Statistical and sequence learning lead to persistent memory in children after a one-year offline period

Extraction of environmental patterns underlies human learning throughout the lifespan and plays a crucial role not only in cognitive but also perceptual, motor, and social skills. At least two types of regularities contribute to acquiring skills: (1) statistical, probability-based regularities, and (2) serial order-based regularities. Memory performance of probability-based and/or serial order-based regularities over short periods (from minutes to weeks) has been widely investigated across the lifespan. However, long-term (months or year-long) memory performance of such knowledge has received relatively less attention and has not been assessed in children yet. Here, we aimed to test the long-term memory performance of probability-based and serial order-based regularities over a 1-year offline period in neurotypical children between the age of 9 and 15. Participants performed a visuomotor four-choice reaction time task designed to measure the acquisition of probability-based and serial order-based regularities simultaneously. Short-term consolidation effects were controlled by retesting their performance after a 5-h delay. They were then retested on the same task 1 year later without any practice between the sessions. Participants successfully acquired both probability-based and serial order-based regularities and retained both types of knowledge over the 1-year period. The successful retention was independent of age. Our study demonstrates that the representation of probability-based and serial order-based regularities remains stable over a long period of time. These findings offer indirect evidence for the developmental invariance model of skill consolidation.


Statistical analysis
Similarly to RT values (see Statistical analyses section of the Manuscript), prior developmental studies showed that age has a large effect on average accuracy [2][3][4] . To test this, we first calculated average accuracy over the 10 epochs (i.e., accuracy data was calculated on all trials, irrespective of trial types). We then correlated the average accuracy with age, which revealed a significant positive correlation (r(68) = .32, p = .007), showing that younger children were less accurate on the task. To control for the effect of average accuracy differences related to age on learning and consolidation of knowledge, we transformed the data in the following way. We divided each participants' raw accuracy values of each trial type and each epoch by 2 their own average performance (i.e., average accuracy) in the first epoch of the task (for a similar approach, see 5,6 ). Participants' performance was around 1 at the beginning of the task and changed as the task progressed. Values above 1 indicated that responses were more accurate on a given trial type than the responses combined to all trial types (i.e., average accuracy) in the very first epoch of the task; and values below 1 meant that responses were less accurate on a given trial type compared to average accuracy in the first epoch. We conducted all analyses in the Supplementary Material on standardized accuracy.
Statistical learning score in the Learning Phase and memory scores in the Testing and Retesting Phases were quantified as the difference between random high and random low trial types in accuracy (accuracy for random high minus accuracy for random low trials). The learning and memory scores of sequence learning were calculated as the difference between pattern and random high trial types in accuracy (accuracy for pattern minus accuracy for random high trials). Higher scores indicate larger statistical or sequence learning/memory. To assess learning and the retention of knowledge, repeated measures ANOVAs and paired-samples ttests were conducted on standardized accuracy data, separately for statistical and sequence

Prerequisite of memory consolidation
To assess memory consolidation, significant learning has to occur preceding the offline period. Therefore, as a first step, we conducted repeated-measures ANOVAs on the Learning 3 Phase to confirm that significant learning has occurred concerning both statistical and sequence learning. ANOVAs were conducted on standardized accuracy separately for statistical and sequence learning.

Do children retain regularities after a one-year offline period?
To test one-year retention of statistical knowledge, we conducted a two-way repeated- Moreover, similarly for the learning scores, to investigate whether individual differences influence the consolidation of statistical or serial-order knowledge, we correlated the offline change scores with working memory capacity, with percentage of perseverative errors on the WCST task, with socioeconomic status and with total problem score on the SDQ.
To control for multiple comparisons, we employed False Discovery Rate correction. None of the correlations reached significance (all ps > .766). We also rerun the ANOVAs on the sample without left-handed participants to control for handedness. The results were identical to the ones on the whole sample. Does age affect the one-year retention of statistical and serial-order regularities? 7 To check the possible association between age and retention, we conducted Pearson's correlation between the offline change scores and age. Regarding statistical knowledge, offline change scores did not show correlation with age (r(68) = .01, p = .92, BF01 = 6.67). Concerning serial-order knowledge, offline change scores in accuracy also did not correlate with age (r(68) = .15, p = .21, BF01 = 3.08).