Plan-based generalization shapes local implicit adaptation to opposing visuomotor transformations

The human ability to use different tools demonstrates our capability of forming and maintaining multiple, context specific motor memories. Experimentally, this ability has been investigated in dual adaptation, where participants adjust their reaching movements to opposing visuomotor transformations. Adaptation in these paradigms occurs by distinct processes, i.e. the development of explicit aiming strategies for each transformation and/or the implicit acquisition of distinct visuomotor mappings. The presence of distinct, transformation-dependent aftereffects has been interpreted as support for the latter. Alternatively, however, distinct aftereffects could reflect adaptation of a single visuomotor map, which is locally adjusted in different regions of the workspace. Indeed, recent studies suggest that explicit aiming strategies direct where in the workspace implicit adaptation occurs. Disentangling these possibilities is critical to understanding how humans acquire and maintain separate motor memories for different skills and tools. We therefore investigated generalization of explicit and implicit adaptation to different directions after participants practiced two opposing cursor rotations, which were associated with separate visual workspaces. Whereas participants learned to compensate opposing rotations by explicit strategies that were specific to the visual workspace cue, aftereffects were not sensitive to visual workspace cues. Instead, aftereffects displayed bimodal generalization patterns that appeared to reflect locally limited learning of both transformations. By varying target arrangements and instructions, we show that these generalization patterns are consistent with implicit adaptation that generalizes locally around (explicit) movement plans associated with opposing visuomotor transformations. Our findings show that strategies can shape implicit adaptation in a complex manner. New & Noteworthy Visuomotor dual adaptation experiments have identified contextual cues that enable learning of separate visuomotor mappings, but little is known about the underlying representations of learning. We report that visual workspace separation as a contextual cue enables participants to compensate opposing cursor rotations by a combination of explicit and implicit processes: Learners developed context-dependent explicit aiming strategies while an implicit visuomotor map represented dual adaptation independent from context by local adaptation around the explicit movement plan.

suggest that explicit aiming strategies direct where in the workspace implicit adaptation 23 occurs. 24 Disentangling these possibilities is critical to understanding how humans acquire and 25 maintain separate motor memories for different skills and tools. We therefore investigated 26 generalization of explicit and implicit adaptation to different directions after participants 27 practiced two opposing cursor rotations, which were associated with separate visual 28 workspaces. Whereas participants learned to compensate opposing rotations by explicit 29 strategies that were specific to the visual workspace cue, aftereffects were not sensitive to 30 visual workspace cues. Instead, aftereffects displayed bimodal generalization patterns that 31 appeared to reflect locally limited learning of both transformations. By varying target 32 arrangements and instructions, we show that these generalization patterns are consistent 33 with implicit adaptation that generalizes locally around (explicit) movement plans associated 34 Dual-adaptation paradigms have served as a useful tool to study this ability. In these 55 paradigms, participants learn to compensate opposing visuomotor transformations, such as 56 visuomotor cursor rotations (Cunningham 1989)  be justified by the omnipresence of these physical cues in natural environments, the above 73 views can be unified by thinking of the motor memory that results from learning as a 74 multidimensional state space that can contain arbitrary psychological and physical cue 75 dimensions (Howard et al. 2013). Under this view, whether or not a cue enables dual 76 adaptation depends on whether different cue characteristics allow for a regional separation 77 in the state space of memory that is sufficient to reduce the overlap between local 78 generalization of multiple transformations and thereby attenuate interference between 79 them. 80 A level of complexity is added to this by recent views that propose at least two 81 qualitatively distinct learning mechanisms in visuomotor adaptation (Taylor and  and to dominantly contribute to aftereffects that persist in the absence of the novel 87 transformation (Heuer and Hegele 2008 participants controlled a cursor on the screen (cyan filled circle, 5.6 mm diameter) via a 143 custom script written in Matlab (MATLAB, RRID:SCR_001622) using Psychophysics toolbox 144 (Brainard 1997; RRID:SCR_002881) . On movement practice trials, participants had to "shoot" 145 the cursor from a visual start (red/green outline circle, 8 mm diameter) through a target (white 146 filled circle, 4.8 mm diameter) by a fast, uncorrected movement of their right hand. Cursor 147 feedback was provided concurrently but was frozen as soon as participants passed the target 148 amplitude. The cursor veridically represented hand position during all familiarization and 149 baseline practice trials (phase explanations below). During rotation practice and maintenance 150 (inserted in-between posttests), the cursor was rotated around the start relative to hand 151 position. The direction of cursor rotation was cued by the location of display on the screen 152 (see below). On movement test trials, the cursor disappeared upon leaving the start circle. If 153 participants took longer than 300 ms from leaving the start circle to reaching target amplitude, 154 the trial was aborted and an error message was displayed ("Zu langsam!", i.e. "Too slow!"). 155 After the end of the reaching movements, arrows at the side of the screen guided participants 156 back to the start location without providing cursor feedback. 157

Visual workspace cue 158
Throughout the experiment, the start locations of the reaching movement alternated 159 between the left and right half of the screen (x-axis shift of ¼ screen width in respective 160 direction). In phases with cursor rotation, these visual workspaces were associated with the 161 cursor rotation sign. We chose this contextual cue because previous research had indicated 162 that it successfully cues separate explicit strategies but not separate, implicit visuomotor maps 163 shown on a given trial, but all generalization targets are displayed here for illustrative 210 purposes. In addition, the actual targets were white. B) Experimental protocol for an 211 exemplary participant of experiment 1. The start location of the hand on the table was  212 identical for both visual workspaces. The presence/absence of the rotation was cued by the 213 color of the start circle and instructed for both, trials with and without feedback. Alternation 214 between visual workspaces was every four trials during familiarization and posttests practice 215 and every eight trials during rotation practice. 216 Experimental Protocol: Experiment 1 217 In experiment 1, participants practiced reaching movements to a single target direction 218 at 90° (with 0° corresponding to movements to the right). Cursor feedback was rotated around 219 the start location with a clockwise (CW) rotation in the left and a counterclockwise (CCW) 220 rotation in the right visual workspace (figure 2A). Movements thus had a common visual target 221 direction but the solutions to the two rotations were separate. Each movement generalization 222 test block contained two sets of trials to nine equally spaced generalization targets from 0° to 223 180°. Pretests thus contained 86 trials, including 36 movement test trials, 18 explicit test trials 224 and a total of 32 movement practice trials. Similarly, posttests contained 138 trials in total. 225

Experiment 2 226
The goal of experiment 2 was to ensure that our findings from experiment 1 were not solely 227 attributable to biomechanical or visual biases independent of learning (Ghilardi et al. 1995;228 Morehead and Ivry 2015). To test this possibility, the practice and generalization targets were 229 moved by 45° CW (i.e. the practice target was at 45° and generalization targets spanned -45° 230 to 135°; Figure 3A). We predicted that if the generalization pattern was solely due to potential 231 biases, then it would be unchanged. However, if the apparent generalization function was the 232 result of learning, then it should be shifted by -45° (i.e. 45° CW) on the generalization direction 233 axis. Apart from these changes, experiment 2 was like experiment 1, except that we increased 234 the number of consecutive movement test sets for each visual workspace and test condition 235 from two to three, thus increasing the number of pretest trials to 122 and posttest trials to 236

Experiment 3 238
To further contrast plan-based and target-based generalization, we designed a 239 paradigm with separate visual target locations and cursor rotations, which were arranged in 240 such a way that the resulting compensation strategy for each target should approximately 241 point at the respective other target when projected to the common physical workspace. This 242 way, plan-and target-based generalization predict opposite generalization patterns. We  This was done by informing participants that they would have to aim roughly toward 1 o'clock 253 in the left workspace and 11 o'clock in the right workspace to hit the respective practice 254 targets. They were also encouraged to fine-adjust those strategies. We hypothesized that this 255 instruction should strengthen the contrast we originally hypothesized in experiment 3 (figure 256 4A). To ensure that participants applied non-overlapping strategies throughout practice, we 257 asked participants after the experiment where they aimed during early, middle, and late 258 practice in the left and right workspace, respectively. However, based on these post-259 experiment reports, we excluded 7 participants who reported not using the clock analogy or 260 aiming less than half an hour in the correct direction away from 12 o'clock for any of those 261 time points (table 1). 262

Data analysis 263
Data were analyzed in Matlab (MATLAB, RRID:SCR_001622), R (R Project for Statistical 264 Computing, RRID:SCR_001905), and jasp (JASP, RRID:SCR_015823). Position data were low-265 pass filtered using Matlab's "filtfilt" command set to a 4 th order Butterworth filter with 10 Hz 266 cutoff frequency. We separately calculated x-and y-velocity using a two-point central 267 difference method and tangential velocity. Movement start was determined as the first frame 268 where participants had left the start circle and tangential velocity exceeded 30 mm*s -1 for at 269 least three consecutive frames. For each trial, we extracted the angular endpoint direction as 270 the angle between the vector from start to target and the vector between the start and the 271 position where the hand passed the target amplitude. We excluded trials where no movement 272 start could be detected or where participants failed to reach the target amplitude (see table  273 1). 274 For pre-and posttests, we calculated medians separately for each visual workspace 275 (combining the groups with different initial workspaces), target direction and type of posttest. 276 Our main variables of interest were generalization patterns of aftereffects and we limit our 277 analysis on explicit judgments and total learning to descriptive reporting. 278 In our analysis of implicit learning, we used two candidate functions to represent our 279 hypotheses for the shape of generalization. The first candidate was a single Gaussian: 280 where is the aftereffect at test direction and the three free parameters are the gain 282 , the mean and the standard deviation . 283 The second candidate was the sum of two Gaussians, henceforth referred to as 284 "bimodal Gaussian": 285 for which we assumed separate amplitudes 0 ; 3 and means 0 ; 3 but the same 287 standard deviation for the two modes. comparison but decided against this option as our focus was to distinguish between types of 303 dual adaptation rather than to infer its exact shape. 304 To test our hypotheses, we fit the two candidate models to the nine group mean data 305 points corresponding to the nine generalization directions of each visual workspace's 306 aftereffect, using Matlab's "fmincon" to maximize the joint likelihood of the residuals. For this, 307 we assumed independent, Gaussian likelihood functions centered on the predicted curve, 308 whose variance we estimated by the mean of squared residuals. As this fitting procedure 309 tended to run into local minima, we repeated each fit 100 times from different starting values 310 selected uniformly from our constraint intervals (constraints were -180° to 180° on a, 0° to 311 180° on b-parameters, or 135° to -45° for experiment 2, and 0° to 180° on c), and used only 312 the fit with the highest joint likelihood. 313 To select the best model, we calculated Bayesian Information Criterion (BIC) as: 314 = ln( ) * + 2 * ln( ) 315 where is the number of data points, is the number of free parameters of the model and 316 is the joint likelihood of the data under the best fit parameters. 317 To compare model parameters, we created 10000 bootstrap samples by selecting N 318 out of our N single participant datasets randomly with replacement and taking the mean 319 across participants for each selection. We then fit our candidate models to each of these 320 means by the same method described above, except that we avoided restarting from different 321 values and used the best fit values from the original dataset as starting values instead. Because 322 the bimodal Gaussian has two identical equivalents for each solution, we sorted the resulting 323 parameters so that b1 was always larger than b2. This procedure gave us a distribution for each 324 parameter from which we calculated two-sided 95% confidence intervals by taking the 2.5 th 325 and 97.5 th percentile value. We considered parameters significantly different from a 326 hypothesized true mean if the latter was outside their 95% confidence interval. Similarly, we 327 considered differences between two parameters significant if the 95% confidence interval of 328 their differences within the bootstrap repeats did not include zero. Additionally, we used t-329 tests to compare aftereffect magnitudes (of the raw, non-bootstrapped data) for specific directions. D: When tested separately, explicit knowledge reflected this cue-dependent, 397 broadly generalizing learning. E: Aftereffects on the other hand appeared independent of 398 the visual workspace cue and exhibited a generalization pattern that was well fit by a sum of 399 two Gaussians (solid red and blue lines). 400

Experiment 2 401
For experiment 2, we predicted a two-peaked generalization pattern of aftereffects, 402 similar to the one we observed in experiment 1, but shifted by 45°. That is, if the pattern in 403 experiment 1 were just biases that did not reflect learning, we would predict it to be exactly 404 the same as in experiment 1, whereas if it were a result of learning, we would predict it to be 405 shifted by -45° on the x-axis, reflecting the -45° shift of the practice targets. conducted experiment 4 where we provided participants with ideal aiming strategies at the 488 onset of rotation practice. We hypothesized that more appropriate strategy application 489 should alleviate interference and restore the predicted, plan-based generalization pattern if 490 our reasoning was correct. 491

Experiment 4 492
Predictions for experiment 4 were the same as they had been for experiment 3, but 493 here we predict more local, direction-specific implicit adaptation because participants should 494 have a more consistent strategy. Indeed, we observed more consistent performance during 495 initial practice and the restitution of flat overall learning and explicit judgment patterns, 496 indicating that participants were able to implement the provided strategy ( fig 5B-D). 497 Consistent with our prediction, the resulting generalization pattern of implicit learning once 498 again had opposite peaks (∆BIC left: 9; right: 9; figure 5E). Parameter histograms display more 499 confined peaks compared to experiment 3 (figure 6), suggesting that the bimodal Gaussian 500 was more appropriate, here. Importantly, the signs of the amplitude parameters were in line 501 with the predictions under plan-based generalization and the confidence intervals on 502 associated amplitude parameters did not include zero In comparison with experiment 3, providing an aiming strategy at the onset of practice 510 alleviated interference in implicit learning, which we interpret to reflect better expression of 511 local generalization due to more appropriate application of spatially separate explicit 512 strategies. The study of visuomotor dual adaptation has frequently been motivated by an interest 540 in understanding how the brain associates contextual cues with separate memories to 541 represent and switch between different visuomotor environments, like controlling tools or 542 Plan or target-based? 587 Our findings contradict conclusions from an earlier study, which inferred the visual 588 target to be the relevant center of local, implicit generalization to different directions (Woolley 589 et al. 2011). We explain this contradiction by the fact that this earlier study only compared the 590 two alternative hypotheses that learning centers on the visual target or the executed 591 movement but did not consider the possibility that it centers on the movement plan. When 592 reinterpreted in the light of this new hypothesis, all results in that study can potentially be 593 explained by plan-based generalization with separate visual targets cuing separate aiming 594 strategies. Specifically, participants in that study learned to compensate opposing cursor 595 rotations when visual targets were separate but ideal physical solutions overlapped. 596 Alternatively to local generalization centering on the visual target, this can be explained by 597 different aiming strategies becoming associated with the separate targets, each of which is 598 less than the optimal, full rotation (Bond and Taylor 2015) and therefore does not overlap 599 with the strategy for the opposing cursor rotation (in contrast to the physical solutions). 600 Similarly, interference scaling inversely with the separation of visual targets (Woolley et al. 601 2011) may also be explained by the degree of overlap between aiming strategies. 602 It is worth nothing that the lack of dual adaptation in an earlier experiment by Woolley 603 and colleagues (2007) may be attributable to the saliency of the visual cues. In this study, they 604 found that practice to the same visual target did not enable dual learning when opposing 605 rotations were cued by screen background colors, but the task relevancy of these cues may 606 not have been noticed by the participants. If the participants did not associate an aiming 607 strategy with the cues, then it would have not allowed plan-based and directionally-608 dependent implicit adaptation to develop; thus, leading to no dual adaptation. 609 Plan or movement-based? 610 Alternatively to plan-based generalization, our findings could be explained by learning 611 generalizing around the movement path, as has been found for force field adaptation 612 Rather than a fixed center of generalization, one might expect that the brain adaptively 630 exploits the task structure by linking memory separation to those cues that are sufficiently 631 distinct. Our data for implicit learning do not support this possibility, as otherwise, we would 632 have expected aftereffects in experiment 3 to be shaped by learning around the separate 633 visual targets rather than interference. However, it is still possible that such a shift in cue 634 relevance may occur under different circumstances (e.g. longer practice). More generally, we 635 may ask if local learning of multiple transformations evolves according to an underlying model 636 that is specifically adapted to the practice scenario or if it is merely the sum of single 637 transformation learning. Previous studies have considered a model-based approach and 638

Disclosures 735
The authors declare no conflicts of interest.