Experimental design and structure of the oculomotor ASRT task.

A) In the task, participants viewed four empty circles arranged in a square in each corner of the screen, with one circle turning blue on each trial. In the stream of stimuli, every second trial was part of an 8-element probabilistic sequence. Random elements were inserted among pattern elements to form the sequence (e.g., 1-R-3-R-2-R-4-R, where numbers indicate the location of one of the four circles on the screen, and R represents random positions). B) Each trial consisted of two phases: an anticipatory phase (response–stimulus interval, RSI) and a response phase. On each trial, one of four empty circles turned blue, signaling the target stimulus. Participants were instructed to shift their gaze as quickly and accurately as possible to the blue circle and maintain fixation for at least 100 ms. Once fixation was detected, the stimulus disappeared, and after a 500-ms RSI, the next target appeared. Oculomotor reaction time (oRT) was defined as the latency from target onset to fixation on the target location. The schematic illustrates the temporal sequence of events: disappearance of the previous stimulus, the anticipatory phase, onset of the current stimulus, response phase, and transition to the next anticipatory phase. C) Formation of triplets in the task. Pattern elements are represented by orange backgrounds (they appear consistently in the same position throughout the task), and random elements are represented by red backgrounds (they appear randomly in one of the four possible positions). Every trial can be identified as the third element of three consecutive trials (a triplet) in a sliding window manner. The probabilistic sequence structure results in some triplets occurring with a higher frequency (high-probability triplets, 62.5% of all trials, indicated with dark blue backgrounds on the figure) than others (low-probability triplets, 37.5% of all trials, indicated with light blue backgrounds on the figure). Statistical learning is operationalized as the performance improvement in high-probability trials compared to low-probability trials. Ten repetitions of the 8-element sequence (80 trials) make up one block of the task. D) The formation of high-probability triplets can involve the occurrence of either two pattern trials with one random trial between them, which occurs in 50% of trials; or two random trials with one pattern trial between them, which occurs in 12.5% of trials. In total, 62.5% of all trials constitute the final element of a high-probability triplet, while the remaining 37.5% are the final elements of a low-probability triplet. E) The task was organized into blocks, each consisting of 80 trials (ten repetitions of an 8-element sequence), preceded by five initial random warm-up trials that were excluded from all analyses. A unit of 5 blocks is referred to as an epoch, which thereby contains 400 trials. Participants were familiarized with the task by completing one practice epoch containing only random trials. The actual task comprised four epochs containing the alternating sequence. After every epoch, calibration was reassessed based on the last 20 trials, and recalibration was performed if necessary.

Data quality measures of eye tracking data

Determination of the predicted stimulus using minimal angular deviation.

The schematic illustrates the method for classifying anticipatory saccades. The saccade vector (solid blue arrow) is defined by the gaze coordinates at saccade onset and offset. Reference vectors (dashed black arrows) connect the onset to the center of each of the potential stimulus locations. We computed the angular difference between the saccade vector and each reference vector; the stimulus location minimizing this deviation (minimal angular deviation; red arc) was identified as the predicted target stimulus.

Metrics used for the analysis of eye tracking data

Categorizing saccades.

During the anticipatory phase (response–stimulus interval, RSI), participants’ first valid saccade was recorded to capture anticipatory eye movements. Saccades toward a high-probability upcoming stimulus was defined as a learning-dependent (LD) anticipation, whereas saccades directed elsewhere were classified as not-learning-dependent (NLD). Each trial was further categorized as correct if the first saccade of the anticipatory phase was directed to where the stimulus subsequently appeared, or as an error if it was directed elsewhere. This resulted in four saccade categories: learning-dependent correct (LDC), learning-dependent error (LDE), not-learning-dependent correct (NLDC), and not-learning-dependent error (NLDE). The schematic illustrates the sequence of events, the detection of anticipatory gaze shifts, and their categorization into these four saccade types.

Schematic illustration of iterative updating.

For each trial, we determined whether the presented triplet (e.g., 2-1-4) had occurred previously. Trials with novel triplets were excluded. For repeated triplets, the participant’s saccade at the current occurrence was compared to their saccade at the preceding occurrence of the same triplet. The schematic depicts this comparison between the previous and current occurrence of an identical triplet, irrespective of whether the earlier prediction was correct.

Statistical learning in the task.

The x-axis represents epochs of the ASRT task (the progression of time). The y-axis represents performance in terms of oRTs (ms). The lines and markers show the trajectory of oRTs as a function of high-probability (dark blue line with circle markers) and low-probability (light blue line with triangle markers) triplets. The difference between high- and low-probability triplets represents statistical learning. Note that stimuli were presented randomly in Epoch 0 (marked as grey), serving as familiarization before the start of the actual task. Error bars show 1 SEM.

The ratio of learning-dependent anticipations in the task.

The x-axis represents epochs of the ASRT task (the progression of time). The y-axis represents epochwise mean LDAR, the proportion of learning-dependent first saccades relative to all gaze shifts (that is, both toward high- and low-probability upcoming stimuli). The mauve line shows the trajectory of LDARs throughout the task. Note that stimuli were presented randomly in Epoch 0 (marked as grey), serving as familiarization before the start of the actual task. Error bars show 1 SEM.

Likelihood of saccade types in the task.

The x-axis represents epochs of the ASRT task (the progression of time). The y-axis represents the likelihood of saccade types, that is, their epochwise proportions standardized against their chance-level probabilities. As a result, a likelihood of 1 reflects chance-level probability (marked by a dashed grey line). The yellow line and circle markers represent the trajectory of the likelihood of learning-dependent correct saccade in the task, the orange line and triangle markers represent that of learning-dependent errors, the blue line and square markers represent that of not-learning-dependent corrects, and the green line and diamond markers represent that of not-learning-dependent errors. Note that stimuli were presented randomly in Epoch 0 (marked as grey), serving as familiarization before the start of the actual task. Error bars show 1 SEM.

The ratio of the iterative updating of saccade types in the task.

The x-axis represents epochs of the ASRT task (the progression of time). The y-axis represents epochwise mean update ratio, that is, the proportion of updated trials relative to all trials for each saccade type, separately. The yellow line and circle markers represent the trajectory of update ratios of learning-dependent correct saccades, the orange line and triangle markers represent that of learning-dependent errors, the blue line and square markers represent that of not-learning-dependent corrects, and the green line and diamond markers represent that of not-learning-dependent errors. Error bars show 1 SEM. Note that in this analysis, the practice (random) epoch is only presented in the visualization but could not be included in the analysis, as that would have altered the iterative measure derived from the analyzed data (since most triplets occurred the first time in this period).

Likelihood of update types in the task.

The y-axis represents the likelihood of update types, that is, their epochwise proportions standardized against their chance-level probabilities. As a result, a likelihood of 1 reflects chance-level probability (marked by a dashed grey line). Error bars show 1 SEM. A) Trajectories of update type likelihoods in the task. The x-axis represents epochs of the ASRT task (the progression of time). The turquoise line and round markers represent the trajectory of the likelihood of LD same occurrences in the task, the purple line and triangle markers represent that of NLD same occurrences, the pink line and square markers represent that of NLD-to-LD updates, the green line and diamond markers represent that of LD-to-NLD updates, and the brown line and star markers represent that of NLD-to-other-NLD updates. B) Distribution of likelihood values across update types. Each dot represents a single trial, with half-violins showing the density of the distribution and boxplots indicating the median and interquartile range. The x-axis represents the different update types.