Neural Oscillatory Signatures of Predictive Processing in Visual Statistical Learning

ABSTRACT

Several studies suggest that neural oscillations play a role in cognition, including predictive processing. Recent models propose that backward alpha‐band traveling waves reflect top‐down predictions, while forward waves may reflect bottom‐up prediction errors. We tested this hypothesis using a visual statistical learning task in which participants (N = 31) detected target shapes presented with varying levels of predictability. Electrophysiological activity and pupillometry were recorded throughout the task. Behavioral results showed faster responses for predictable targets, and pupil dilation increased for unexpected shapes. Evoked response potential analyses revealed predictability effects on the P300 component across occipital and frontal electrodes, along with modulation of alpha oscillations. However, traveling wave analyses did not show a clear effect of predictability between conditions. Instead, wave patterns showed a modest association with individual differences in cognitive strategy, with stronger top‐down alpha‐band waves in participants who relied more on statistical regularities. Overall, these findings challenge the view that alpha‐band traveling waves implement predictive coding during visual perception, suggesting instead that they may reflect more general cognitive strategies rather than specific predictive processes.

Several studies suggest that alpha‐band traveling‐waves support predictive processing. We tested this hypothesis using a visual statistical learning task with different sequence predictabilities. Behavioral, pupillometry, and ERP analyses revealed that participants correctly learned the statistical regularities. However, traveling‐waves were not modulated by sequence predictability. Importantly, alpha power and wave patterns showed modest association with individual's cognitive strategy: prior‐driven individuals showed weaker alpha power and stronger top‐down alpha‐band waves.

1. Introduction

The brain can be interpreted as a predictive machine, capable of identifying statistical regularities to optimize interactions with the environment [1, 2, 3]. According to the Bayesian brain theory, our brain constantly attempts to infer the causes of the surroundings by continuously updating an internal model of the world, thereby generating probabilistic beliefs about the future [4, 5, 6, 7, 8, 9]. Specifically, hierarchically higher brain areas generate predictions about the causes of sensory input. At the same time, lower regions inform the update of such predictions via prediction errors (PEs) (i.e., the difference between top‐down predictions and the actual activity) [10].

Statistical learning (SL) is a widely used paradigm for investigating these mechanisms. It refers to the ability to learn statistical regularities, such as the sequential structure of a sequence of items [11, 12, 13, 14, 15]. During SL experiments, several neurophysiological correlates have been proposed as markers of predictive processes, including evoked response potentials (ERPs) [12, 16, 17], hemodynamic responses [18], functional connectivity (FC) [19, 20], and neural oscillations [21, 22, 23, 24, 25].

Regarding neural oscillations, an increasing number of studies have begun to consider not only their temporal dynamics but also their spatial component, specifically their propagation across the cortex as traveling waves (TWs) [26]. In scalp electrophysiological (EEG) recordings, recent studies have associated TW propagation with distinct cognitive phenomena, such as visual perception [27, 28], working memory [29], as well as motor excitability [30].

Interestingly, recent work has specifically linked alpha‐band (8−12 Hz) TWs to predictive processes [31, 32]. Alpha oscillations have long been associated with top‐down predictive control. For example, previous experimental work has shown that pre‐stimulus alpha oscillations are enhanced for predicted visual stimuli compared to unpredicted ones, suggesting that alpha oscillations may carry top‐down sensory predictions [24, 33]. Recent magnetoencephalogram (MEG) neurofeedback work further provides causal evidence supporting parietal alpha activity as a candidate mechanism for top‐down control: parietal alpha synchrony can be voluntarily modulated, and such modulation causally relates to attentional biases [34]. Furthermore, another recent MEG work reveals how rhythmic activity can control object‐based attention and predict its detection [35]. Other lines of work have also related alpha oscillations to temporal predictability [22, 36, 37, 38]. Beyond the widely recognized role of stationary alpha oscillations in predictive processing, computational simulations have proposed that alpha‐band TWs may emerge from cortico−cortical interactions implementing predictive coding mechanisms [31, 39]. According to these models, forward (FW) waves propagating from occipital to frontal areas encode sensory information and PEs. In contrast, backward (BW) waves, spreading from frontal to occipital regions, are believed to carry top‐down predictions.

Despite recent work addressing the relationship between alpha‐band TWs and predictive coding [22, 32, 40, 41], direct experimental evidence supporting this relationship remains lacking. Here, we assess this compelling hypothesis using an SL paradigm while measuring EEG and pupil responses. Participants performed a visual detection task, in which they identified a target shape embedded in a sequence of geometric stimuli. Conditional probabilities were manipulated to systematically vary sequence predictability across multiple levels, spanning from highly predictable to entirely unpredictable. Based on the literature, we hypothesized that BW waves, reflecting top‐down predictions, would increase with more predictable sequences. In addition, our method of controlling sequence predictability enabled us to define unexpected events, such that violations became increasingly surprising as predictability increased. This approach allowed us to examine whether FW waves reflect PEs and, specifically, whether these responses are modulated by the degree of unpredictability associated with the transition. SL was assessed behaviorally using reaction times as a function of target transition predictability. In addition, ERPs and pupillary responses time‐locked to shape onset were quantified for each condition. Cortical TWs were also quantified using two distinct and complementary analytical approaches. Overall, we present a comprehensive description of behavioral and EEG measures to characterize the correlates of visual SL.

2. Materials and Methods

2.1. Participants

Thirty‐two healthy young adults participated in this study; all of them had normal or corrected‐to‐normal vision. One of them had to be removed from the analysis due to poor behavioral performance (more than 30% of missed targets, compared to the group mean of 2.95%). The following analyses are based on 31 participants (23 males, mean age = 26.2, SD = 2.90, range = 22−33). All participants gave informed consent and were reimbursed for their time. All procedures were approved by the Comité de protection des Personnes Sud Méditerranée 1 (ethics approval number 2022‐A02453‐40), adhered to the guidelines for research at the Centre de Recherche Cerveau et Cognition, and were conducted according to ethical standards of the 1964 Helsinki Declaration.

2.2. Apparatus

The experiment took place in a dark and quiet room.

All tests were conducted on a PC (Precision 5820 Tower, Dell Inc., Round Rock, TX, USA) with an NVIDIA graphics card (T1000 8GB, Nvidia Corporation, Santa Clara, CA, USA). Visual stimuli were generated and controlled using MATLAB (R2019b, The MathWorks Inc., Natick, MA, USA) and PsychToolbox [42, 43, 44].

All the stimuli were displayed on a monitor (Display++ LCD Monitor, 1440 × 1080 pixels, 100 Hz refresh rate, Cambridge Research Systems, UK). For the entire duration of the experiment, participants had their heads stabilized by a chin rest positioned 57 cm from the screen. Before each session, participants could adjust the chin rest to improve their posture. Continuous brain activity was recorded from the subjects using a 64‐channel active BioSemi EEG system, at a sampling rate of 2048 Hz. The pupil diameter was measured using an EyeLink 1000 Plus video‐based eye tracker (SR Research), which recorded monocular pupil size (in arbitrary units) and eye movements at 1000 Hz. Calibration of the eye tracker was performed once at the beginning of the experiment or every time the participant adjusted the chin rest.

2.3. Task and Stimuli

Participants performed a visual detection task in which four white geometrical shapes (square, circle, triangle, and diamond) were presented on a black screen, one at a time, in a continuous stream at a 1 Hz temporal frequency (Figure 1A). The four shapes had a radius of 3 degrees and a thickness of 0.5 degrees of visual angle. Shapes appeared centrally, slightly above the fixation cross (0.66 degrees of visual angle from the center of the shape), which was white and centered, with a radius of 0.33 degrees of visual angle.

FIGURE 1.

Experimental design and wave quantification methods. (A) Trial design. Each trial begins with the presentation of the Target, which is shown here as a green triangle. Once the sequence of shapes begins, each shape lasts 1 s. Subjects were instructed to respond as fast as possible when detecting the target. (B) The sequence followed a probabilistic Markovian process, where each shape can transition to another shape with a certain probability defined by the experimental condition. (C) Probability tables for all five conditions arranged in order of increasing predictability. Each table shows the transition probability (in percent) between any two shapes. For example, for the rightmost one, after the square, there is a 5% probability of a circle or triangle, and a 90% probability of a diamond. The circle and triangle shapes are considered “rare” transitions, while the diamond is the “expected” one. (D) TW quantification methods. Upper panels: 2D‐FFT. The raw EEG signals are extracted from the seven midline electrodes (Fz, FCz, Cz, CPz, Pz, POz, Oz) and stacked to obtain 2D maps. After applying a 2D‐FFT, we obtain a spectrum with temporal and spatial frequencies on the x‐ and y‐axes, respectively. The maximum values in the upper and lower quadrants represent the strength of forward and backward waves, respectively. Lower panel: A spherical wave fit is applied to the alpha‐band phase map within a fixed ROI (after applying a power threshold). For each time point, the best fit is selected to quantify wave direction and spatial frequency.

The experiment consisted of 15 blocks (∼4 min each), each comprising five trials. Each trial consisted of a 36‐shape sequence, which the participants initiated by pressing a button. Before each trial, one of the four shapes was designated as the target for that specific trial. Participants were instructed to press the spacebar as fast as possible whenever the target shape appeared. Short breaks were allowed between blocks, and the full experiment lasted about 90 min.

At the end of each block, participants received point‐based feedback on their reaction time (RT): they earned or lost 1 point depending on whether their RT was faster/slower than in the previous block. This feedback was added to further incentivize fast responses that rely more strongly on the learned regularity. Lastly, at the end of each block, participants were given a questionnaire in which they were asked to rate, on a scale of 1−10, the overall perceived predictability of the stream of shapes in that block.

2.4. Experimental Design and Procedure

The sequence of shapes within each trial followed a probabilistic Markovian process (Figure 1B), where each shape transitions to one of the three other shapes with different probabilities. We manipulated the predictability of the sequence across five conditions (Figure 1C), defining rare and expected transitions (Table 1). In the four conditions with nonrandom transitions (C2−C5), expected transitions have probabilities of 0.9, 0.8, 0.6, and 0.475, while rare transitions have probabilities of 0.05, 0.1, and 0.2, respectively. Note that condition C3 in the table had a slightly different structure in which two expected transitions had a probability of 0.475, and one rare transition had a probability of 0.05. Lastly, one condition (i.e., C1 in the table) was completely unpredictable, with all the transitions having the same probability.

TABLE 1.

Probabilities of the shape transitions and entropy for each experimental condition.

	C1	C2	C3	C4	C5
Rare event probability	– 33%	20%	5%	10%	5%
Expected event probability		60%	47.5%	80%	90%
Entropy	1.097	0.950	0.859	0.639	0.394

Note: From condition 1 to condition 5, the reliability of the sequence increases, as indicated by the decrease in entropy, which is measured as $-{\sum }_i^{N}p(x_i)\ast \mathrm{lo}{\mathrm{g}}_2(p(x_i))$, where $p(x_i)$ indicates the transition probabilities.

The transition matrix remained constant across the five trials within each block. Throughout the entire experiment, three blocks per condition were presented in a different randomized order to each subject, with 180 shapes per block (540 for each condition). Target shape identity was checked for balance, and it was varied pseudorandomly across trials in order to maintain attention. The subdivision of trials was intended solely to allow participants to take short breaks and to change the target.

Before the experiment began, participants were informed that difficulty would vary between blocks, without, however, being given specific instructions about the specifics of the probabilistic rules, and instructed to respond to the target as quickly as possible.

2.5. Data Analysis

2.5.1. Behavioral Analysis

During the experiment, we recorded participants’ RTs, their performances (hit rate, miss rate, and false alarm rate), and the score regarding the perceived predictability of the block sequence. We also considered answers provided up to 200 ms before shape onset as anticipated target detections, and we computed, for each condition, the percentage of anticipated targets. Since these anticipations are indicative of participants’ learning, we included those responses in the calculation of hits, miss, and false alarms, but we excluded them from the RT measures. For all measures except RT, we performed repeated‐measures ANOVAs, considering CONDITION as a fixed factor. For the RT, we performed repeated‐measures ANOVAs considering CONDITION and EVENT TYPE (i.e., rare vs. expected shape) as fixed factors.

We also conducted a control analysis to assess whether shape identity influenced RT. Specifically, we performed a repeated‐measure ANOVA on RT, including CONDITION and SHAPE IDENTITY as factors. Furthermore, we computed, for each participant, the slope of predictability ratings across conditions as an index of sensitivity to difficulty variations between blocks, with steeper slopes indicating greater awareness. This slope was then included as a covariate in repeated‐measures ANOVAs conducted on pupil and ERP measures.

In addition to the main analyses, we conducted an exploratory analysis motivated by the possibility that not all participants effectively used the learned patterns to guide task performance, and may instead have passively attended to the visual stimulation—potentially obscuring any effect of prior modulation on TWs. To examine this, we defined a learning index (LI) to assess the extent to which participants used or did not use the statistical regularities. To do so, we calculated, for each condition separately (except C1, in which there was no regularity, hence no rare or expected events), the $L{I}_{cond}$ as follows:

$$L{I}_{cond}=\frac{(R{T}_{Rare}-R{T}_{Expected})}{R{T}_{Median}},$$

where $R{T}_{Rare}$ and $R{T}_{Expected}$ are the median RT for the rare and expected targets, and $R{T}_{Median}$ is the median RT over all target shapes. Importantly, only for the LI computation, we included the RTs of anticipated targets described above and, for these target detections, we considered negative RTs. This decision comes from the fact that anticipated targets provide a measure of participants’ learning that complements RT and better captures predictability effects. To assess the effect of condition on this index, we performed repeated‐measures ANOVAs, with CONDITION as a fixed factor.

For each participant, we also calculated the LI across conditions as follows:

$$L{I}_{general}=\frac{(R{T}_{Rare\left(C2-C5\right)}-R{T}_{Expected\left(C2-C5\right)})}{R{T}_{Median}},$$

where $R{T}_{Rare(C2-C5)}$ and $R{T}_{Expected(C2-C5)}$ are the median RT across conditions C2−C5 for the rare and expected targets, and $R{T}_{Median}$ is the median RT over all target shapes. The $L{I}_{general}$ index gives us a measure of the overall strategy employed by each subject across conditions. We then split participants based on whether they used the statistical regularities, using a median split. Following the terminology introduced in previous work [45, 105], we label the two groups Believers and Empiricists, based on whether they rely more on statistical rules (the former) or the sensory information (the latter). For each group, except RT and anticipated targets (i.e., the measures used to define the LI), we performed repeated‐measures ANOVAs on the same dependent variables, considering CONDITION as a fixed factor and GROUP as a between‐subjects factor. We also included Kendall's correlation analysis between the $L{I}_{general}$ and each performance variable averaged across conditions (hit, miss, and false alarms), and the slope of the predictability ratings.

2.5.2. Pupillometry

All pupil traces were preprocessed using MATLAB custom scripts. First, we smoothed and down‐sampled the data using a moving average with a window size of 100 time points and no overlap, thereby reducing the sampling rate from 1000 to 10 Hz. Next, we identified and removed eye blinks by differentiating the signal and applying a threshold estimated from a linear function of the standard deviation (STD) across blocks and subjects. Additionally, we filtered the data by removing all data points that fall 2 STDs away from the average, before interpolating the missing signal using linear interpolation. Lastly, we segmented the data from −0.2 to 3 s around each shape onset and baseline‐corrected the data, using a baseline between −0.1 s to the shape onset.

Since target events are known to elicit a significantly stronger pupil response than nontarget events [46], our analysis here is only focused on nontarget events (target effect quantification and surprisal following target events analysis is shown in Supplementary Materials). In order to compare pupil responses after rare and expected events, we calculated the mean pupil response amplitude between 0 and 1 s after rare and expected nontarget events. Additionally, we analyzed, in the same time window, the peak latency difference between rare and expected nontarget events in all conditions. We define latency as the time point at which the pupil reaches its maximum response to both rare and expected events. For these two measures, amplitude and peak latency, we performed repeated‐measures ANOVAs, considering CONDITION and EVENT TYPE as fixed factors, and slope of predictability ratings as a between‐subjects covariate.

2.5.3. Electrophysiology

2.5.3.1. Preprocessing

Custom functions of the EEGLAB toolbox [47] were used for the EEG preprocessing. We first applied average referencing and removed power‐line artifacts using a notch filter (47–53 Hz). To remove slow drifts, we applied two different a high‐pass filters depending on the analysis: 0.5 Hz for ERP analyses and 2 Hz for the spectral power and TW analyses. We cut off higher frequencies with a low‐pass filter (60 Hz). The data were then down‐sampled to 160 Hz, and noisy channels were rejected. We then performed independent component analysis (ICA) to identify artifacts in the data and used the ICLabel plugin to automatically detect artifactual ICA components. Specifically, we flagged muscle, eye, and heart components identified with a probability of 80% or more and removed them. On average, 0.03% of the detected components were rejected; the number of rejected components ranged from 0 to 2 (mean = 1.55, SD = 0.55), indicating limited variability. After this step, the removed channels were interpolated using superfast spherical interpolation.

2.5.3.2. ERPs Quantification and Statistics

Average ERPs were computed separately for each participant, electrode, and experimental condition. We epoched the data from −1.5 to 2 s around the shape onset. We applied a baseline correction from −0.2 to 0 s before shape onset. For each condition, ERP responses were divided into target and nontarget events, and then further into rare and expected events (excluding C1, which has no rare or expected events).

Similarly to pupil diameter analysis, since target events are known to elicit a stronger and slower P300 component compared to nontarget events [48, 49], our analysis here is only focused on nontarget events (target analysis is shown in Supplementary Materials). The P300 is usually measured within a time window of 250–500 ms after event onset [50]. Therefore, we measured the P300 amplitude (µV) as the average value over this time window, and P300 latency (ms) as the time from stimulus onset to the point of maximum positive amplitude within the same time window. On both measures, amplitude and latency, we performed repeated‐measures ANOVAs with CONDITION and EVENT TYPE as fixed factors, and slope of predictability ratings as a between‐subjects covariate. The analysis was performed on two midline electrodes, Pz and Fz, considered representatives of the two P300 subcomponents P3a, which shows a fronto‐central distribution, and P3b, which exhibits a centro‐parietal topography [50]. To ensure complete transparency, the corresponding analyses for all seven midline electrodes used in the 2D‐FFT analyses (Oz, POz, Pz, CPz, Cz, FCz, and Fz) are provided in the Supplementary Materials.

2.5.4. Alpha Power Analysis

To obtain the power spectra, we created data epochs from −1.5 to 2 s around each shape onset in the preprocessed data. For each condition, we calculated the time−frequency response by applying a continuous wavelet transform implemented in MATLAB (cwt function), with the analytic Morlet (“amor”) wavelet, on each event separately and averaging the resulting spectra. The transform was computed over a frequency range of 2–40 Hz. Frequencies were derived from the corresponding wavelet scales given the sampling rate, and default settings for the Morlet wavelet (including time–frequency resolution trade‐off) were retained.

The analysis of alpha power was not driven by the primary hypothesis of the manuscript, but rather constitutes an exploratory follow‐up motivated by the pattern of LI results observed in relation to TWs. Specifically, following previous literature [45, 105], we averaged over the alpha band (7−13 Hz) between 0 and 1 s after event onset and computed the ∆α index for each participant and experimental condition as follows:

$$\mathrm{\Delta }{\alpha }_i=\alpha \_\mathrm{P}{\mathrm{z}}_{C1\left(random\right)}-{{\alpha }_{\mathrm{Pz}}}_{Ci},$$

where $\alpha \_\mathrm{P}{\mathrm{z}}_{C1(random)}$ and $\alpha \_\mathrm{P}{\mathrm{z}}_{Ci}$ represents the average alpha power in electrode Pz in the random condition (C1) and in the other conditions. Because condition order was randomized across blocks, the random condition does not serve as a temporal baseline, but rather as a condition‐level reference. The ∆α provides an index of occipital alpha modulation. To assess the effect of condition on this index, we performed repeated‐measures ANOVAs, with CONDITION as a fixed factor. To compare this index with the LI defined above, we performed, for each condition, Kendall's correlation analysis between the $L{I}_{cond}$ and the ∆α. Lastly, on the average alpha power of the electrodes Pz, Oz, Cz, and Fz, we performed repeated‐measures ANOVAs, with CONDITION as a fixed factor and, to examine the effect of the $L{I}_{general}$, we added GROUP as a between‐subjects factor. We also performed Kendall's correlation analysis between the $L{I}_{general}$ and the average alpha power on electrodes Pz, Oz, Cz, and Fz, across conditions.

2.5.5. Wave Quantification

We quantify the presence of TWs and their direction using two different and complementary methods. The first method is based on a 2D fast Fourier transform (2D‐FFT) [31] (Figure 1D, upper panel). For each trial, we extracted EEG signals from seven midline electrodes (from posterior to frontal: Oz, POz, Pz, CPz, Cz, FCz, Fz) to form a 2D (electrode‐time) map. We applied a 500 ms sliding window with a 100 ms overlap to each trial and transformed the data using a 2D‐FFT. This transform yields a 2D‐spectral representation, with temporal frequencies along the horizontal axis and spatial frequencies along the vertical axis. The horizontal midline indicates stationary oscillations with no spatial propagation (i.e., standing waves), while the upper and bottom quadrants reflect FW and BW waves, respectively. We extracted the maximum value across all spatial frequencies from the upper and lower quadrants of the 2D‐FFT spectrum to obtain two 1D‐spectra over temporal frequencies for both FW and BW waves. For each spatiotemporal map, we normalized both spectra using the mean 1D‐FFT over the seven electrodes [29], and we extracted the alpha band. This procedure yields a measure of wave intensity in dB units, as used in previous work [27, 51, 104]. Eventually, we extracted the average alpha FW and BW waves across all blocks and, on both measures separately, we performed repeated‐measures ANOVAs considering CONDITION as a fixed factor.

The second method employs a sphere‐fitting procedure [103] and was recently introduced for the detection and quantification of planar TWs in scalp‐EEG signals (Figure 1D, lower panel). This method was adapted from a previous intracortical recording‐based method [52] and was applied here with a fixed region of interest (ROI) and frequency of interest (FOI). As we did not expect any lateralization, we defined a narrow central ROI (N = 19 electrodes) extending one electrode to either side from the midline. The FOI comprised the alpha band (7−13 Hz), as in the previous analysis. In the first step, the method identifies clusters of true oscillatory activity (as compared to the aperiodic activity), achieved by estimating background noise via an aperiodic fit on the data. The aperiodic component was estimated using the spectral parameterization approach of Donoghue et al. [53]. Power spectral density was computed via FFT for each electrode, and the aperiodic component was extracted using the FOOOF implementation in FieldTrip [54]. This aperiodic activity was used to generate surrogate data via inverse FFT with chance‐level oscillatory power. Wavelet transforms of these surrogate data yielded frequency‐wise null distributions, which served as a baseline for extracting oscillatory clusters. Here, since ROI and FOI are fixed, the clusters are defined only in the temporal dimension, as consecutive periods of above‐threshold alpha power. A spherical planar wave is then fit to the spatiotemporal phase patterns within each cluster. For each time point, the best fit provides measures of wave direction (WD), spatial frequency, and goodness‐of‐fit. Using these results, we calculated the probability of different states based on WD, considering only fits for which the goodness‐of‐fit was above a certain threshold (phase gradient directionality, PGD>0.5), an arbitrary threshold corresponding to an intermediate goodness‐of‐fit that has been adopted in previous TW studies to retain only sufficiently coherent wave patterns [52, 55, 103]. These states are FW, BW, and mediolateral waves within a range of 45° (i.e., ±22.5° from the midline). To control for variability in the number of retained data points, we expressed WDs as proportions, computed by dividing the number of time points in each direction by the total number of retained time points. This approach prevents differences in sample size across conditions from biasing the results. We computed the probability for each state and performed two kinds of analyses on these measures.

First, we performed a global (time‐averaged) analysis: we quantified FW and BW TWs across all time points of the block, obtaining an overall measure of wave directionality independent of event timing. On these measures, we conducted repeated‐measures ANOVAs, with CONDITION as a fixed factor for FW and BW separately. In order to assess the relationship with overall FW and BW waves and the participant's strategy used to perform the task, we also estimated the $L{I}_{general}$ group effect by adding the factor GROUP as a between‐subject factor in the repeated‐measures ANOVA. Then, we performed Kendall's correlation analysis between BW and FW waves and the $L{I}_{general}$ and between FW and BW waves and ∆α averaged across conditions.

Second, to investigate whether TWs are modulated by event onset, we performed an event‐locked analysis on the segmented epochs from −1.5 to 2 s around each shape onset. This analysis was not applied to the 2D‐FFT method due to its relatively poor time resolution. We conducted a time‐resolved analysis aligned to event onset, performing a time point‐by‐time point multiway ANOVA with false discovery rate (FDR) correction to test for the effects of multiple factors (CONDITION and EVENT TYPE or TARGET), thereby explicitly considering temporal dynamics relative to the stimulus. For FW waves, we focused on the post‐stimulus interval, as they are hypothesized to reflect PEs and/or target‐related processing. Accordingly, FW activity was baseline‐corrected using the −0.3 to 0 s interval preceding event onset. Conversely, BW waves were examined in the pre‐stimulus interval, where they are thought to carry top‐down predictions. In this case, no appropriate baseline period was available: a post‐stimulus baseline would be confounded by stimulus‐evoked responses, while an earlier pre‐stimulus baseline would similarly subtract the anticipatory activity that constituted the signal of interest.

2.6. Statistical Analysis

The time point‐by‐time point ANOVA with FDR correction for the TWs was performed in MATLAB. The remaining statistical analyses were performed in JASP [56]. For all measures on which we performed repeated‐measures ANOVA or Kendall's correlation, we used both classical and Bayesian methods, and we reported both p‐values (p), as a measure of the significance of the effect, and Bayes factor (BF), as a measure of its effect size. Bayesian analyses provide BFs, which quantify the ratio between the null and alternative hypotheses. In this study, we report BFs as BF₁₀, where larger values provide stronger evidence in favor of the alternative hypothesis.

3. Results

3.1. Behavioral Performances

The repeated‐measures ANOVA analysis of the behavioral performances (Figure 2A) showed a significant CONDITION effect for False Alarms (BF₁₀>3 and p <0.05), but no significant effect of CONDITION for both Miss and Hit (BF₁₀ = 0.3 and p >0.05). We found a significant effect of CONDITION also for the perceived predictability scores (questionnaire ratings) (BF₁₀ =${10}^{22}$ and p <0.001), with higher rates for more predictable sequences, and for anticipated targets (BF₁₀>${10}^4$ and p <0.001), with higher target anticipation for predictable conditions. Regarding the RT (Figure 2B, rightmost panel), we found a very strong effect of EVENT TYPE and its interaction with CONDITION (BF₁₀>${10}^5$ and p <0.001 for both), and no significant effect of CONDITION (BF₁₀<0.3 and p >0.05). Overall, these results suggest that the regularities influenced participants’ behavior and that they were aware of them, as indicated by the RTs and questionnaire ratings, respectively.

FIGURE 2.

(A, B) Behavioral results. (A) From left to right panel: percentage of hits, miss, and false alarms, perceived sequence predictability for the two groups of subjects. (B) The graph on the left represents the $L{I}_{cond}$ as a function of condition. The right panel is an illustrative graph of the RT difference between rare and expected target events for the two groups (Believers on the left and Empiricists on the right). (C, D) Pupillary responses. (C) Pupil diameter dynamics for nontarget events: pupillary response as a function of time after shape onset (at t = 0) for rare and expected transitions (in red and green, respectively) for each condition. (D) Average pupil diameter amplitude (left panel) between 0 and 1 s for nontarget events as a function of experimental condition; pupil peak latency (right panel) as a function of experimental condition for nontarget events. The box chart shows the median, the lower and upper quartiles, and the minimum and maximum values that are not outliers (computed using the interquartile range). In the pupil diameter dynamic graphs, the shaded area represents the standard error of the mean. C1 = random condition [0.33 0.33 0.33], C2 = condition [0.60 0.20 0.20], C3 = condition [0.475 0.475 0.05], C4 = condition [0.80 0.10 0.10], C5 = condition [0.90 0.05 0.05].

As a control analysis, to assess whether shape identity influenced RT, we performed a repeated‐measures ANOVA on RT, including CONDITION and SHAPE IDENTITY as factors. The analysis revealed a weak effect of SHAPE IDENTITY (BF₁₀ = 2.6, p = 0.001), a strong effect of CONDITION (BF₁₀ = ${10}^{13}$, p <0.001), and strong evidence against an interaction between the two factors (BF₁₀<0.3, p >0.05), suggesting that the main effect of CONDITION remains robust and is not driven, nor modulated, by differences in target identity.

To further characterize participants’ strategies, we used reaction times to define an LI to assess whether they used statistical regularities (Figure 2B, left panel). We found that this index increased with predictability when computed separately per condition ($L{I}_{cond}$, see Methods for details), suggesting that participants rely more on the regularities as the sequence predictability increases (repeated‐measures ANOVA, effect of CONDITION: BF₁₀ =${10}^8$ and p <0.001).

Next, we split participants into two groups based on the LI computed over all conditions ($L{I}_{general}$), and we compared behavioral outcomes between the two groups. As expected, the behavioral results (Figure 2A,B) show significant differences between the two groups. Figure 2B (right panel) illustrates the RT difference between rare and expected events underlying the LI and group definitions: both groups respond faster to expected events, with a larger RT decrease in Believers than in Empiricists. Regarding the percentage of miss hit and false alarms, repeated‐measures ANOVA showed a strong effect of GROUP (BF₁₀>3 and p <0.05), but no significant interaction between GROUP and CONDITION (BF₁₀<0.3 and p >0.05). Kendall's correlation between $L{I}_{general}$ and average hit, miss, and false alarms average across conditions revealed a strong correlation (BF₁₀>>3 and p <0.05). In other words, the Believer group has significantly higher miss and false alarms and fewer hits rate than the “Empiricists,” independent of the condition, confirming a much more liberal approach for the Believers. Concerning the perceived predictability rating, we found a strong effect of CONDITION and GROUP‐CONDITION interaction (BF₁₀>3 and p <0.001), but no effect of GROUP (BF₁₀<0.3 and p >0.05), but Kendall's correlation between $L{I}_{general}$ and the predictability rating slope revealed a strong correlation (BF₁₀>>3 and p <0.05), suggesting that, while both groups were aware of the regularity level of the experimental condition, subjects who relied more strongly on predictions were also more explicitly aware of them. These results confirm that the two groups reflect opposite strategies: one more conservative, relying mostly on sensory evidence while disregarding predictability, and one more liberal, using statistics to anticipate the target's occurrence.

3.2. Pupillometry

The goal of the pupil analysis was to demonstrate the occurrence of SL and thereby corroborate that participants learned the regularities. Because pupil dilation is known to increase following rare events, we expected pupil responses to reflect SL. Figure 2C shows the difference in the dynamics of pupillary response for rare and expected nontarget events.

The effect of EVENT TYPE, that is, rare or expected events, is calculated by determining the mean pupil diameter amplitude and peak latency after rare and expected nontarget events between 0 and 1 s after event onset (Figure 2D). As shown in Figure 2D (left panel), for the amplitude, repeated‐measures ANOVAs indicate a weak but significant effect of CONDITION (0.3< BF₁₀<3 and p <0.001) and a strong effect of EVENT TYPE and interaction (BF₁₀>>3 and p <0.001). For peak latency (Figure 2D, right panel), instead, ANOVA analysis indicates a strong effect of CONDITION, EVENT TYPE, and interaction (BF₁₀>>3 and p <0.05). Regarding the effect of predictability ratings, including the slope of these ratings as a covariate in the repeated‐measures ANOVA provided evidence against an influence of participants’ statistical awareness on pupil responses. Specifically, no effect was observed for either pupil latency or amplitude (BF₁₀<0.3 and p >0.05). All in all, these results show that pupillary responses are larger and slower for rare events, depending on the condition. These results confirm that participants learn the statistical regularities and are in line with previous studies [57, 58, 59, 60].

3.3. Evoked Response Analysis

The goal of the ERP analysis, similarly to the pupil analysis, was to demonstrate the occurrence of SL and thereby corroborate that participants learned the regularities. Regarding the ERP analysis (Figure 3), we examined differences in responses to rare and expected nontarget events. Notably, ERPs’ late positive components, in particular the P300, have been associated with the processing of unexpected events [50, 61]. In particular, surprising events elicit a larger P300 component [50, 61, 62, 63, 64, 65, 66, 67]. We, therefore, tested whether, in our design, the amplitude and latency of the P300 component are affected by EVENT TYPE and condition. Since we did not expect any laterality, we focused the analysis on two midline electrodes (Pz, Fz), while also inspecting the topographic distribution of the effect. Correspondent analysis for all seven midline electrodes used in the 2D‐FFT analyses (Oz, POz, Pz, CPz, Cz, FCz, and Fz) is provided in the Supplementary Materials.

FIGURE 3.

ERP following nontarget events. (A) ERP dynamic. ERP responses to rare and expected events (in red and green, respectively) at electrodes Pz and Fz across the five conditions. (B) P300 statistic. In the upper panels, the average P300 amplitude (calculated as the average amplitude between 0.25 and 0.5 s after shape onset); in the lower panels, the P300 latency (calculated as the time of maximum amplitude between 0.25 and 0.5 s after shape onset), both for rare and expected events as a function of condition for electrodes Pz and Fz. (C) P300 topography. Topography, for conditions two to five, of the difference between the rare and expected P300 amplitude (first line) and latency (second line). The box charts show the median, the lower and upper quartiles, and the minimum and maximum values that are not outliers (computed using the interquartile range). C1 = random condition [0.33 0.33 0.33], C2 = condition [0.60 0.20 0.20], C3 = condition [0.475 0.475 0.05], C4 = condition [0.80 0.10 0.10], C5 = condition [0.90 0.05 0.05].

Amplitude analysis (Figure 3B, upper panel) revealed that, for electrode Fz, there is a weak effect of CONDITION (BF₁₀ = 1 and p <0.05), and a strong effect of EVENT TYPE and factor interaction (BF₁₀>>3 and p <0.001); for Pz, there is no effect of CONDITION (BF₁₀<0.3 and p >0.05), and a strong effect of EVENT TYPE or factor interaction (BF₁₀>>3<0.3 and p <0.001). Regarding the effect of predictability ratings, including the slope of these ratings as a covariate in the repeated‐measures ANOVA provided evidence against an influence of participants’ statistical awareness on P300 amplitude for both Fz and Pz electrodes (0.3< BF₁₀<3 and p >0.05). The topography of the amplitude difference between rare and expected events (Figure 3C, upper panel) shows a stronger difference in centro‐frontal areas, which increases with the condition. This suggests that the fronto‐central P300 component increased following a rare event compared to an expected one, and that this difference is larger with rarer events, suggesting the involvement of frontal areas in detecting violations in the statistical regularities [14, 68−70].

Peak latency analysis (Figure 3B, lower panel) showed that, for electrode Pz, there is no effect of CONDITION, EVENT TYPE, and their interaction (BF₁₀<0.3 and p >0.05); for electrode Fz, there is no effect of CONDITION (BF₁₀<0.3 and p >0.05), and a strong effect of EVENT TYPE and factor interaction (BF₁₀>>3 and p <0.001). Regarding the effect of predictability ratings, including the slope of these ratings as a covariate in the repeated‐measures ANOVA provided inconclusive evidence against an influence of participants’ statistical awareness on P300 latency for both Fz and Pz electrodes (0.3< BF₁₀<3 and p <0.05). We investigated the topography of the latency difference (Figure 3C, lower panel) between rare and expected events and observed a stronger lag in frontal areas that increases with the condition, indicating that the fronto‐central P300 component is slower after a rare event than after an expected one. Also, latency is not affected by sequence predictability. Still, in frontal electrodes, we observed a difference in latency between rare and expected events for more predictable conditions (C4 and C5).

3.4. Alpha‐Band Oscillatory Activity

3.4.1. Alpha‐Band Power

Regarding the power analysis (Figure 4), we first examined the overall occipital alpha‐power difference between the conditions. According to previous literature [45, 105], parieto‐occipital alpha power is modulated by participants’ task strategy, leading to decreased power for a prior‐driven strategy and increased power for a stimulus‐driven strategy. As we hypothesized that participants are likely to switch their target detection strategy from stimulus‐driven to prior‐driven as the sequence becomes more predictable, we investigated whether sequence predictability affects occipital alpha power by calculating the ∆α index (see Methods for details). This index shows the extent to which each participant undergoes occipital alpha modulation in each condition relative to the random (stimulus‐driven) condition. The bigger ∆α is, the more the subject undergoes occipital alpha power suppression. Repeated‐measures ANOVA showed that for ∆α (Figure 4A), there is an effect of CONDITION (BF₁₀ = 3.6 and p <0.05): ∆α increases with sequence predictability, suggesting, in accordance with previous literature [45, 105], that participants undergo a strategy change with the different conditions that is reflected by occipital alpha suppression. We also correlated the ∆α index with the behavioral $L{I}_{cond}$ index, since the latter suggested that participants shift strategy going toward a prior‐driven with sequence predictability, and that previous literature [45, 105] indicated that participants who use more regularities (i.e., higher $L{I}_{cond}$) also have larger occipital alpha power modulation (higher ∆α). We found evidence in favor of a lack of correlation between the two measures (BF₁₀<0.3 and p >0.05), suggesting that they may reflect different mechanisms.

FIGURE 4.

Alpha power analysis. (A) Occipital ∆α index. The panel shows the ∆α index as a function of sequence predictability. (B) Topography of alpha power. Average alpha power across experimental conditions for Believers (left panel) and Empiricists (right panel). (C) Alpha power across conditions. The panels show the average alpha power for the two participants’ groups (Believers in dark gray and Empiricists in light gray), as a function of sequence predictability, for the electrodes Oz, Pz, Cz, and Fz. The box charts show the median, the lower and upper quartiles, and the minimum and maximum values that are not outliers (computed using the interquartile range). C1 = random condition [0.33 0.33 0.33], C2 = condition [0.60 0.20 0.20], C3 = condition [0.475 0.475 0.05], C4 = condition [0.80 0.10 0.10], C5 = condition [0.90 0.05 0.05].

We then investigated the difference in alpha power between the two participant groups. Figure 4C shows the average alpha power of the four midline electrodes for the two groups. Repeated‐measures ANOVA showed that for electrode Oz, there is a weak effect of CONDITION (BF₁₀ = 1.8 and p <0.05); for electrodes Pz, Cz, and Fz, there is a strong effect of CONDITION (BF₁₀>>3 and p <0.05). This result indicates a reduction in overall alpha power under more predictable conditions, especially in central areas, in line with previous literature [45, 105] that showed that prior‐driven conditions result in desynchronization of alpha power, whereas higher alpha power is observed in stimulus‐driven conditions. Furthermore, for all four electrodes, there is an inconclusive effect of GROUP (0.3< BF₁₀<3 and p >0.05) and no interaction CONDITION‐GROUP for either electrode (BF₁₀<0.3 and p >0.05). Despite the inconclusive results, the alpha power topography shown in Figure 4B (averaged across conditions) suggests a trend in line with previous results, with the group of the Believers having lower alpha power compared to the Empiricists. Furthermore, the correlation between $L{I}_{general}$ and alpha power across conditions for four midline electrodes revealed no effect (Kendall correlations, BF₁₀<0.3 and p >0.05).

3.4.2. Traveling Waves

Concerning the alpha‐band TW analysis (Figure 5A−C), we focused on waves propagating along the anterior−posterior axis, from the occipital to the frontal regions (FW) and in the opposite direction (BW). TWs were assessed using two complementary approaches: the 2D‐FFT and sphere‐fitting methods, which, as discussed in previous work [103], differ significantly in several aspects. The sphere‐fitting method provides substantially higher temporal resolution, as it estimates a phase linear gradient at each time point. On the other hand, the 2D‐FFT considers overlapping time windows of 500 ms, which can introduce temporal smearing effects. In addition, the sphere‐fitting approach considers only trials and time points with high spectral power, whereas the 2D‐FFT relies on the average across all trials.

FIGURE 5.

Alpha‐band traveling waves analysis. (A) Global waves analysis. Average FW and BW wave strength across all blocks as a function of sequence predictability for 2D‐FFT (left panels) and for sphere‐fitting (right panels) methods. (B, C) Event‐locked analysis. (B) Event‐locked dynamics for FW (left) and BW (right) waves, irrespective of event type, as a function of experimental condition. FW are baseline‐corrected using the −0.3 and 0 s interval preceding event onset, whereas BW waves were not baseline‐corrected. (C) Event‐locked dynamics of FW and BW waves according to event type. Left panel: FW wave dynamics (baseline‐corrected from −0.3 to 0 s before event onset) following rare (red) and expected (green) events, averaged across conditions for visual clarity. Central panel: FW wave dynamics (baseline‐corrected from −0.3 to 0 s before event onset) following target (light blue) and nontarget (dark blue) events, averaged across conditions for visual clarity. Right panel: BW wave dynamics (not baseline‐corrected) before target (light blue) and nontarget (dark blue) events, averaged across conditions for visual clarity. (D, E) Traveling wave learning index analysis. (D) Average FW and BW wave strength for the two participant groups (defined according to the learning index) as a function of sequence predictability. (E) Correlation between the learning index and overall BW and FW waves, averaged across experimental conditions. The scattered line represents the least‐squares fit.

In all panels, the shaded area represents the standard error of the mean. The box charts show the median, the lower and upper quartiles, and the minimum and maximum values that are not outliers (computed using the interquartile range). C1 = random condition [0.33 0.33 0.33], C2 = condition [0.60 0.20 0.20], C3 = condition [0.475 0.475 0.05], C4 = condition [0.80 0.10 0.10], C5 = condition [0.90 0.05 0.05].

In this work, we performed two analyses: a global analysis and an event‐based one. Concerning the global analysis (Figure 5A), we tested whether FW and BW waves are modulated by the predictability condition across all blocks (regardless of type and event onset). In particular, we hypothesized that participants would rely more on sensory evidence rather than predictions in more unpredictable conditions (i.e., C1), and this would be reflected in an overall increase in FW waves; conversely, in more predictable conditions (i.e., C5), participants would rely more on the regularities, thus having an overall increase in BW waves. For both FW and BW and using both TW detection methods, we found a convincing lack of effect for the factor CONDITION (BF₁₀<0.3 and p >0.05), thus providing no evidence toward the hypothesis that alpha‐band TWs reflect the learning of statistical regularities.

We then performed an event‐locked analysis (Figure 5B,C) in which we investigated whether TWs are modulated by event onset. Given the relatively poor temporal resolution of the 2D‐FFT method, we focused this analysis on the sphere‐fitting method. We first investigated changes in FW and BW waves around shape onset (regardless of the type of event) as a function of the condition (Figure 5B). FW waves (Figure 5B, left panel), baseline‐corrected between −0.3 and 0 s before event onset, revealed no difference between conditions, as confirmed by a time point‐by‐time point multiway ANOVA considering the effect of CONDITION and including FDR correction (for all time points, p >>0.05). Similar results were obtained for the BW waves (Figure 5B, right panel; all ps >>0.05), which we analyzed using a similar approach but without baseline correction, as in this case, no suitable baseline was available: a post‐stimulus baseline would include evoked responses, whereas an earlier pre‐stimulus baseline would remove the anticipatory activity of interest. These results provide clear evidence against the hypothesis that alpha band FW and BW waves are modulated by sequence predictability in relation to event onset.

We then investigated whether the event nature (target, nontarget, rare or expected) modulates wave strength (Figure 5C). We observed no difference in baseline‐corrected FW waves between rare and expected events, as well as between target and no target (Figure 5C, left and central panels; all ps >>0.05 in a time point‐by‐time point multiway ANOVA with CONDITION and TARGET or EVENT TYPE as factors). Interestingly, and contrary to previous hypotheses [31, 32, 40, 71], this result suggests that FW waves may not reflect PEs during SL, nor do they relate to the saliency of the target onset. Concerning the BW waves (Figure 5C, rightmost panel), our analysis did not detect any difference between expected target and nontarget conditions, as confirmed by a time point‐by‐time point multiway ANOVA with CONDITION and TARGET as factors (all FDR‐corrected p >>0.05). This last analysis supports the hypothesis that BW waves are not modulated by sequence predictability and target prediction.

3.4.3. Traveling Waves and Learning Index

To characterize the relationship between participants’ behavioral strategies and TWs, we performed the same LI analysis on the global TW measures derived from the sphere‐fitting method (Figure 5D,E). As shown in Figure 5D (left panel), we found no effect of either CONDITION or GROUP for the FW waves, nor their interaction (BF₁₀<0.3 or 0.3< BF₁₀<3 and p >0.05). For BW waves (Figure 5D, right panel), the analysis revealed no effect of either CONDITION or their interaction (BF₁₀<0.3 and p >0.05), but a weak effect of GROUP (BF₁₀ = 1.6 and p <0.05), indicating a higher amount of BW waves in the Believers group. Interestingly, a Kendall's correlation between $L{I}_{general}$ and TWs averaged across condition (Figure 5E) revealed a correlation for BW waves (BF₁₀ = 2.2 and a p <0.05), but not for FW waves (BF₁₀<0.3 and p >0.05). This result suggests that BW waves may index different learning strategies, in line with previous hypothesis [105]. Future work will evaluate this compelling hypothesis more directly.

4. Discussion

The goal of the present study was to explore the link between alpha‐band TWs and predictive processes using a visual SL paradigm. Our results show that regularities influenced participants’ behavior both in their RT and awareness of the sequence predictability (higher perceived predictability ratings were assigned to more predictable sequences). Importantly, we show that physiological measures, including pupil size, ERP responses, and spectral power, were also modulated by different levels of regularity. Lastly, our results provide evidence against the hypothesis that alpha‐band TWs broadly reflect predictive processes, as alpha waves were not modulated by sequence predictability or event saliency or surprisal. However, we did find anecdotal evidence for modulation of overall BW waves in relation to the participant's strategy. Participants who used the regularities more had a higher occurrence of BW waves compared to those who relied more on the stimuli, highlighting a possible role of these waves in shaping cognitive strategy [105].

Our behavioral results are in line with previous work [17, 20, 72, 73, 74, 75] showing that the regularities induced by SL paradigms improve target detection timing by allowing participants to predict and anticipate target occurrence. It is well known that brain arousal affects pupil size, and this effect is thought to reflect increased sympathetic activity [76]. One way to induce arousal is surprisal, that is, the degree of an observation's unexpectedness. In particular, pupil dilation has been shown to reflect conscious and unconscious surprise, with an inverse relationship between stimulus probability and pupil size [57, 58, 59, 60, 77, 78, 79, 80]. In line with these findings, our data show slower, more pronounced pupil dilation following novel or surprising information than following expected information, with an effect increasing with the rarity of the event. We also found a strong modulation by both event surprisal and sequence predictability in the ERP analysis of the late component, P300. The P300 has previously been shown to be enhanced by surprising events [62, 63, 64, 65, 66, 67], and has been related to context‐updating mechanisms [50, 62, 67, 81], and to the Bayesian brain hypothesis [63, 64, 65, 66]. In this framework, the P300 would be interpreted as a result of PE transmission. Fronto‐central P300 component, also called P3a or Novelty P300, seems to depend on the novelty of stimuli, and it is thought to reflect the frontal lobe function of novelty processing [17, 50, 74, 75]. In line with this interpretation, we found that for nontarget events, the amplitude of the fronto‐central P300 component is higher, and its latency is slower, following unexpected shape transitions as compared to expected ones, and this effect increases as the predictability of the stream of shapes is higher (i.e., the more surprising the unexpected event is). However, this stationary ERP effect was not accompanied by a corresponding increase in TWs propagating along the cortex, as we observed no effect of novelty on FW TW measures. This apparent dissociation may reflect the limited sensitivity of our methods for quantifying TWs. Alternatively, it is possible that the novelty‐related P300 response may predominantly reflect a spatially stationary process, rather than activity that propagates across the cortex in the form of TWs. Another possibility is that TW dynamics associated with novelty processing occurred outside the alpha frequency band.

In our paradigm, participants were explicitly informed that target detection difficulty would vary across blocks, based on evidence that such instructions can enhance SL by improving sensitivity to regularities [82, 83, 84]. This effect is thought to reflect increased engagement of attention‐dependent mechanisms [84, 85], which may also promote the formation of conscious hypotheses, influencing pupil dilation and ERP responses. However, control analysis ruled out this possibility, confirming the robustness of both ERP and pupil findings.

Therefore, along with the behavioral results, the pupillary and ERP results provide robust evidence that participants learned the statistical regularities embedded in the sequence.

Previous work has proposed the hypothesis that FW and BW alpha‐band TWs relate to predictive processes [31, 32]. Computational models of cortico−cortical interactions [31, 39] further suggest that alpha‐band FW waves convey bottom‐up to sensory information and PEs, while BW waves carry top‐down predictions. Recent experimental work seems to provide indirect evidence in favor of this interpretation. In particular, supporting the theoretical framework that suggests modulation of precision‐weighted PEs in specific neuroatypical populations [86, 87], experimental work found altered top‐down and bottom‐up alpha‐band TWs in schizophrenia patients [40] and in autistic populations [102]. Similarly, psychedelic drugs have been proposed to relax the precision of high‐level priors or beliefs, eliciting an increase in bottom‐up, PE‐related activity [88]. Experimental results analyzing alpha‐band TWs in healthy subjects during psychedelics intake provided evidence corroborating this interpretation [41]. Together, these findings indirectly suggest that experimentally manipulating predictive processes should alter the balance between FW and BW alpha‐band TWs, with stronger top‐down predictions favoring BW waves and increased sensory PEs favoring FW waves. In this work, we investigated this hypothesis for the first time in scalp EEG recordings using a visual SL paradigm. Our paradigm manipulated shape‐sequence predictability to induce expectations and PEs. We hypothesized that: (1) sequence predictability would modulate overall FW and BW activity across blocks, with a more predictable block being dominated by showing a predominance of BW; (2) FW and BW would vary with event onset and type (rare vs. expected; target vs. nontarget). Specifically, we predicted stronger FW responses to salient events (rare and targets) compared to nonsalient events (expected and nontargets), consistent with FW reflecting PEs. Furthermore, if pre‐stimulus BW carries prior information, we expected higher BW before target events (given their task relevance) than nontargets, with this increase scaling with event expectedness. Contrary to our hypotheses, although behavioral and physiological data confirmed that participants learned the statistical regularities, our findings do not support the idea that alpha‐band TWs reflect predictive processes in visual SL. FW and BW waves were not modulated by sequence predictability, either overall or at event onset. FW did not index PEs or target salience, and BW was unaffected by predictability or target expectation. Importantly, even participants who actively used predictions to perform the task, the Believers showed no modulation of TWs by sequence predictability. Thus, excluding participants who did not rely on predictions did not alter the pattern of results. This may indicate that our paradigm did not induce sufficiently strong expectations to modulate wave strength, or that any modulation was too subtle to detect. Alternatively, TWs may not carry predictive coding signals, or may do so only in other contexts, such as encoding temporal rather than visual‐feature predictions.

It is worth noting that experimental work with intracortical recordings found a relationship between the phase of alpha‐band oscillations and the predictability of cues and targets [71], suggesting that different experimental designs or recordings with a higher signal‐to‐noise ratio could better delineate the validity of this hypothesis. One main limitation of prior work using scalp‐EEG recordings is that earlier results were mainly obtained during closed‐eyes resting states [40, 41], that is, in the absence of visual stimulation. It is possible that the high‐amplitude visual responses evoked by repeated stimulation in our paradigm masked any modulation of BW and FW waves induced by the predictability. A different design may provide a means to better disentangle visual responses from higher‐order predictive processes. Moreover, these studies focused on long‐term, global shifts in the balance between FW and BW waves rather than on short‐term modulations driven by trial‐by‐trial predictions [40, 41]. Interestingly, the only weak effect we found for TWs was between groups of subjects (with Believers, i.e., subjects who relied more on sequence regularities and exhibited more BW waves). This could suggest that modulation of TWs reflects global network states on a longer time‐scale (e.g., cognitive strategy, arousal) rather than local processing dynamics at a time‐scale of a few oscillatory cycles, as in the event response. This interpretation is also in line with the modulation of TWs by attentional state [89]. Future studies may rely more strongly on comparisons between groups of subjects or induce modulations at longer time scales.

It is important to note that a precise understanding of the neural correlates of macroscopic TWs is still being developed. It has been shown that two spatially discrete dipole sources at the scalp level [90] or multiple discrete clusters of time‐lagged activity [91] could explain the observed cortical TW measured by EEG and MEG, consistent with the idea that TWs at the scalp level result from the summation of neuronal activity generated by phase‐lagged dipoles. These accounts, all assuming interareal communication as the correlate of macroscale waves, formed the basis for our hypotheses about a possible association between TWs and top‐down modulation. However, recent studies have shown that mesoscopic TWs (i.e., within a single cortical area) can also give rise to global waves in EEG/MEG [92, 101]. This account is supported by recordings at the cortical level showing that the evoked response in early visual areas (V1/V2) propagates locally as a TW [26, 93]. A potential influence of these mesoscale components provides an alternative explanation for why we did not find a direct modulation of TWs by expectation.

Importantly, the small effect we observed in the exploratory analysis of the total amount of BW as a function of participants’ task strategy matches that observed previously [105]. However, unlike that study, we did not find the reverse effect for FW waves. This discrepancy is likely due to differences in the task between the two experiments: their study used a target detection paradigm with high visual demand, whereas in our task, the target simply had to be reported. Since, according to our hypothesis, FW waves reflect visual sampling and processing, a detection task employing a difficult‐to‐perceive target could elicit a higher number of FW waves than an easily detectable target.

Remarkably, we replicate the modulation of occipital alpha amplitude following a strategy shift, showing increased alpha suppression in conditions where participants rely more on prior expectations compared to stimulus‐driven conditions. We also measured a behavioral marker of the participant's strategy change across conditions (the $L{I}_{cond}$ index), indicating a shift toward a prior‐driven strategy for more predictable conditions. These two measures provide both behavioral and physiological evidence of the effect induced by sequence predictability, but, interestingly, we found that these two indices did not correlate, suggesting that they may reflect different mechanisms. One possible interpretation is that stronger alpha suppression in predictable conditions reflects increased attentional allocation [35, 94, 95, 96, 97], consistent with classical views of alpha activity, rather than strategy‐dependent modulation. Attentional demands may differ across conditions: as participants learned sequence regularities, they may have become more engaged in target detection, whereas random sequences promoted a more passive attentional state. However, despite these attentional differences, BW waves were not modulated, contrasting with previous links between top‐down waves and visual attention [89, 98, 99], and suggesting that the relationship between TWs and attentional state may be more task‐dependent than previously assumed.

Unlike Tarasi and colleagues, who report that a bias shift toward a prior‐driven strategy is accompanied by occipital alpha suppression, an increase in BW waves, and a decrease in FW waves, in our experimental design, the strategy changes and alpha suppression were not accompanied by a modulation of overall FW and BW waves. However, in line with their study, we observed a weak relationship between BW waves and the participant's overall strategy. Given the small effect size, this provides only anecdotal evidence for the hypothesis that the magnitude of alpha‐band BW TWs relates to the differences in predictive styles: prior‐driven individuals (Believers) showed an increase in BW waves compared to sensory‐driven individuals (Empiricists). Revisiting the predictive account of TWs, we could hypothesize that BW waves reflect top‐down processes by modulating the alpha power in lower regions, which is assumed to integrate prior information and modulate decision‐making outcomes [45, 100]. Our results only partially support this interpretation, as we observed only a trend in the difference in occipital alpha power between the two groups, and the effect on TWs was limited. A possible explanation for this difference could be differences in the experimental design or in how we defined the two groups: we categorized participants based on their behavioral outcome, while previous studies 45, 105 defined it based on differences in occipital alpha power desynchronization. Future work will be needed to further disentangle the relationships between these variables.

Author Contributions

M.P.: Conceptualization, data curation, investigation; formal analysis, methodology, Writing – original draft. J.C.B.S.: Methodology, software, Writing – review and editing. A.A.: Conceptualization, funding acquisition, project administration, supervision, Writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

nyas70424‐sup‐0001‐SuppMat.docx

nyas70424‐sup‐0002‐FigureS1.pdf

nyas70424‐sup‐0003‐FigureS2.pdf

nyas70424‐sup‐0004‐FigureS3.pdf