Strategy-based motor learning decreases the post-movement b power

Motor learning depends on the joint contribution of several processes including cognitive strategies aiming at goal achievement and prediction error-driven implicit adaptation. Understanding this functional interplay and its clinical implications requires insight into the individual learning processes, including at a neural level. Here, we set out to examine the impactoflearningacognitivestrategy,overandaboveimplicitadaptation,ontheoscillatory post-movement b rebound (PMBR), which typically decreases in power following (visuo) motorperturbations.


Introduction
The ability to adjust movements according to current environmental demandsdmotor learningdis fundamental to survival. Several component processes jointly contribute to motor learning . One component that has attracted considerable attention is learning by using a cognitive strategy (McDougle, Ivry, & Taylor, 2016;McDougle & Taylor, 2019;Taylor, Krakauer, & Ivry, 2014;Taylor & Ivry, 2011). Strategy-based learning occurs when a movement fails to achieve a desired outcome (goal achievement error), and action selection is therefore revised (McDougle et al., 2016;Morehead, Qasim, Crossley, & Ivry, 2015;Taylor & Ivry, 2014). For reaching movements, revised action selection can correspond to aiming elsewhere than directly at the target when the previous reach missed that target.
However, motor learning continues even when participants commit to a given strategy (Mazzoni & Krakauer, 2006), or when they are told to give up any strategy that they have been using (Morehead et al., 2015). Such learning has been called implicit, in the sense that it is not deliberate, and may even be undesired, given the task at hand (Hadjiosif & Krakauer, 2021;Mazzoni & Krakauer, 2006). One important factor thought to drive implicit learning is a discrepancy between the actual and the (implicitly) predicted movement outcome, i.e., prediction error (Shadmehr, Smith, & Krakauer, 2010; see Kim, Parvin, & Ivry, 2019, for an additional influence of goal achivement error on implicit learning). A prediction error can exist even when a movement achieves the desired goal (Mazzoni & Krakauer, 2006). Consequently, the motor system is continuously adapting its output by adjusting predictions of movement outcomes through a process of internal model recalibration, which depends on the cerebellum (Morehead, Taylor, Parvin, & Ivry, 2017;Taylor, Klemfuss, & Ivry, 2010;Tseng, Diedrichsen, Krakauer, Shadmehr, & Bastian, 2007).
Implicit adaptation operates in parallel to cognitive strategies (Mazzoni & Krakauer, 2006), and can compensate for noise in low-fidelity explicit learning (Miyamoto, Wang, & Smith, 2020). On the other hand, cognitive strategies may help compensate for impaired implicit learning, e.g., in patients with cerebellar degeneration (Taylor et al., 2010;Wong, Marvel, Taylor, & Krakauer, 2019). To understand this interplay, and its clinical implications, it is important to examine the two forms of learning individually, and thus to isolate them experimentally (Donchin & Timmann, 2019).
Isolating different forms of learning might be achieved with the help of electroencephalography (EEG). Several EEG signals are modulated during motor learning (for a recent review, see Reuter, Booms, & Leow, 2022). Among these, neural oscillations, particularly in the b frequency band (i.e.,~15e30 Hz) have received considerable attention. b power changes systematically around the time of a movement: during the movement, it decreases; following movement offset, it increases again (postmovement b rebound, PMBR, e.g., Pfurtscheller & Da Silva, 1999). The PMBR decreases in amplitude in reaching tasks once a visuomotor rotation or force-field is introduced (Alayrangues, Torrecillos, Jahani, & Malfait, 2019;Darch, Cerminara, Gilchrist, & Apps, 2020;Klimpke, Henkel, Heinze, & Stenner, 2020; Palmer, Auksztulewicz, Ondobaka, & Kilner, 2019; Tan, Wade, & Brown, 2016;Tan, Jenkinson, & Brown, 2014;Tan, Zavala, et al., 2014;Torrecillos, Alayrangues, Kilavik, & Malfait, 2015). However, whether this change is related to learning a strategy or to implicit learning, remains largely unclear (but see Jahani, Schwey, Bernier, &Malfait, 2020, andKlimpke et al., 2020, for attempts to disentangle EEG modulations associated with a cognitive strategy vs. implicit learning). Consequently, in this study, we aim to identify how a task that requires strategic re-aiming over and above implicit learning changes the PMBR, compared to a task that excludes strategic re-aiming (in the sense of aiming elsewhere than directly at the target to achieve a goal), and isolates implicit learning. To start with, let us consider two important methodological aspects.
First, Morehead et al. (2017) introduced an experimental paradigm that allows isolating implicit learning. In this paradigm, visual feedback is clamped at a given rotation relative to the target and is therefore invariant to participants' movement direction. Participants know they cannot influence the direction in which visual feedback is moving. Therefore, they ignore the rotation and aim directly at the target. Nevertheless, healthy participants adapt their movements (Morehead et al. 2017;Kim et al., 2018Kim et al., & 2019Avraham et al., 2021;, a process that depends on the integrity of the cerebellum (Morehead et al., 2017). Here, we isolated implicit learning by implementing a condition in which the rotated feedback was clamped, and participants were instructed to aim directly at the target. We compared performance and EEG during this task to a second task, in which participants were instructed to re-aim in order to compensate for a visuomotor rotation (i.e., a rotation that is contingent on movement direction).
Second, in many motor learning experiments, adaptation is studied across an extended period of time, throughout which a kinematic or dynamic perturbation remains switched on. Strategic re-aiming is particularly pronounced during early learning, i.e., in the first few trials (Butcher et al., 2017;Taylor, Krakauer, & Ivry, 2014). However, to achieve sufficient signalto-noise ratio, EEG typically requires more than a few trials. To overcome this challenge, we investigated learning across pairs of two consecutive rotated trials, which were unpredictably interspersed among many non-rotated trials (see also Torrecillos et al., 2015, for a similar "distributed learning" EEG paradigm). In most trials, participants performed centre-out reaches in which the feedback veridically followed their movements (2/3 of the trials). In 1/3 of the trials, the visual feedback was rotated, always for two consecutive trials, which were pseudo-randomly interspersed between non-rotated trials. In the condition involving a strategy (Compensate condition), participants learnt about the direction and angle of visuomotor rotation in the first trial, and then aimed in the opposite direction to counteract the rotation in the second trial (for a similar learning-execution structure, see McDougle & Taylor, 2019). This strategy could not yet be used in the first trial with a rotation, because that trial, and the magnitude and direction of rotation, were unpredictable. Therefore, mental processes involved in re-aiming had to occur between visual feedback on the first rotated trial, and movement onset on the second rotated trial. In the condition involving implicit learning without any re-aiming (Ignore condition), participants were told to ignore the rotated (clamped) feedback in the two consecutive trials, and to continue aiming directly at the target.
We expected that both conditions would lead to implicit learning, evident in an after-effect in the trial following each pair of rotations. In addition, we expected prominent reaiming in the second rotated trial in the Compensate condition, but not in the Ignore condition. At a neurophysiological level, we hypothesized that the PMBR would decrease more strongly in the Compensate condition, compared to the Ignore condition. Data from previous studies indicate that factors promoting strategic re-aiming, such as large goal achievement errors, or a change in context (Morehead et al., 2015), also result in a more pronounced decrease of the PMBR (Tan et al., 2016;Tan, Jenkinson, & Brown, 2014). We therefore hypothesized that the PMBR decrease observed in some of the previous literature is at least partly due to re-aiming, and that reaiming in our study should lead to a more pronounced decrease of the PMBR than implicit adaptation only.

2.
Materials and methods

Participants
Data were collected from 30 healthy participants (15 male & 15 female, mean age: 23.8 y. o., age range: 19e32 y. o.). We report how we determined our sample size, all data exclusions, all inclusion/exclusion criteria, whether inclusion/exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study. We estimated that a sample size of 30 participants would provide sufficient power, given previous visuomotor rotation studies which observed a decrease of PMBR with substantially smaller sample sizes (e.g., Tan et al., 2016;Tan, Jenkinson, & Brown, 2014;Torrecillos et al., 2015). Participants gave written informed consent for study participation and were excluded/included based on a priori defined criteria. That is, four participants (3 male & 1 female) were excluded from the analyses due to failure to follow task instructions i.e., ignore/compensate for the rotation, as evident in the changes in movement direction from the first to the second rotated trial (see Task & Procedure). Specifically, we identified trials with changes to movement direction in the second rotated trial that were very large or very small given instructions to ignore or compensate, respectively (i.e., a change of more than 15 in the Ignore condition, or of less than 15 in the Compensate condition). We then excluded participants for whom more than 30% of the trials were identified as such. We only included participants who were right-handed (Oldfield, 1971), reported corrected-tonormal vision, and had no history of neurological or psychiatric disorders, nor reported regular intake of any drugs. The Ethics Committee of the Medical Faculty of the Otto-von-Guericke University Magdeburg approved of the study procedure, which was in agreement with the Declaration of Helsinki. Participants received monetary compensation of 8 euros/hour. No part of the study procedures or analyses was pre-registered prior to the research being conducted.

Task and procedure
To ensure that a sufficient number of trials would be available, each participant was invited to take part in the experiment at the Leibniz Institute for Neurobiology Magdeburg on three days (mean number of days between sessions: 2.7; range: 1e10). We chose to collect data across three days per participant because the total time to collect a sufficient number of trials in a single session would have been minimum 4 h. For each experimental session, they sat in a comfortable office chair, in a dimly lit and electrically shielded, double-walled sound booth (Industrial Acoustics Company). A custombuilt, 2-layered table (Fig. 1A) was placed at a comfortable reaching distance in front of them. A graphics tablet (Wacom Intuos Pro Large, Kazo, Japan; sampling rate of 200 Hz, active area of 311 Â 216 mm) was placed at the lower level, on which participants performed centre-out reaching movements starting from a home position, and "slicing" through a target, with a stylus held in their right hand. Participants had no view of their moving hand, and instead received online visual feedback on an LCD monitor placed at the top level (refresh rate of 60 Hz). The task and stimuli delivery were implemented via the Presentation software (Neurobehavioral Systems). The stimulation files (together with the analysis files for both kinematics and EEG data) can be accessed at: https:// zenodo.org/record/7868424#.ZElV_XZBy71. A cursor (red dot, 5 mm) was displayed on the monitor at the top (black background), exactly above the tip of the stylus (Fig. 1A). When participants moved the stylus over the tablet, the cursor on the monitor moved along. Fig. 1B displays the structure of events within one trial. At the start of each trial, participants had to move the cursor into the home position (a white ring, outer diameter 8.5 mm, displayed in the lower half of the screen, roughly aligned to the body midline) and hold still. After 2000e2500 ms, the target appeared as a white ring (outer diameter 6 mm), always at a fixed location, 2 cm away from the home position. We chose a short distance between home position and target to minimize muscle artifacts from larger movements. After 1500 ms, the target turned green (filled ring), indicating that the movement could from now on be initiated. This delay between first target presentation and "go" cue reduced potential response time differences between the experimental conditions described below. Once initiated, the movement trajectory had to follow a straight line, and movement velocity had to be fast: if the duration between movement onset and the moment of exceeding a radial distance of 2 cm (¼the target distance) was below 50 ms or above 160 ms, the message "Too fast/Too slow" was displayed on the screen, respectively. The upper of the two limits ensured that online corrections were kept at a minimum (Tseng et al., 2007;Torrecillos et al., 2015). Trials containing such timing errors were later excluded from the analyses. Similarly, if the movement was initiated before the "Go" cue, the message "Too early" was displayed on the screen. These trials were also excluded from the analyses. At movement offset, the target disappeared, and participants had to hold still for a variable interval between 1600 and 2100 msdthis was implemented to allow a sufficiently large time window for investigating the PMBR. Movement extent beyond the target was considered irrelevant, promoting a feedforward mode of control, and further minimizing feedback corrections. Finally, a circle whose radius corresponded to the current distance of the hand from the home position, guided participants back to the home position, minimizing the possibility to learn from visual c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 feedback of the return movement, so that learning was largely restricted to visual feedback from the outward movement. If participants did not hold still (tolerance of 5 mm movement) between movement offset and presentation of the circle guiding them back to the home position, the message "Hold still" was displayed on the screen. Trials containing such errors were later excluded from the analyses.
In most trials (24 per block of 36), the cursor trajectory veridically followed the hand trajectory while in few trials (6 pairs, i.e., 12 of the 36 trials of a block), the cursor trajectory was unpredictably rotated (see first rotation trials in Fig. 1C). In two blocked conditions, we implemented either a visuomotor rotation, where the cursor feedback was rotated relative to participants' movement trajectories, or an error-clamp rotation, where the cursor feedback was rotated relative to the target. In both cases, same rotation magnitude and direction remained switched on for two consecutive trials, which were pseudo-randomly interspersed between non-rotated trials, with the following constraints: the first two trials of each block were always non-rotated, and there were at least two non-rotated trials between the rotated pairs. As the first rotated trial was (relatively) unpredictable, participants were expected to aim directly at the target in that trial, as in the non-rotated trials.
Importantly, for the second rotated trial, instructions differed between conditions. For the visuomotor perturbation, participants were instructed to develop and use a fully compensatory strategy, that is, to aim in the opposite direction relative to the rotation, such that the red cursor would "slice" through the target (Compensate condition, see the corresponding second rotation in Fig. 1C). In contrast, for the error-clamp perturbation, participants were instructed to ignore the rotated feedback, and to keep on aiming directly at the target Ignore condition). Participants knew they could not counteract the rotation by using a compensatory strategy in the Ignore condition because the cursor feedback was invariant to the hand movement direction. Indeed, even if they aimed away from the target (see the corresponding The apparatus consisted of a custom-built, 2-layered table, with a graphics tablet at the lower level on which participants performed reaching movements, and an LCD monitor at the top level, on which they received online visual feedback. B: At the start of each block, the cursor (red dot) was brought into the home position (white circle), from which the centre-out movements started. 1500 ms after target presentation, the target turned green as a Go cue. Once the movement ended (and after holding still for 1600e2100 ms), the return movement was visually guided by a circle whose radius corresponded to the current distance of the hand from the home position. C: After the cursor initially followed the hand trajectory veridically, a rotation was introduced, either relative to participants' movements (in Compensate, upper row), or invariant to participants' movements (but relative to the target, in Ignore, lower row). On a second rotated trial, participants had to either re-aim to compensate for the rotation (Compensate) or ignore the rotation and keep on aiming at the target (Ignore). On the next trial, the rotation was removed, and the cursor again veridically followed the hand trajectory, which was expected to display an after-effect (i.e., a small deviation relative to the target, opposite to the rotation) in both conditions. second rotation in Fig. 1C), the cursor feedback moved in the same direction as in the first rotated trial.
To minimise the possibility that participants developed a single, fixed strategy early during the experiment, and used that strategy throughout the experiment, there were three rotation magnitudes, in both directions. The rotation magnitudes could be either 30 , 37,5 , or 45 , each either clockwise (CW) or counterclockwise (CCW; both relative to the hand trajectories in Compensate, and relative to the target in Ignore). These six rotations were presented equally often, and in a pseudo-random order. Within each pair of consecutive trials, the rotation magnitude and direction remained the same from the first to the second rotated trial.
For each of the two conditions, we recorded 15 blocks of 36 trials each (5 blocks of each condition in each of the three experimental sessions). All blocks belonging to one condition were run consecutively in each session before a switch to the other condition. The order of conditions was counter-balanced, such that the number of times that Compensate or Ignore were run first was equal between participants, and across sessions (i.e., for each session, each condition was run first an equal number of times across all participants). Each experimental block contained a total number of 36 trials, out of which 24 were non-rotated, and 6 represented pairs of consecutive trials that included a rotation. Of main interest were the pairs of rotated trials, as well as the trial just before each pair, and the trial right after the rotation: for each of these four trial types, 90 trials were collected in total. Participants took self-paced breaks between blocks.
In addition to the experimental blocks described above, three practice blocks were run before each condition. On the first session only, the first practice block contained 15 nonrotated trials, to familiarize participants with the general requirements regarding their reaching movements. The second and third practice blocks were run on each of the three sessions. On the second practice block, participants encountered 20 trials, each of which included a rotation, for which they received feedback regarding both the cursor (red, see Fig. 1C), as well as their hand trajectory (yellow, see Fig. 1C) e this was implemented to ensure that participants learn that they should compensate in the Compensate condition, and that they could not, and should not try to compensate, in the Ignore condition. The third practice was a single block of the same task as during the actual experimental block (containing 24 non-rotated and 6 pairs of rotated trials). The practice blocks and associated task-specific instructions (see Supplementary Material) were presented to the participants at the start of each condition.

Analysis of kinematics data
Movement onset was defined as the time at which the cursor first leaved the home position. Movement offset was defined as the time following movement onset at which the cursor no longer moved for at least two consecutive vertical refresh frames (i.e., for at least 33.3 ms) and was at least 2 cm away from the home position (i.e., at the target distance). Maximum speed was calculated for the time window between movement onset and 100 ms after "slicing" through the target).
The main parameter of interest was movement direction, which was calculated for all four trial types described in Fig. 1C: before rotation, first rotation, second rotation, and after rotation. This was defined relative to the target, as the angle between the line connecting the point at which the red cursor reached the point of maximum velocity and the centre of the home position, and the line connecting the home position and the target. Movement direction was computed across rotated trials with the same rotation magnitude (30 , 37,5 , or 45 ), collapsing across rotations directions (i.e., we flipped signs for CCW rotations). Based on movement onset and movement offset, several additional parameters were calculated, including: movement duration, movement extent (beyond the target), and movement curvature (i.e., linearity index). Linearity index was defined as the maximum perpendicular distance of the actual movement trajectory to a straight-line connection between the location at movement onset, and the location at movement offset, divided by the distance between the home position and the endpoint (Atkeson & Hollerbach, 1985). Finally, response time was computed as the time between the "Go" cue (target turning green, see Fig. 1B) and movement onset.
Besides excluding from all analyses trials containing the four error types that were signalled to participants during task performance, described above ("Too slow", "Too fast", "Too early", and "Hold still"), we also excluded trials that followed those containing a "Too fast" or a "Too slow" error type. More specifically, we excluded the second reach within a rotated duplet if the first one was excluded, as well as the non-rotated trial following a rotated pair in which any of the two rotated trials was excluded. Finally, we excluded trials in which changes to movement direction in the second rotated trial indicated that the participant accidentally tried to compensate for a clamped rotation in the Ignore condition (change in movement direction above þ15 or below À15 ), or failed to compensate for a visuomotor rotation in the Compensate condition (change in movement direction between À15 and þ15 ). On average across participants, a total of 81.5 trials (range: 31e205) were excluded (from the total number of 1080 recorded trials).
Differences in movement direction were analysed in a 2 Â 4 ANOVA with factors Condition (Compensate vs. Ignore) Â Trial type (before rotation, first rotation, second rotation, and after rotation). To ensure that any condition differences in the EEG were not confounded by differences in kinematics, we additionally performed (Bayesian) pairwise comparisons of movement speed, duration, extent, curvature, and response time of the rotated trials of interest.

Analysis of EEG data
In each of the three sessions, EEG data was recorded at a sampling rate of 500 Hz with a system equipped with 35 AgeAgCl passive electrodes, using a BrainAmp amplifier and the Vision Recorder software (Brain Products GmbH, Gilching, Germany). Two electrodes were placed on the mastoids, the right of which served as online reference. The ground electrode was placed at the Fpz location. Three electrodes were used to record EOG activity, two of which were placed on the left and right outer canthi, and one below the left eye. The remaining 29 electrodes (Fp1/2, F3/4, F7/8, FC1/2, C3/4, CP1/2, T7/8, P3/4, P7/8, PO3/4, PO7/8, O9/10, Fz, Cz, Pz, Oz, Iz) were mounted in an elastic cap (EasyCap GmbH, W€ orthsee, Germany) following the extended international 10e20 system (Chatrian, Lettich, & Nelson, 1985). Impedances were kept at or below 10 kU. The raw EEG (as well as kinematics) data can be accessed at: https://zenodo.org/record/7440442#.Y5xd_ 3bMK5c.
EEG preprocessing was carried out in MatLab (The Mathworks Inc., Nattick, Massachusetts, USA) using the FieldTrip toolbox (Oostenveld, Fries, Maris, & Schoffelen, 2011). For each session, the following steps were applied before concatenating across sessions. Continuous data were first filtered using a 100 Hz low-pass and a .1 Hz high-pass windowed sinc finite impulse response (FIR) filter (Hamming window, filter order 66-low-pass and 8250-high-pass). To optimize identification of eye movement artefacts using Independent Component Analysis (ICA) at a later stage of our preprocessing pipeline, we created a copy of the raw, continuous dataset, which was filtered using a higher-cutoff (1 Hz) high-pass filter (Hamming window, filter order 826), following the 100 Hz lowpass windowed FIR filter (same parameters as before). Both sets of data (i.e., the actual data to be eventually analysed, and the data optimized for the ICA) were then epoched around movement offset (±2 s) for the PMBR component. Using ft_rejectvisual.m, epochs were visually inspected, and trials with exceptionally high fluctuations were rejected (settings: 'maxzval' and 'meanzval'); on average, 4.9 epochs were excluded at this step (range: 0e9). Channels containing extreme amplitudes were removed using a deviation criterion (threshold ¼ 3) based on "the robust z score of the robust standard deviation for each channel" (Bigdely-Shamlo, Mullen, Kothe, Su, & Robbins, 2015). On average, .7 channels were excluded (range: 0e4). An ICA was run using standard FieldTrip settings ("runica") on the higher-cutoff (1 Hz) filtered data set. We identified eye movement and muscle artifacts by visual inspection. Obtained ICA weights were then applied to the .1 Hz high-pass filter dataset. On average, 3,8 principal components (range: 2e7) were removed. The missing channels were interpolated. Epochs still representing large amplitude deviations (defined based on kurtosis) after the ICA, were removed. On average, 23 epochs were excluded at this this step (range: 1e102). Finally, the data from the three sessions were concatenated. Data was then re-referenced to a common average of all electrodes (except for EOG electrodes).
At the next step, Fourier transformed data segments, sampled every 20 ms, were multiplied with a Fouriertransformed Hanning taper (of length 400 ms). Spectral power was computed as the squared absolute of the Fourier transform for frequencies between 2.5 and 40 Hz, in steps of 2.5 Hz. Baseline was defined as the mean power between 1800 and 200 ms before target presentation averaged across all trials from both conditions, i.e., from the inter-trial interval, during which participants were holding the stylus still at the home position. Based on visual inspection of the data, we first identified a region of interest (ROI) referring to the channels that showed a prominent PMBR across both conditions in the non-rotated trials, namely Fz, FC1, FC2, Cz, C3, C4, CP1, CP2, P3, P4 (Fig. 4A). Following the suggestion of one of our reviewers, control analyses were conducted for which we alternatively defined a ROI based on a cluster-based permutation test. For this test, we compared b power (15e30 Hz) across time points in a post-movement time window (200e1000 ms) to baseline power, computed from the intertrial interval as described above ("activation vs. baseline" in FieldTrip terminology; run for data obtained in non-rotated trials collapsed across conditions). This revealed a cluster of 24 electrodes in which post-movement b power was higher than at baseline. All statistical results are qualitatively unchanged when comparing EEG data between conditions across this cluster, instead of the ROI defined by visual inspection.
Next, a time-frequency window of interest was defined based on visual inspection of the data in the non-rotated trials: this consisted of the activity between 200 and 1000 ms after movement offset, at frequencies specific to the b band activity, namely in between 15 and 30 Hz (Fig. 4B). Participant-specific averages were computed for the power in the time-frequency windows of interest corresponding to the averaged activity from the electrodes in the region of interest. That is, we obtained one value per condition, trial type, and participant across the time-frequency window of interest and the identified ROI. Finally, similarly to movement direction, the EEG time-frequency data were also analysed in a 2 Â 4 design with factors Condition (Compensate vs. Ignore) Â Trial type (before rotation vs. first rotation vs. second rotation vs. after rotation).

Statistical analyses
For all statistical comparisons, we performed Bayesian repeated-measures ANOVAs (rANOVAs) and t-tests using the JASP .14.1.0 software (JASP Team, 2021). Bayesian rANOVAs were calculated to test all alternative models, including main effects and interactions, against the null model, which only included the random factor i.e., participants' variation. The Bayes factor (BF 10 ) was calculated using standard JASP settings (10.000 sample repetitions, the null hypothesis corresponding to a standardized effect size d ¼ 0, while the alternative hypothesis was defined as a Cauchy prior distribution centered around 0; Rouder, Morey, Speckman, & Province, 2012). BF Inclusion calculated across matched models (i.e., models that include vs. do not include the effect) which provide a measure of change odds from prior to posterior distribution, were next calculated if more than one model supported the alternative hypothesis (Mathôt, 2017). Bayesian t-tests followed up on the effects of the models including interactions. In accordance with existing recommendations on how to interpret the Bayes factor (Lee & Wagenmakers, 2013;Jeffreys, 1961), as well as with previous studies reporting Bayes factors (e.g., Korka et al., 2019Korka et al., , 2020Korka et al., , & 2021, data were taken as moderate evidence for the alternative (or null) hypothesis if the BF 10 was greater than 3 (or lower than .33), while values close to 1 were considered only weakly informative. Values greater than 10 (or smaller than .1) were considered strong evidence for the alternative (or null) hypothesis. Additionally, in Tables 1e6, we report P-values, for which statistical significance was defined at the .05 alpha-level, together with eta-squared (h 2 ) effect sizes for rANOVAs or Cohen's d for follow-up pairwise comparisons.    c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 3. Fig. 2A shows movement direction relative to the target for the four trial types of interest in both conditions (positive values represent movement direction opposite to the rotation). The Bayesian rANOVA revealed that, compared against the null model, all alternative models brought strong evidence for their respective alternative hypotheses (see Table 1). Averaged across matched models, the BF Inclusion brought strong evidence for the main effects of Condition (BF Inclusion ¼ 7.807eþ10), Trial type (BF Inclusion ¼ 6.825eþ30), as well as the interaction term (BF Inclusion ¼ 7.045eþ117).

Kinematics
As we were primarily interested in movement direction changes due to implicit learning on the one hand and reaiming on the other hand, the interaction term was further examined by planned pairwise comparisons as follows. The effect of implicit learning was tested by comparing the trials before and after the rotation in each condition, for which the Bayesian evidence brought strong support for the alternative hypothesis in both cases (before vs. after rotation in Compensate: BF 10 ¼ 333124.84; before vs. after rotation in Ignore: BF 10 ¼ 1.793eþ10). The effect of re-aiming was tested by comparing the trials before the rotation with those on the second rotation, in each condition, for which the Bayesian evidence also brought strong support for the alternative hypothesis in both cases (before vs. second rotation in Compensate: BF 10 ¼ 1.040eþ22; before vs. second rotation in Ignore: BF 10 ¼ 5.465eþ9). While this difference in Ignore likely reflects implicit learning already after the first rotated trial (rather than re-aiming), it was next tested if movement direction in the second rotated trial is different between conditions. We calculated the differences between the trials before and after the rotation, and those between before the rotation and second rotation, in each condition, and further compared these difference scores. The Bayesian evidence did not support differences from before to after the rotation (before rotation-after rotation in Compensate vs. before rotation-after rotation in Ignore: BF 10 ¼ .25), while strong support was brought in favour of the alternative hypothesis regarding the differences from before the rotation to the second rotation (before rotation-second rotation in Compensate vs. before rotation-second rotation in Ignore: BF 10 ¼ 7.875eþ20). The results of these pairwise comparisons are reported in Table 2.
Next, we examined whether participants followed the task instructions on the second rotated trial, by either compensating according to the rotation magnitude, or ignoring the rotated feedback, which should result in similar performances across rotation magnitudes in Ignore (Kim et al., 2018). Oneway ANOVAs testing the differences between the three rotation magnitudes (30 vs. 37.5 vs. 45 ) was calculated for each condition. As also indicated by Fig. 2B, the data brought strong evidence for the alternative hypothesis in Compensate (BF 10 ¼ 56680.48) but not in Ignore (BF 10 ¼ .15). Pairwise comparisons evidenced that in Compensate, the 37.5 rotation led to aiming further away from the target than in the 30 rotation  c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 (moderate evidence, BF 10 ¼ 5.47), and the 45 rotation led to aiming further away from the target than in the 37.5 rotation (strong evidence, BF 10 ¼ 85.35). The analyses of movement direction as a function of rotation magnitude are presented in Table 3. Finally, no evidence was found for the existence of condition differences in movement speed (BF 10 ¼ .22), duration (BF 10 ¼ .28), extent (BF 10 ¼ .20), curvature (BF 10 ¼ .20), and response time (BF 10 ¼ .28), on the first rotated trials. These can additionally be observed in Fig. 3 and Table 4.
To conclude, our data indicate that both conditions lead to implicit learning, which occurred to a similar degree in both cases, evident in similar after-effects in the two conditions. A re-aiming effect is observed in Compensatedimportantly, this increases according to the rotation magnitude. Furthermore, the condition differences in the EEG signal that we report next are not likely to be confounded by differences in kinematics regarding the movement speed, duration, extent, curvature, and response time. Fig. 4A displays the topographical distribution based on which the region of interest (ROI) was defined. Fig. 4B displays the time and frequency resolved power locked to movement offset in the non-rotated trials (before the first rotation) e averaged across both conditionsdbased on which the timefrequency window of interest was defined. Fig. 5 displays the time-frequency differences in the four trial types of interest, in both conditions. The Bayesian rANOVA revealed that compared against the null model, all alternative models brought strong evidence for their respective alternative hypotheses (see Table 5). Averaged across matched models, the BF Inclusion brought strong evidence for the main effects of Condition (BF Inclusion ¼ 7817.64) and Trial type (BF Inclusion-¼ 6.976eþ8), as well as strong evidence for the interaction term (BF Inclusion ¼ 10.85).

EEG
Of main interest are the PMBR signal changes as a function of introducing, maintaining, and removing the rotation. We therefore examined the interaction term further by planned  c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 pairwise comparisons. These included comparisons of changes from before the rotation to the first rotated trial, from the first to the second rotated trial, and from before to after the rotation, within each condition. Most importantly, given that the perturbation in the first rotated trial implied a change in behaviour in one condition (Compensate) but not the other (Ignore), our main interest was in a comparison of the change in PMBR amplitude from before a rotation to the first rotated trial between conditions. To ensure that any potential PMBR differences between conditions are not confounded by existing differences between conditions at the level of the nonrotated trials, we additionally compared the trials before the rotation and the trials after the rotation, between conditions. The results of these pairwise comparisons are reported in Table 6.
The Bayesian t-tests suggested strong support for an amplitude decrease following the first rotated trial in both conditions (Compensate: BF 10 ¼ 1713.50; Ignore: BF 10 ¼ 24.54). To test if this amplitude decrease is different between conditions, we calculated the differences between the signal before the rotation, and the signal in the first rotation, in each condition, and further compared these two difference scores, for which the Bayesian evidence brought very strong support in favour of the alternative hypothesis (before rotation-first rotation in Compensate vs. before rotation-first rotation in Ignore: BF 10 ¼ 175.04).
Regarding the signal in the first rotation by comparison to that in the second rotation, there was moderate evidence of differences in Ignore (BF 10 ¼ 5.07), but not in Compensate (BF 10 ¼ .42). The comparison of non-rotated trials before the c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 rotation vs. after the rotation did not bring evidence for condition differences in either condition (Compensate: BF 10 ¼ .22; Ignore: BF 10 ¼ .21). Finally, there were no differences between conditions at the level of the non-rotated trials, both in the case of the trials before, as well as in the case of trials after the rotation (Compensate, before rotation vs. Ignore, before rotation: BF 10 ¼ .26; Compensate, after rotation vs. Ignore, after rotation: To conclude, our data indicated that once the rotation was first introduced, a decrease in the PMBR amplitude could be observed in both conditions, but this decrease was more pronounced in Compensate. Once the rotation was removed, PMBR amplitude returned to similar levels as in the trial before the rotation, in both conditions.

Correlation of kinematics and EEG data
Following one of our reviewer's suggestions, we investigated whether the PMBR amplitude is related to subsequent reaiming in Compensate. For each participant, we extracted single-trial PMBR amplitude on the first rotated trial (averaged across the time-frequency window and ROI described above).
To reduce the sensitivity to noisy trials, single-trial, full-epoch baseline correction was performed (Grandchamp & Delorme, 2011). We then performed two separate regression analyses. We regressed single-trial PMBR for each participant on signed goal achievement error in the second rotated trial, or on its absolute value, where goal achievement error is defined as the difference between the direction of the rotated feedback in the second rotated trial and the direction of target location. The absolute value of the goal achievement error is a measure of accuracy (lower values indicating higher accuracy), while the signed goal achievement error indicates to what extent a participant over-or undercompensated for a rotation on a given trial. Subject-wise regression coefficients were tested against zero at the group level, using a Bayesian t-test. We found no reliable support for a relation between PMBR in the first rotated trial and accuracy, or signed goal achievement error, in the second rotated trial (signed goal achievement error: BF 10 ¼ .98; accuracy (¼absolute value of goal achievement error): BF 10 ¼ .51; both err% .00004).

Discussion
In this study, we aimed to measure the separate impact of learning a cognitive strategy, over and above implicit adaptation, on the power of the post-movement b rebound (PMBR).
To this end, we isolated implicit learning by using an errorclamp paradigm (Morehead et al., 2017) and compared it to a condition that additionally involved strategic re-aiming to compensate for a visuomotor rotation. In agreement with previous results (e.g., Morehead et al., 2017), our behavioural results indicated that the amount of implicit learning was similar between the visuomotor and error-clamp rotations, as evidenced by a comparison of non-rotated trials before and after the rotation pairs. Differences in movement direction in the second rotated trials between conditions indicated that participants successfully acquired re-aiming strategies that compensated for the rotation magnitude and direction. In further agreement with previous results (Darch et al., 2020;Klimpke et al., 2020;Palmer et al., 2019;Tan et al., 2016;Tan, Jenkinson, & Brown, 2014;Tan, Zavala, et al., 2014), we observed that the PMBR decreased in amplitude following the first rotation in both conditions. Crucially, this effect was larger when participants had to acquire a cognitive strategy, indicating that the post-movement b power is modulated by the cognitive demands of motor learning. Earlier results indicated that the PMBR decrease following perturbed feedback (i.e., rotations) reflects a process of error evaluation (Tan, Jenkinson, & Brown, 2014) depending on the information flow from the basal ganglia towards the sensorimotor cortex, which may have a role in modifying subsequent behaviour such as re-aiming (Tan, Zavala, et al., 2014). Our results are congruent with this interpretation: we see greater PMBR decrease when participants produce goal achievement errors (i.e., in the first rotated trial of the condition involving the strategy use), indicating that indeed, this signal likely reflects the evaluation of a behaviourally significant error. A pronounced decrease of PMBR has been observed for large goal achievement errors in particular (Tan, Jenkinson, & Brown, 2014;Torrecillos et al., 2015), which, in turn, promote strategic re-aiming (Morehead et al., 2015). For instance, a visuomotor rotation of 60 leads to both (large) PMBR decrease (Tan et al., 2016), as well as an emphasis on strategy-based learning over implicit adaptation, given that "the larger performance changes observed with large perturbations [are] primarily due to changes in the explicit aiming process" (Morehead et al., 2015). Morehead et al. (2015) further argued that a "large error can become a cue for the recall of aiming strategies". That is, knowledge of a change in context can promote the use of cognitive strategies. Interestingly, given the same goal achievement error, the PMBR decreases more strongly when that error indicates a change in context, compared to when it does not (Tan et al., 2016). While previous findings thus support the idea that the acquisition (or use) of a cognitive strategy decreases the PMBR, the influence of strategic reaiming on the PMBR has never been explicitly addressed. The present results thus fill this gap and demonstrate that planning for strategic re-aiming for the next movement modulates this signal.
Yet, it remains for future research to demonstrate if the flow of information between the cerebellum, basal ganglia, and sensorimotor cortex differs between implicit adaptation and re-aiming. Patients with spinocerebellar ataxia show reduced PMBR (following voluntary movement; Aoh et al., 2019), and, cerebellar degeneration impairs strategy-based learning, beyond the well-established deficits in implicit learning (Butcher et al., 2017;Wong et al., 2019). While data from Klimpke et al. (2020) indicated that cerebellar degeneration indeed influences the dynamics of PMBR during learning, future research may disentangle subcortico-cortical neural circuits involved in strategy-based vs. implicit learning.
The data of Tan, Jenkinson, and colleagues (2014) indicated that PMBR amplitude negatively correlates with the size of the goal achievement errors. In the present data, the correlation between the movement direction (reflecting the angular error) and the PMBR signal in the first rotated trial was only weakly informative (Bayes factor around 1, thus not reported in c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 Results), possibly because our range of errors (i.e., 30 , 37.5 , and 45 ) was not wide enough to detect a correlation, by contrast to Tan, Jenkinson, and Brown (2014) who used a much larger range of error magnitudes (0e40 ). Here, we additionally investigated whether PMBR amplitude in the first rotated trial predicts re-aiming in the second trial, to examine whether the PMBR amplitude may indeed (partly) reflect subsequent re-aiming. Again, the evidence was rather weakly informative, indicating that future studies should aim for increased power (i.e., larger number of trials) when performing correlations between brain and behavioural data.
An alternative interpretation of the decrease in PMBR is that PMBR responds to saliency associated with the perturbed feedback (rather than the evaluation of a goal achievement error and strategic re-aiming; Torrecillos et al., 2015). Our results could be taken as evidence that saliency plays a role in the overall amplitude decrease (as we see it in both conditions, following the first rotated feedback), but it cannot explain the differences between our two conditions. That is, while saliency, understood as "popping out" is kept constant, the Compensate condition still leads to a larger decrease of the PMBR. If saliency is understood to include motivational factors, the difference in task-relevance between our two rotation types may have rendered the first rotation "more salient" in Compensate than in Ignore. This difference in task-relevance also points to attention as one factor likely involved in cognitive strategies for re-aiming, by contrast to ignoring the rotated feedback. Our study was not designed to identify the precise cognitive components of strategic re-aiming which are reflected in the decrease of the PMBR. Rather, our goal was to test whether the decrease in PMBR during motor learning observed previously is (partly) explained by mental processing involved in cognitive strategies. Torrecillos et al. (2015) observe that perturbations with no explicit task relevance, such as an unexpected rotation or a target jump, decrease the PMBR on a single trial level. They conclude that their results "demand an interpretative framework general enough to also incorporate the modulation of the PMBR in response to unexpected events that do not result in sensorimotor remapping and subsequent changes in the motor command". Our own results, on the other hand, demand an interpretative framework that includes task-relevance in a context of re-aiming.
To summarize, the present results extend previous findings by indicating that in the context of motor learning, the PMBR decrease is related to error evaluation (Tan et al., 2016;Tan, Jenkinson, & Brown, 2014;Tan, Zavala, et al., 2014), especially under explicit re-aiming instructions. Saliency of the rotated feedback, in a "popping out" sense, is not the only factor driving this change (although it may contribute to the effect; Torrecillos, et al., 2015). Instead, here, the PMBR decrease is additionally driven by behaviourally relevant goal achievement errors and re-aiming. Additional support for our interpretation comes from Haar & Faisal (2020), whose results indicated that individual differences in PMBR predicted billiard performance. Specifically, the PMBR was reduced with less directional errors in a sub-set of participants, whom, the authors speculated, were likely to use reward-based learning as the predominant mechanism, rather than error-based adaptation (Haar & Faisal, 2020). Since explicit control is a necessary factor for reinforcement learning (e.g., Codol, Holland, & Galea, 2018), one may reasonably assume that goal echievement error evaluation influences the PMBR decrease even in such a real-world task involving well-planned movement strategies. Similarly, Ricci et al. (2020) reported a negative correlation between the PMBR amplitude and directional errors at baseline.
Besides cerebellar ataxia, another clinical disorder characterized by reduced PMBR is obsessive-compulsive disorder (OCD; Leocani et al., 2001). Patients with OCD often report a feeling that their actions are incomplete (Ecker, Kupfer, & G€ onner, 2014;, which may drive the repetitive checking behaviour that represents a major symptom in OCD (Ball, Baer, & Otto, 1996). It is tempting to speculate that a feeling of incompleteness may correspond to a behaviourally relevant (subjective) goal achievement error, reflected in the PMBR amplitude.
We observe a decrease of PMBR following the rotation in the condition isolating implicit learning, too (albeit less pronounced compared to strategy learning). Besides a potential role of saliency as discussed above, the PMBR decrease in the Ignore condition may be related to aspects of implicit learning, as previous interpretations alternatively proposed that this signal may simultaneously reflect the sensory processing of prediction errors as well as the processing of output evaluation that is necessary for implementing a motor strategy (Tan et al., 2016). In this context, our results could be explained by additivity of implicit and explicit learning, which jointly modulate the PMBR amplitude, determining lower effects when one learning mechanism acts in isolation and larger effects when both mechanisms act simultaneously. This hypothesis needs further testing by isolating implicit and explicit learning in separate conditions and comparing those with a third condition that involves both simultaneously. Thoroughly isolating both learning mechanisms without changes to physical stimulation, kinematics, or sensorimotor contingencies, presents a practical and methodological challenge. Furthermore, recent work trying to separate the behavioural effects of implicit and explicit learning suggests that this relationship is more complicated than merely additive (Marius't Hart et al., 2022).
The present study comes with a few limitations as well as important differences relative to previous studies, which we discuss next. First, the unexpected rotations and rarity of these events make it difficult to disentangle the effect of saliency from those of strategic vs. implicit learning on the PMBR amplitude. Next, we do not/cannot investigate strategy-based learning in the (complete) absence of implicit learning. Conversely, implicit learning may not be devoid of strategy use in our design: participants may develop tactics to help with aiming directly at the target. In addition, based on the present dataset, we cannot show that the PMBR amplitude is associated with behavioural learning parameters, in the absence of a reliable correlation with movement direction. The PMBR may alternatively be involved in a process "upstream" of learning, which signals the need to adjust behaviour (after which learning per se starts). For example, there is evidence to indicate that in primates, b power increases in the supplementary and pre-supplementary motor areas before a Go cue, when producing a learnt sequence of arm movements from memory ("maintaining" the same sequence), compared to trials that required updating that sequence based on new c o r t e x 1 6 6 ( 2 0 2 3 ) 4 3 e5 8 instructions (Hosaka, Nakajima, Aihara, Yamaguchi, & Mushiake, 2016).
Moreover, target distance relative to the starting position was short (2 cm), by comparison to other EEG studies investigating the PMBR dynamics in visuomotor learning paradigms (e.g., Tan et al., 2016;Tan, Jenkinson, & Brown, 2014;Tan, Zavala, et al., 2014;Torrecillos et al., 2015). While this likely minimized EEG movement-related artifacts, we acknowledge that the generalizability of our results might be limited, given that larger movement extents might promote stronger strategic adjustments in the context of counteracting rotations.
Likewise, we chose a single target location to facilitate strategy use, and minimise heterogeneity in EEG signals across trials introduced by strongly varying movement directions. Previous studies have indicated that increasing the number of possible target locations leads to more thorough (but slightly slower) explicit learning and reduced implicit learning (Bond & Taylor, 2015), which might in turn also be reflected in the PMBR dynamics. Data from McDougle & Taylor (2019) additionally indicated that the number of target locations (2 vs. 4) changes how participants develop a cognitive strategy. Specifically, with two target locations, they likely remember where they had to move given the current target location, rotation magnitude, and direction (i.e., a categorical task), while with four target locations, they likely use a more parametric mental rotation strategy. It is thus possible that participants in our study relied on a categorical strategy rather than on a parametric transformation (mental rotation), leaving it to future studies to disentangle if and to what extend these two classes of strategies affect the PMBR amplitude.
Previous studies have suggested that eye movements may play a role in strategy-based learning (de Brouwer, Albaghdadi, Flanagan, & Gallivan, 2018) or reveal distinct components of strategy-based learning (Bromberg, Donchin, & Haar, 2019). In the present study, we removed eye movement-related activity by means of ICA (including components representing blinks, corneo-retinal dipoles, and saccadic spike potentials) to the best of our ability. We additionally instructed participants to hold their gaze fixed on either the home position or the target position. They were asked to move their eyes directly to the target position when the home position disappeared, and back to the home position when the target position disappeared. They were also explicitly asked not to follow the red dot with their eyes. However, given that we did not record eye-tracking data, we cannot be sure to what extent participants followed these instructions. Therefore, we cannot exclude a potential involvement of hidden oculomotor processes in overall PMBR amplitude.
While motor learning studies often involve re-aiming strategies that develop over multiple trials (e.g., Mazzoni & Krakauer, 2006;Taylor, Krakauer, & Ivry, 2014), here, participants had one chance to implement a compensatory strategy. This might limit the generalizability of our findings to more ecological situations in which developing a strategy takes time and is self-motivated. Previous results from our group implementing trial-by trial learning indicated that when healthy participants had to discover a compensatory strategy by themselves, the PMBR decreased relative to baseline, more so than when the strategy was instructed (Klimpke et al., 2020). Nevertheless, the presence of task-relevant errors either following the first unpredictably rotated trials here, or produced while participants discovered a compensatory strategy by themselves in Klimpke et al. (2020), both lead to a stronger PMBR decrease than implicit learning alone.
Finally, in the present study, motor learning is considered primarily in connection with the visual feedback which varies across conditions and movement types, while learning is influenced by weighting of different sensory modalities, where proprioception may play a key role too, particularly in implicit learning . Disentangling precisely to what extent proprioception contributes when re-aiming is involved in a visuomotor rotation task remains a task for future studies.

Open practices section
The study in this article earned Open Data and Open Material badges for transparent practices. The data for this study is available at https://zenodo.org/record/7440442#.Y5xd_ 3bMK5c and materials at https://zenodo.org/record/ 7868424#.ZElV_XZBy71.

Author contributions
BK and MPS designed the study. MPS programmed the experimental task. BK, IA, and FD were responsible for data collection. BK and MPS analysed the data. BK wrote the manuscript draft. MPS, MW, IA, and FD contributed fruitful discussions, provided feedback and contributed to revisions of the manuscript.

Declaration of competing interest
The authors declare no competing interests.