 pairs × 4 trials / pairs = 32 trials in total). After each practice, participants completed the training phases (training phase 1: 4 object pairs × 30 trials = 120 trials in total; training phase 2: 8 object pairs × 30 trials = 240 trials in total). In addition, animate detection and attention check trials (see above) were pseudo-randomly interspersed throughout the training phases without repetitions in successive trials. Afterwards, participants completed the test phase (12 pairs × 16 trials = 192 trials in total). Crucially, for each leading object, both expected and unexpected trailing objects belonged to the same category (electronic or non-electronic). This ensured that differences in RTs during object categorization would not arise by mere response adjustments costs, but instead reflected perceptual surprise to unexpected trailing objects.

Finally, at the end of the experiment participants performed a pair recognition task to probe their explicit knowledge of the statistical regularities. Before starting the recognition task, participants were informed about the presence of statistical regularities among leading and trailing images in the previous experimental phases (i.e., training phases 1 and 2), and they were asked to indicate whether the trailing object was likely or unlikely given the leading stimulus according to what they saw during these previous phases. Participants familiarized themselves with the procedure via a brief practice (12 pairs × 2 trials / pairs = 24 trials in total) before completing the recognition task (12 pairs × 8 trials / pairs = 96 trials in total).

Exclusion and inclusion criteria.

The online experiment was terminated if the percentage of correct responses during object categorization was below 80% (threshold was defined based on a preliminary pilot study) in any training or test phase (see ‘Experimental design’ and Fig 1A) or if the percentage of correct responses in attention check trials was below 80% in any of the experimental phases (see section ‘Experimental design’).

Prior to the main data analysis, we discarded trials with no responses, wrong responses, or anticipated responses (i.e., response time < 200 ms). We also rejected trial outliers (response times exceeding 3 MAD from mean RT of each participant) and subject outliers (participants whose RTs exceeded 3 MAD from the group mean). For the accuracy analysis of the pair recognition task, we rejected trial outliers in terms of response speed (response times exceeding 3 MAD from mean RT of each participant).

Data analysis.

We analyzed the RT data in the test phase in order to test for incidental learning of predictable stimulus transitions: upon learning, participants were hypothesized to react faster to expected relative to unexpected trailing stimuli (Richter et al., 2018, Richter & de Lange, 2019). We did not statistically analyze the accuracy data in the test phase, given that the categorization task was not challenging, and performance was near ceiling levels (97% in Experiment 1 and 97% in Experiment 2). Furthermore, we analyzed the accuracy data in the pair recognition test to assess participants’ explicit knowledge about learnt statistical regularities. For both analyses, we used a Bayesian mixed effect model approach. Data were analyzed using the brm function of the BRMS package [62] in R. Furthermore, supplementary tables (see S1 File) we provide post-hoc Bayesian mixed effect models that follow significant interaction effects.

Analysis of RT data in test phase. Firstly, we modeled the behavioral data of the antedating condition, where one leading stimulus was followed by one trailing stimulus. This served as a sanity check to verify the baseline assumption that participants were able to learn the temporal association between the leading and trailing stimuli. The model of the antedating (A) condition included reaction time as dependent variable and Expectation (unexpected / expected) as a fixed factor. To model the overall effect of time on task, we included Exposure as a continuous numeric predictor. Exposure was scaled between -1 and 1 to be numerically in the same range as the other factors, which aids model convergence. For the interpretation of the results, the model coefficient for Exposure represents the increase in RT from the first to the last exposure. Finally, we included the interaction between Exposure and Expectation in the model, to probe extinction of the learnt associations. Namely, during the test phase participants were exposed equally often to expected and unexpected stimulus pairs, potentially resulting in extinction of the RT advantage for expected stimuli over time. The model included a full random effect structure (i.e., a random intercept and slopes for all within-participant effects) to account for individual variance.

Secondly, we determined whether there was blocking by jointly modeling the blocked (B) and control (D) conditions. The model of blocked and control conditions included reaction time as a dependent variable and Expectation (unexpected / expected), Condition (control / blocked) and Exposure as fixed independent variables. We included the interaction between Expectation and Condition to test for the blocking effect. The contrasts of the factors Expectation and Condition were coded as successive difference contrasts. Exposure was a continuous predictor scaled between -1 and 1, as in the antedating condition analysis. Again, we also modeled extinction (Expectation × Exposure interaction) and its interaction with Condition to probe for potential differences in extinction between conditions. We adjusted the priors of the main effect of Expectation and Exposure and the prior of their interaction based on the posteriors of pilot experiments. Each prior was centered according to the median of the respective posterior estimate, and its standard deviation equated to the posterior estimate error times two to make the priors less informative. The prior for the Condition effect and its interaction with Expectation, i.e., blocking effect, was centered at zero. Note that specifying the priors in this way turns the estimates of Expectation and Exposure effects of Experiment 1 into the combined evidence from pilot experiments and Experiment 1. Crucially, the pattern of results from Experiment 1 was exactly the same when not only the priors for the Condition effect but also for Expectation and Exposure were centered at zero. Further details and the complete model parametrization can be found in the R codes provided on the Donders Repository. The response time data was modelled using the ex-gaussian family and four chains with 25,000 iterations each (12,500 warm up) per chain and inspected for chain convergence. We report posterior fixed effects model coefficients. Coefficients were accepted as convincing statistical evidence, analogously to statistically significant in a frequentist framework, if the associated 95% posterior credible intervals were non-overlapping with zero.

Analyses of accuracy data in pair recognition test. Firstly, we determined whether accuracy was above chance level within each condition (antedating / blocked / control). Hence, we created three separate binomial mixed-effects models with response error as dependent variable. If accuracy was above chance level within each condition, we then determined whether there was a blocking effect in the explicit knowledge of implicitly learned associations. To do so, we created a binomial mixed-effects model with response error as binary dependent variable and Condition (blocked / control) as fixed factor. The models included a full random effect structure (i.e., a random intercept and slopes for the within-participant effects). The models were constructed using weakly informative priors centered at zero. All accuracy models were fit using Bernoulli family and four chains with 25,000 iterations each (12,500 warm up) per chain and inspected for chain convergence. With respect to significance and amount of evidence we used the same criteria as for the RT data.

Results

Analyses of RT data in test phase

Firstly, we compared the reaction times of expected and unexpected trials in the antedating condition (see Table 2). We observed faster reaction times in expected (460 ms) than in unexpected (477 ms) trials (b = 10.81, CI = [5.04, 16.16], Cohen’s d_z = 0.61, see Fig 1D), indicating successful learning of conditional probabilities and the consequent behavioral benefit of expectation in terms of response speed. In addition, we evaluated how this learning effect changed across exposure. Again, we observed an interaction effect between expectation and exposure (b = -9.01, CI = [-16.83, -1.18]), indicating that learning showed rapid extinction (expectation effect for run 1: 26 ms, run 2: 11 ms; see Fig 1E).

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Table 2. Posterior fixed effects of the model of antedating condition on reaction times in Experiment 1. Estimate, estimation error, lower/upper limit of 95% profile credible intervals.

https://doi.org/10.1371/journal.pone.0306797.t002

Next, we modeled the blocked and control conditions to test whether we found blocking (see Table 3 and Fig 1F). There was an interaction effect between expectation and condition (b = -9.48, CI = [-18.26, -0.45], Cohen’s d_z = -0.26, see Fig 1B. We performed separate analyses for the blocked and control conditions to test for the presence of an expectation effect in each condition respectively. The reaction times in expected (481 ms) and unexpected (489) trials were not different from each other in the control condition (b = 4.36, CI = [-0.73, 9.51], Cohen’s d_z = 0.20, see S1 Table in S1 File). On the other hand, reaction times were clearly faster in expected (469 ms) than in unexpected (488 ms) trials of the blocked condition (b = 10.11, CI = [4.82, 15.16], Cohen’s d_z = 0.65, see S2 Table in S1 File). Interestingly, this is exactly the opposite pattern of what would be expected under blocking, and rather supports better learning of the associations among blocked stimuli than control stimuli. Extinction was not different between blocked and control conditions (b = -1.63, CI = [-14.19, 11.00]; expectation effect in blocked condition for run 1: 13 ms, run 2: 18 ms; expectation effect in control condition for run 1: 6 ms, run 2: 3 ms; see Fig 1C).

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Table 3. Posterior fixed effects of the model of blocked and control conditions on reaction times in Experiment 1. Estimate, estimation error, lower/upper limit of 95% profile credible intervals.

https://doi.org/10.1371/journal.pone.0306797.t003

Analysis of accuracy data in pair recognition test

Participants showed slightly above-chance level performance in indicating whether the trailing object was likely or unlikely given the leading object in the antedating (proportion correct = 59%; b = 0.39, CI = [0.26, 0.51]), blocked (proportion correct = 57%; b = 0.29, CI = [0.17, 0.42]) and control (proportion correct = 59%; b = 0.39, CI = [0.24, 0.54]) conditions (see Fig 1G). Response errors did not differ between the blocked and control conditions (b = -0.1, CI = [-0.08, 0.29]), indicating the absence of blocking effect for the explicit knowledge of incidentally learned associations.

Experiment 2

In Experiment 1, we observed a stronger reaction time benefit for B→X compared to control, indicating successful learning and the absence of forward blocking. We speculated that this pattern of results may be explained by the following process: upon learning the A→X association in the first training phase, attention may have shifted to the novel (and therefore potentially more salient) leading image B during the second training phase, thereby enhancing the learning of the B→X association. Importantly, this attentional mechanism is not at play in the related, but distinct paradigm of backward blocking [11]. Here, the order of training phases is reversed compared to forward blocking. Observers are first trained with AB→X association and presented in a subsequent training phase with the A→X association. As a result, both leading objects A and B are equally novel and salient during the first training phase and therefore should be learnt equally well. Therefore, we reasoned that backward blocking may allow us to study blocking without the potentially confounding factors related to novelty and salience. Crucially, this paradigm also allowed us to test for the first time whether retrospective revaluation takes place during incidental statistical learning.