Learning from the path not taken: Sensory prediction errors are sufficient for implicit adaptation of withheld movements

51 Prediction errors guide many forms of learning, providing teaching signals that help us improve our 52 performance. Implicit motor adaptation, for instance, is driven by sensory prediction errors (SPEs), which 53 occur when the expected and observed consequences of a movement differ. Traditionally, SPE 54 computation is thought to require movement execution. However, recent work suggesting that the brain 55 generates and accounts for sensory predictions based on motor imagery or planning alone calls this 56 assumption into question. Here, by measuring implicit adaptation during a visuomotor task, we tested 57 whether motor planning and well-timed sensory feedback are sufficient for SPE computation. Human 58 participants were cued to reach to a target and were, on a subset of trials, rapidly cued to withhold these 59 movements. Errors displayed both on trials with and without movements induced single-trial implicit 60 learning. Learning following trials without movements persisted even when movement trials had never been 61 paired with errors, and when the direction of movement and sensory feedback trajectories were decoupled. 62 These observations demonstrate that the brain can compute SPEs without generating overt movements, 63 leading to the adaptation of planned movements even when they are not performed. 64 65 HIGHLIGHTS 66 • The brain can learn to update movements that are not performed, representing a mechanism for 67 learning based only on movement planning and sensory expectation. 68 • Supports a fundamental role for prediction in adaptation. 69 • Provides further support for the role of forward models in predictive motor control. 70 71


INTRODUCTION 74
Prediction errors help to optimize behavior by driving learning processes that correct for our 75 mistakes. Accordingly, they are thought to be a fundamental computation of the nervous system. 1 Specific 76 types of prediction errors are associated with specific learning processes, and sensory prediction errors 77 (SPEs) are the teachers of the implicit motor system, triggering adaptation and refinement of movements. 2-78 6 Traditionally, SPEs are thought to be computed by comparing the expected and observed consequences 79 of a movement, with movement execution being a critical element in this process. 4,7 However, the 80 predictions factoring into SPE computation are thought to be generated by an internal forward model, which 81 estimates the consequences of movements before relevant sensory feedback can reach the brain. 7 This 82 predictive capacity suggests that the forward model predicts the sensory consequences of an intended 83 movement regardless of whether that movement occurs. That is, because movements are synchronous 84 with the sensory outcomes that they produce, motor execution cannot itself be necessary for the generation 85 of predictions by the forward model. 86 subject's (top) and the group's (bottom) mean ± SEM changes in reach paths across triplets with a rotation 167 applied (green: triplets with perturbations on Movement trials, magenta: triplets with perturbations on  Movement trials, solid lines: perturbation was a CW rotation, dashed lines: perturbation was a CCW 169 rotation). (c) STL across Movement (green) and No-Movement (magenta) triplets for all participants (n = 170 20). In the reference frame used here, positive changes in hand angle are CCW. Please refer to 171 Supplemental Table 1  Stop" show data from the in-lab experiment where participants saw 15° rotated feedback on Movement 190 trials (i.e., data from Fig. 2), "Rotation online, Go" and "Rotation online, Stop" show data from the online 191 experiment where participants saw 0-15° rotated feedback on Movement trials (i.e., data from Supplemental 192 Fig. 2). "Clamp online, Go" and "Clamp online, Stop" show data from the online experiment where 193 participants saw 0-15° error-clamed feedback (i.e., data from Supplemental Fig., 4). "Rotation 0 go" and 194 "Clamp 0 go" show data from the online experiments where participants saw 0° perturbed feedback on 195 Movement trials. Abbreviations: E,experiment. 196 197 To address whether the STL measured represented genuine implicit learning, we checked whether 198 adaptation persisted beyond the trial after an error was experienced. We examined participants' hand 199 angles on the second trial after a perturbation relative to the pre-perturbation baseline trial (i.e., hand angle 200 on trial 1 of triplet t + 1 relative to hand angle on trial 1 of triplet t, subsequently referred to as remembered 201 STL, Fig. 2a). Because visual feedback was withheld on both trial types, this approach provided a pure 202 measure of persistent memory in the absence of error-driven changes in performance. Hand angle 203 remained adapted in the direction opposite the rotation on trials with nonzero perturbations regardless of 204 movement condition (Fig. 2d), suggesting that genuine implicit learning was observed in response to errors 205 under both movement conditions. Closer examination of the relative ratio of remembered STL to initial STL 206 revealed that retention of adaptation differed significantly from zero after both Movement (t(19) = 26.20,padj 207 = 6.71 x 10 -16 , Cohen's d = 5.86) and No-Movement triplets (t(19) = 9.20, padj = 2.98 x 10 -8 , Cohen's d = 208 Sensory prediction error without movement -9 2.06). Moreover, the amount of retention observed was not statistically significantly different between the 209 movement conditions (t(19) = 2.07, padj = 0.053, Fig. 2e). 210 To assess the potential similarity of mechanisms underlying adaptation after errors on Movement 211 and No-Movement trials, we compared STL amplitude under each condition, reasoning that there should 212 be a reliable relationship between the two measures if STL is supported by the same mechanism for both 213 Movement and No-Movement trials. When we considered instances of STL in the direction that would 214 compensate for the observed error (the direction opposite the rotation, i.e., the "Right-Way"), within-subject 215 changes in hand angle were correlated between Movement and No-Movement trials (Pearson's r = 0.55, p 216 = 0.01; Fig. 2f). Conversely, changes in hand angle in the direction that would exacerbate the observed 217 error (the direction of the rotation, i.e., the "Wrong-Way") were uncorrelated between Movement and No-218 Movement trials (Pearson's r = 0.17, p = 0.48, Fig. 2g). Together, these observations suggest that the 219 same learning process may underlie adaptive single-trial learning events in response to errors on both kinds 220 of trials, while maladaptive changes in hand-angle may be attributable to noise. 221

Implicit motor adaptation proceeds after simulated errors in an online visuomotor task 222
Illustrating that the above observations are reproducible and generalize across experimental 223 contexts, we again observed that simulated errors in No-Movement trials also induced motor adaptation in 224 an online, crowd-sourced version of the task. Participants (n = 40) made hand movements using their 225 computer mouse or trackpad to move a cursor towards a target. As in the experiment described above, 226 trials were presented in triplets, allowing us to measure STL that occurred in response to cursor feedback 227 presented during Movement and No-Movement trials at the center of each triplet ( Fig. 1b-d). For this online 228 study, triplets with 0° perturbations/simulated errors were also included to provide an estimate of baseline 229 changes in hand angle, in the event that participants exhibited strong movement biases in the online 230 platform. 231 Participants showed STL that was directionally appropriate for the perturbation applied during both 232 Movement and No-Movement trials (Supplemental Fig. 2a We note that rotated visual feedback on Movement trials was sensitive to people's actual reaching 281 directions. That is, the rotation was simply added to the measured reach direction, as is typical in visuomotor 282 rotation tasks. It is possible that these directional contingencies affected participants' responses to error, 283 potentially encouraging them to attempt to deliberately control the cursor's position via an explicit re-aiming 284 process. 18 To rule this out, we recruited a new group of participants (n = 37) to perform a variant of the task 285 where the visual cursor moved in a fixed path ("error-clamped" feedback 17 ; Supplemental perturbations are applied to cursor feedback, the cursor's movement direction is contingent upon the 292 participant's movement direction, although there is an experimenter-induced offset. If a rotation is 293 consistently applied, participants explicit aiming strategies are a viable supplement for imperfect implicit 294 motor performance. When error-clamp perturbations are applied to cursor feedback, the cursor travels in a 295 fixed direction, regardless of the direction that the hand travels, rendering explicit aiming strategies useless. 296 Thus, error-clamp perturbations are often used in studies attempting to isolate implicit motor adaptation 297 processes. 298 Replicating and extending the findings from the two studies employing rotated cursor feedback, 299 participants assigned to the error-clamp condition exhibited STL after Movement and No-Movement trials 300 (Supplemental Fig. 4a-c; please refer to supplemental material for details). We also observed significant  indicate that the change in hand angle proceeded opposite the direction of the perturbation (i.e., in the 328 direction that would counter the error). (e) Remembered STL shown as the ratio of relative hand angle 2 329 trials after experiencing a perturbation to the relative hand angle 1 trial after the perturbation (STL). 330 Remembered STL was significantly greater than 0 after both Movement (green; one-sample t-test: t(36) = 331 11.31, padj = 6.23 x 10 -13 , Cohen's d = 1.86) and No-Movement triplets (magenta, one-sample signed-rank 332 test: V = 579, padj = 5.95 x 10 -5 , r = 0.64), but did not exhibit statistically significant differences between 333 movement conditions (paired t-test: t ( showing data from trials on which STL proceeded in the same direction as the error-clamp (i.e., the "Wrong-339 Way"). Wrong-Way changes in hand angle were not statistically significantly correlated between Movement 340 and No-Movement trials (r = 0.33, padj = 0.06). These observations support the idea that the same learning 341 process may underlie adaptive single-trial learning events in response to errors on both kinds of trials, while 342 maladaptive changes in hand-angle may be attributable to potential sources of random noise. Boxplot 343 centers: median, notch: 95% confidence interval of the median, box edges: 1 st and 3 rd quartiles, whiskers: 344 most extreme value within 1.5*interquartile range of the median. Statistical significance (* = p < 0.05; n.s. 345 = p ≥ 0.05) is indicated for selected comparisons. Abbreviations: STLsingle-trial learning, Δchange, 346 CWclockwise, CCWcounterclockwise. 347 results argue against this interpretation as they suggest a shared learning mechanism across movement 356 conditions, we opted to directly test this alternative explanation in another pair of experiments. Here, we 357 only included 0° rotated (Fig. 3a, left, n = 24 participants) or clamped (Fig. 3a, right, n = 37 participants) 358 error feedback on Movement trials, but maintained 0° or 15° CW/CCW errors on the No-Movement trials. 359

DISCUSSION 390
The results presented above demonstrate that movements can be implicitly refined even when they 391 are not performed. Participants who were cued to perform a movement towards a target but suppressed 392 that movement after observation of a Stop cue showed consistent, robust STL in response to simulated 393 errors (Figs. 2-3, Supplemental Fig. 2, Supplemental Fig. 4). As implicit learning necessarily proceeds 394 following SPEs, our data also provide evidence that SPEs are computed even when movements are not 395 performed. These findings strongly support the fundamental assumptions of predictive processing frameworks of motor adaptation, where precise sensory predictions are generated from a movement intent 397 (or "plan", "goal") and compared against sensory observations to induce error-based learning. 12,25 398 We argue that we have measured learning via an implicit process, and, by extension, that the STL 399 observed in our study provides evidence that SPEs are computed regardless of whether a movement is 400 performed. Although it is important to note that visuomotor learning tasks do sometimes recruit cognitive 401 learning strategies (e.g., the deliberate "re-aiming" of movements), multiple factors indicate that our studies 402 successfully measured implicit adaptation. 18,28,29 First, in line with previous work isolating the implicit 403 adaptation process, participants were instructed to ignore the visually displayed cursor and try to contact 404 the target on every trial, a straightforward technique which has been consistently shown to eliminate the 405 explicit re-aiming of movements. 15,17,22,23,26 Second, the randomization of both the presence and direction 406 of visual errors also discourages explicit learning, reducing motivation to apply ineffective re-aiming 407 strategies (see 30 ). Third, we excluded data from participants who did not understand or recall the instruction 408 to always aim directly at the target (see Methods), decreasing the likelihood that strategic re-aiming 409 contaminated the analysis. Fourth, adaptation persisted into subsequent no-feedback trials ( Fig. 2d-e, Fig.  410 3e, Supplemental Fig. 2d-e, Supplemental Fig. 4d-e), a finding that is consistent with lingering implicit 411 motor learning; it is unlikely that strategies would be maintained through trials where no feedback is present. 412 Fifth, the magnitude of STL observed was consistent with multiple previous studies that measured implicit 413 motor adaptation rates (Supplemental Fig. 1). 17,23,31 Lastly, the adaptation effects observed in the No-414 Movement conditions were not attributable to recall of learning that occurred on Movement trials ( Fig. 3. 415 Our data thus provide striking evidence that movement is not required for implicit adaptation, and, by 416 extension, SPE computation. 417 While motor planning and concurrent sensory observations are sufficient to drive SPE computation 418 and motor adaptation, our data also indicate that errors paired with movements support a greater degree 419 of learning than errors without preceding movements, as participants showed significantly stronger STL 420 over triplets with Movement trials versus No-Movement trials. This suggests that movement provides 421 additional training input beyond what erroneous visual feedback provides alone. Alternately (though not 422 mutually exclusive), it may be that the absence of movement-related proprioceptive feedback dampens the 423 SPE signals that drive adaptation, perhaps by failing to counterbalance signals predicting proprioceptive 424 feedback. 8,32 Simpler explanations are that participants simply did not recognize the Go cue to set a 425 movement goal and plan a movement on a subset of the No-Movement trials, and/or that the timing of the 426 simulated error was inherently too variable relative to the behaviorally unobservable internal prediction. 427 Further experimentation will be required to address these possibilities. Nonetheless, our data demonstrate 428 the significant influence of the brain's prediction signals on learningeven without the ability to directly 429 attribute sensory feedback to an actual movement, prediction of a planned movement's sensory 430 consequences supports the error computations that drive adaptation of future behavior. 431 While our results demonstrate that overt movement is not necessary for motor adaptation, we are 432 not able to discern whether the generation of a descending motor command is a necessary component for 433 updating the forward model. To reliably elicit prediction generation from the forward model, we employed a 434 motor inhibition paradigm, briefly cueing participants to reach before presenting them with an abrupt stop 435 signal. This strategy is likely to have recruited mechanisms of motor inhibition beyond the primary motor 436 cortex, leaving open the possibility that a descending motor command and not an upstream motor plan per 437 se provide the necessary input for forward model adaptation. [33][34][35] Future experimentation quantifying neural 438 (EEG) or physiological (EMG) signals during this task and measuring their relationship with adaptation on 439 No-Movement trials will be crucial for addressing this point. Inspired by work in non-human primates, we 440 speculate that similar motor cortical preparatory states in the Movement and No-Movement conditions may 441 produce comparable inputs to downstream internal models. 36 442 The current report provides evidence that implicit motor adaptation can proceed without movement, 443 adding to a substantial body of work indicating that many forms of motor learning do not strictly require 444 movement-based practice. For instance, in 35 , after human participants observed others adapting to a force 445 field applied during reaching movements, the observers were able to partially compensate for that same 446 force field when they encountered it. Interestingly, this observational learning did not proceed if participants 447 were executing other movements during the observation period. This finding combined with subsequent 448 neuroimaging data showing that observational learning recruits brain areas associated with motor planning 449 were taken to suggest that engagement in a covert motor planning process may be the critical element 450 allowing for force-field adaptation following error observation without movement. [37][38][39] Together, this related 451 prior work and the evidence we have provided that motor planning is sufficient for the generation of sensory predictions and can support SPE computations suggest that there are multiple routes to inducing motor 453 planning and ultimately driving motor adaptation processes. 454 Other reports in the motor learning literature have provided evidence for cognitive compensation 455 for observed motor errors during reaching, improved visual tracking following observation of target 456 movement without engagement in visual pursuit, and improvement in movement speeds as a result of 457 mental imagery training, highlighting the breadth of motor performance-related processes that can be 458 trained without engagement in physical movements. 19,20,40,41 Together with the findings related to implicit 459 motor adaptation discussed above, this work suggests that many features of motor performance can be 460 improved by training regiments that do not involve movement. This work points to a potential opportunity 461 for the development of motor training or rehabilitation protocols that can be used when people are unable 462 to physically perform target motor behaviors, perhaps improving performance beyond what physical 463 practice can do alone. 464 Finally, our results echo the fact that other types of learning also appear to occur without overt task 465 execution. Outside of motor learning, fear associations can be extinguished by instructing participants to 466 imagine a fear-predicting stimulus even when they are not presented with the stimulus, with this 467 "imagination" protocol generating neural signatures of the negative prediction errors observed during 468 naturalistic fear extinction. 42,43 Considering this prior work and the findings presented in this study, it may 469 be that the generation of predictions for comparison with subsequent sensory observations is sufficient for 470 error-based learning across motor and non-motor domains alike. In other words, task execution may not 471 always be required for learning, so long as the predictions and observations needed to compute errors are 472 both present. 473 1. Friston, K. The free-energy principle: a unified brain theory? Nat Rev Neurosci 11, 127-138 (2010 Seventy-five participants were excluded (10 from the dataset collected for Supplemental Fig. 2, 13 from the 615 dataset collected for Supplemental Fig. 4, 26 from the dataset collected for the rotation perturbation 616 experiments described in Fig. 3, and 26 from the dataset collected for the error-clamp perturbation 617 experiments described in Fig. 3) for failure to sufficiently recall task instructions, as ascertained by a 618 questionnaire at the end of the experiment, leaving 158 participants for our analyses. See the Questionnaire 619 section below the Test phase sections for more details. We note that all the key results described here (i.e., 620 statistically significant learning after No-Movement trials) held with or without these exclusions; we opted to 621 be conservative in our exclusion criteria to limit potential effects of explicit learning. We note that the although we observed that participants using a trackpad exhibited longer reaction times than others, 646 consistent with a previous report. 48 647 Mouse position sampling rates depended on the exact hardware that each participant used to 648 complete the task. Sampling rates were likely affected by features of the specific mouse used, along with 649 features of the specific computer used, as computers may limit the rate at which the browser samples data 650 in order to cope with limited processing power. In general, sampling rates were around 60 Hz (median ± 651 interquartile range across all 213 online participants recruited: 62.46 ± 2.17 Hz) but ranged from 19.23 Hz 652 to 249.69 Hz. Note that the vast majority of sampling rates were near 60 Hz: Only 5% of sampling rates 653 were < 41.79 Hz, and only 5% of sampling rates were > 126.65 Hz. 654 655 Baseline training phase. For in-lab participants, the robot moved the participant's hand to a central starting 656 location (depicted by a grey circle) at the middle of the display while hand and cursor feedback were hidden. 657 They were instructed to hold their hand still in the starting location util the target turned green, at which 658 point they should make a straight slicing movement through the target. After a 100 ms delay, the robot 659 moved the hand back to the starting location. Participants completed 5 of these trials with online and 660 endpoint cursor feedback, followed by 5 trials without visual feedback of the cursor location. Endpoint 661 feedback was constituted by the cursor remaining at the position where it had passed the target radius for 662 50 ms. Participants then completed 10 alternating trials on which the target turned green and stayed green 663 (Execution, 'Go' trials) and on which the target turned magenta 100 ms after turning green, signaling that 664 participants should withhold their movement (No-Movement, 'Stop' trials). After this baseline phase, 665 participants were instructed to continue following these instructions for the remainder of the experiment.
Online participants experienced an identical baseline phase, with the exception that they were 667 instructed to move their mouse into a central starting location on the first trial and subsequently saw their 668 mouse cursor reappear near the starting location 100 ms after the completion of the reaching movement, 669 so that participants could quickly return to the start location to initiate the next trial. 670 671 Test phase: Rotation and Error-Clamp Experiments (Fig. 2, Supplemental Fig. 2, Supplemental Fig. 4). 672 During the test phase, 480 (in-lab) or 270 (online) total trials were divided into 3-trial triplets (Fig. 1c) participants viewed a brief animation of the cursor moving straight to the center of the target following a 679 trajectory deflected by ±15° from the target center. Animation onset latency was set as a running median 680 of the participant's reaction times on the previous 5 trials. Animation duration was set as a running median 681 of the participant's movement times on the previous 5 trials. If a participant took longer than 400 ms to 682 execute a movement, 800 ms to initiate the movement, their reach trajectory changed by >10° during the 683 movement, or the reach terminated ≥ 60° away from the target, they received a warning and a 4s time-out. 684 If a participant moved their hand (>5 mm in-lab [radius of the starting location]; anything >0 pixels online) 685 on a No-Movement trial, the trial was immediately aborted, and they received a warning and a 4s time-out. 686 The Stop manipulation was successful: Across the experiments, participants erroneously moved on 34.39 687 ± 20.63% (mean ± standard deviation) of Stop trials, suggesting that, for the most part, they were 688 consistently planning movements on Stop trials. 689 For in-lab studies, we used 4 possible triplet perturbation trial types (Movement/No-Movement: 690 ±15°), each of which occurred 40 times throughout each session. For online studies, we used 6 possible 691 triplet perturbation trial types (Movement/No-Movement: ±15° or 0°), each of which occurred 15 times 692 throughout each session. Triplets were pseudorandomly presented within each block, with the constraints 693 that a single rotation (±15° or 0°) could not occur on more than 2 consecutive triplets and that the same movement condition (i.e., Movement or No-Movement) could not occur on more than 3 consecutive triplets. 695 Three repetitions of each triplet type occurred in blocks of 18 triplets, and participants received a break after 696 each of these blocks. 697

698
Test phase: Rotation and Error-Clamp Experiments with 0° Perturbations on Movement Trials (Fig. 3). 699 Experiments were conducted as described above for the other online experiments, with the exception of 700 the details described in this section. For the experiments described in Fig. 3a- with the constraints that a single non-zero rotation (15° clockwise, 15° counterclockwise) could not occur 707 on more than 2 consecutive triplets. 708 For the experiments described in Fig. 3e- Questionnaire: As we could not receive verbal confirmation that participants understood the task 715 instructions in the online version of the task, we asked subjects to fill out a brief questionnaire to query their 716 understanding of the task. The questionnaire asked participants to attest whether or not 1) their goal was 717 to move the real mouse and not the cursor straight through the green targets and whether or not 2) their 718 goal was to move the white cursor (not the real mouse) straight through the green targets. Participants 719 could select the options, "True," "False," or "Not Sure." Participants were considered to have understood 720 the instructions if they answered both questions correctly (i.e., answered "True" to question 1 and "False" 721 to question 2). The majority of participants answered both questions correctly (138 of 213 participants [65%]), suggesting that most participants understood the task instructions. Nonetheless, these participants 723 made up the dataset for all reported analyses for the online experiments, and all other online participants 724 were excluded from analyses to exclude potential effects of explicit re-aiming. 725 726 Data analysis. Data were processed in Python 3.8.5 and Matlab 2018a. Trials with movement were 727 excluded from analysis 1) if any of the reaches in the triplet were not straight (aspect ratio > participant-728 wise mean + 3 * participant-wise standard deviation), 2) if the participant received any warning for failure 729 to follow task instructions (see Feedback for failure to follow task instructions, above), or 3) if the triplet 730 included a No-Movement No-Go perturbation trial with any detectable mouse movement (>0 pixels online, 731 >5 mm in lab). 732 Reach endpoint angle was computed as the angular distance between the center of the target and 733 the point at which the mouse passed the target's radial distance. Because mouse sampling rates did not 734 always allow us to measure mouse position at the exact target radius during the online study, we used the 735 last sample before and the first sample after the mouse passed the target radius to compute an interpolated 736 mouse position at the target radius, as described in a previous report. 48 We note that analyses comparing 737 these measures to measurements at the last sample of the reach (even when it was beyond the target) or 738 the hand angle at peak velocity did not result in substantially different hand angle measurements or 739 statistical outcomes. 740 Single-trial learning (STL) was measured as the difference between reach endpoint angle on the 741 third and first trial of each triplet. For our initial analyses, the sign of STL corresponded to the direction of 742 the relative change in hand angle, with clockwise changes in hand angle taking a negative sign and 743 counterclockwise changes in hand angle taking a positive sign. When we collapsed STL data across 744 rotation directions, we normalized the sign of STL so that changes in hand angle opposite the direction of 745 the imposed rotation took a positive sign and changes in the direction of the rotation took a negative sign. 746 Remembered STL was quantified as the difference between reach endpoint angle on the first trial 747 of one triplet and reach endpoint angle on the first trial of the previous triplet. When remembered STL is 748 reported as a ratio, this value was computed by dividing remembered STL by the STL attributable to a given 749 triplet.
Statistics. Statistical tests were conducted in R (v. 4.0.3; packages rstatix 49 , coin 50 , MuMIn 51 , 752 lmerTest 52 , lme4 53 , r2glmm 54 , emmeans 55 , effsize 56 , effectsize 57 , magrittr 58 , ggplot2 59 , ggpubr 60 , 753 ggeffects 61 ). Data from in-lab experiments were analyzed using a two-way repeated measures ANOVA. If 754 an ANOVA showed a significant main effect or interaction, post-hoc pairwise tests were performed. When 755 samples failed to satisfy the normality assumption of the pairwise t-test (assessed via a Shapiro-Wilk test), 756 we used the more robust paired-samples Wilcoxon signed-rank test. Otherwise, we used the more powerful 757 paired t-test. Effect sizes for ANOVA main effects/interactions were quantified via generalized η 2 (η 2 ), we 758 quantified the effect sizes for t-tests using Cohen's d, and we used the Wilcoxon effect size (r) to quantify 759 effect sizes for signed-rank tests. For these and all subsequent analyses, we corrected for multiple 760 comparisons using the false-discovery rate approach to maintain family-wise alpha at 0.05. 761 Data from the experiments conducted online did not satisfy multiple assumptions of the two-way 762 repeated measures ANOVA (non-existence of extreme outliers, sphericity), so we employed a linear mixed 763 modeling (LMM; R package lmerTest and lme4) approach for analysis of these data. All LMM's included 764 fixed effects of perturbation size and movement condition, as well as random effects of subject. Degrees of 765 freedom were estimated using the Kenward-Rogers approach, and LMM outcomes were reported using 766 ANOVA-style statistics. Partial R 2 was computed to report effect sizes for the LMM factors (R package 767 r2glmm). Post-hoc pairwise comparisons were performed between estimated marginal means computed 768 from the LMM (R package emmeans). 769 For one-off comparisons between samples or to distributions with 0-mean, we checked samples 770 for normality. When samples were normally distributed, we ran t-tests and computed Cohen's d to report 771 effect sizes for statistically significant results. Otherwise, we ran Wilcoxon-signed rank tests and measured 772 effect sizes using the Wilcoxon effect size (r). 773 showing how the forward model may support implicit motor adaptation in the presence of sensory feedback 776 not causally related to self-generated movement. (b) Schematic of events on trials with visual feedback. 777 The robotic apparatus brought the participant's hand to the starting location to initiate a trial. On Movement 778 trials (top), the target turned green ('GO'), cueing participants to reach through the target. On trials with 779 visual feedback, participants observed a white feedback cursor move along a rotated trajectory ('Rotation'). Supplemental Table 1  18   11 Supplemental Table 2  19 Learning Rate (degrees/trial)   partial R 2 = 0.002), as well as a significant interaction (F(2, 2229) = 12.40, p = 4.41 x 10 -6 , partial R 2 = 0.01).