Experimental setup and procedures

A) Setup for the experiment. B) Illustration of experimental workspace for the Algorithmic group (blue) and C) the Retrieval group (orange) during training. A 45° visuomotor rotation was applied to the Critical target and all Non-Critical targets (filled) for the Algorithmic group, while no rotation was applied to the Non-Critical targets for the Retrieval group (empty). The 60° gap was applied to separate the space between the critical and Non-Critical targets. D) Probe targets (empty) neighbored the Critical target. No feedback was provided during Exclusion trials and participants were instructed to withhold strategy use. E) No rotation was applied during baseline (80 trials), a rotation was applied during training (356 trials), Exclusion trials (7 trial mini-blocks) were intermittently dispersed during training (49 Exclusion trials in total), and cursor feedback was withheld during the washout block at the end of training (48 trials).

Adaptation performance, reaction time, and implicit generalization functions for the algorithmic and retrieval strategies in Experiment 1, with potential confounds controlled relatively loosely.

A) Adaptation performance measured at the Critical target location, reflected by the hand angles reaching near 45°. Vertical dashed lines indicate onset and offset of the training phase. Each data point represents binned hand angles for one cycle of training (see supplementary material for complete time course data). A mini workspace diagram is included in each figure to show the target locations where data are demonstrated. B) Absolute hand angle error (unsigned error) is calculated for all Non-Critical target locations to reflect the accuracy of performance. Given that each group had distinct task instructions at the Non-Critical target, absolute hand angle error can ensure a numerical comparison. C) Reaction time for the Critical target and D) Reaction time for Non-Critical target locations. E) Two generalization curves (right y-axis) for the algorithmic (blue) and retrieval (orange) groups are shown across the corresponding probe target locations (x-axis, -45° – 45°). Beneath these curves, bar plots illustrate the distribution of reach directions for each group (left y-axis), with darker colors indicating reaches to the Critical target and lighter colors representing reaches to adjacent Non-Critical target locations (±60°). Note that implicit recalibration can be acquired within the area containing the blue or light blue bars due to the use of continuous feedback; in contrast, no feedback was shown for the reaches represented by the lighter orange bar in the retrieval group, which would not produce the implicit recalibration. The shaded gray region marks the “aiming zone,” where participants were most likely to aim when counteracting the 45° rotation at the Critical target. The amplitude, mean, and width parameters displayed in the figure were derived from Gaussian function fits.

A stricter control narrows down the implicit generalization function in the algorithmic group

A) Diagram of workspace setup and target locations for algorithmic strategies in Experiment 2. Participants receive delayed endpoint feedback at all Non-Critical targets, so that implicit recalibration at all Non-Critical targets should not occur. The continuous online feedback was applied to the Critical target, enabling implicit recalibration. The Critical target is selected at least ±90° away from Non-Critical targets to further attenuate the influence of aiming for adapting 45° rotations at the Non-Critical targets. B) Diagram of workspace setup and target locations for retrieval strategies in Experiment 2. The feedback type and workspace setup remain consistent with the algorithmic group. But participants were required to aim directly at the Non-Critical target location. C) Hand angle for the Critical target locations. D) Absolute hand angle error for the Non-Critical target location. E) Reaction time for the Critical target location. F) Reaction time for the Non-Critical target location. G) Generalization curves for algorithmic and retrieval strategies. Beneath the curves, bars represent the distribution of reaches for each group. The shaded gray region marks the “aiming zone,” where participants were most likely to aim when counteracting the 45° rotation at the Critical target. The amplitude, mean, and width parameters displayed in the figure were derived from Gaussian function fits.

Experimental design incorporating an error-clamp paradigm to assess the influence of strategy use on implicit recalibration.

The examples of particular workspace scenarios used in Experiment 3 for the algorithmic and retrieval groups. A) The scenario for trials reaching toward the 45° location relative to the Critical target with 15° error-clamped feedback. Note that both groups lack a landmark for the 45° location, and only this scenario has the error-clamped feedback. B) The scenario for trials reaching toward the 75° relative to the Critical target. For the algorithmic group, the 75° location relative to the Critical target must be computed using a mental rotation strategy because no visual target is presented. In contrast, for the retrieval group, a target is displayed at the location that is 75° relative to the Critical target. Participants were asked to simply reach toward it. C) The scenario for trials requiring reaching toward the 105°; no target is present for the algorithmic group while a target is presented for the retrieval group. For any Non-Critical angular direction (any reach location other than 45°), no cursor feedback or clamped feedback was imposed. D) The 7 probe targets (including the Critical target) are selected for measuring implicit recalibration during the Exclusion blocks.

With the strongest control for confounds, implicit generalization function becomes comparable between two groups.

A) Hand angles at the 45° location relative to the Critical target. B) Absolute hand angle errors at the Non-Critical locations. C) Reaction times at the 45° location relative to the Critical target. D) Reaction time at the Non-Critical locations. E) Generalization curves for algorithmic and retrieval strategies. Beneath the curves, bars represent the distribution of reach direction for each group. The shaded gray region marks the “aiming zone,” where participants were most likely to aim when reaching the 45° target relative to the Critical target. The amplitude, mean, and width parameters displayed in the figure were derived from Gaussian function fits.

Residual analysis of the implicit generalization function by subtracting retrieval from algorithmic

A) Contrast of generalization function after fitting the model using algorithmic - retrieval strategies. X axis represents probing target locations, and Y axis represents the magnitude of hand angle. The positive value indicates that algorithmic strategy resulted in greater implicit recalibration at the probe target location. B) The difference in probability of reach direction across workspace (−180° – 180°). A positive value indicates that algorithmic strategies reach that area more frequently. In Exp1, there were no implicit recalibrations at the Non-Critical target in the retrieval group. When comparing the probability of reach directions for the Non-Critical target, we used the Algorithmic strategy minus zero. The implicit recalibration at the Non-Critical targets showed a clear spillover effect because the residual of reach-angle probability is highly consistent with the residual of generalization function. C) Residual width of the generalization function across all three experiments. From Experiment 1 to 3, the width of generalization function gradually reduced with the extent of experimental control. D) Residual center of the generalization function across all three experiments. E) Residual amplitude of the generalization function across all three experiments. In C – E, data was derived from bootstrap, and error bars indicate the 95% confidence interval.

Full time course analysis for adaptation performance and reaction time, and control analysis in Experiment 1

A) signed hand angle and C) reaction time at the critical target. On the x-axis, the numbers indicate the cumulative trial count for reaches made to the critical target only. Dashed vertical lines mark the boundaries of the exclusion blocks (Blocks 1–7). Within each exclusion block, the error bars show the mean hand angle, reflecting implicit recalibration, and the mean reaction time measured at the critical target. B) Signed hand angle and D) reaction time at the non-critical targets. Here, the x-axis indicates the cumulative trial count for reaches made to the non-critical targets only. During each exclusion block, the error bars represent the average performance across the probe targets, excluding the critical target. E–F) Mean reaction time during Exclusion and training trials for the Algorithmic and Retrieval groups, also normalized to baseline performance. G–H) Mean hand angle during Exclusion trials at the critical and non-critical targets for the Algorithmic and Retrieval groups, shown as an index of implicit recalibration. These values were normalized to baseline performance.

Full time course analysis for adaptation performance and reaction time, and control analysis in Experiment 2

A) signed hand angle and C) reaction time at the critical target. On the x-axis, the numbers indicate the cumulative trial count for reaches made to the critical target only. Dashed vertical lines mark the boundaries of the exclusion blocks (Blocks 1–7). Within each exclusion block, the error bars show the mean hand angle, reflecting implicit recalibration, and the mean reaction time measured at the critical target. B) Signed hand angle and D) reaction time at the non-critical targets. Here, the x-axis indicates the cumulative trial count for reaches made to the non-critical targets only. During each exclusion block, the error bars represent the average performance across the probe targets, excluding the critical target. E–F) Mean reaction time during Exclusion and training trials for the Algorithmic and Retrieval groups, also normalized to baseline performance. G–H) Mean hand angle during Exclusion trials at the critical and non-critical targets for the Algorithmic and Retrieval groups, shown as an index of implicit recalibration. These values were normalized to baseline performance.

Full time course analysis for adaptation performance and reaction time, and control analysis in Experiment 3

A) signed hand angle and C) reaction time at the critical target. On the x-axis, the numbers indicate the cumulative trial count for reaches made to the critical target only. Dashed vertical lines mark the boundaries of the exclusion blocks (Blocks 1–7). Within each exclusion block, the error bars show the mean hand angle, reflecting implicit recalibration, and the mean reaction time measured at the critical target. B) Signed hand angle errors and D) reaction time at the non-critical targets. Here, the x-axis indicates the cumulative trial count for reaches made to the non-critical targets only. During each exclusion block, the error bars represent the average performance across the probe targets, excluding the critical target. The signed error is computed by subtracting the actual hand angle from the instructed reach angle. E–F) Mean reaction time during Exclusion and training trials for the Algorithmic and Retrieval groups, also normalized to baseline performance. G–H) Mean hand angle during Exclusion trials at the critical and non-critical targets for the Algorithmic and Retrieval groups, shown as an index of implicit recalibration. These values were normalized to baseline performance.

The extent of adaptation reflected by hand angles at a trial just prior to Exclusion blocks, and reaction time while performing during Exclusion trials.

A–C) Hand reaching angles (°) for the single-trial performance at the critical target immediately preceding each Exclusion block across all seven blocks in Experiments 1, 2, and 3. These “top-up” trials were used to verify that both groups achieved comparable levels of adaptation before entering the Exclusion blocks, thereby preventing bias arising from potential time-dependent memory decay in implicit recalibration. The dash line represents the goal adaptation angle of 45°. As shown in figures, the algorithmic group (blue) and retrieval group (orange) reached comparable level of adaptation close to the goal 45° preceding each Exclusion block. D–F) Mean reaction times for all Exclusion trials within each block. During these trials, participants were instructed to withhold any strategy use, and thus the algorithmic group was expected to reach toward the probing targets as quickly as the retrieval group.

Gaussian fits for Experiment 1 – 3.

A) The model fitting of the Gaussian function between hand angles and the 7 probe target locations (−45 ° to 45 °) in Experiment 1. The Algorithmic group is in blue, and the Retrieval group is in orange. B) The model fitting of the Gaussian function in Experiment 2. C) The model fitting of the Gaussian function in Experiment 3. Hand angles in all Experiments are normalized to the baseline.

Distributions of reaching direction variability reflected by standard deviation

Implicit recalibration is thought to generalize around the planned movement direction, with each reach producing a small Gaussian-like kernel centered on that plan. Greater variability in reaching direction disperses these planned movement centers, so that learning accumulates across multiple nearby locations. The sum of these kernels broadens the overall generalization function across the workspace. To test this account, we examined movement variability at the critical target, reasoning that group differences in reach-direction variability could contribute to differences in the width of the implicit generalization function. Variability for each group was quantified as the standard deviation of endpoint hand angle at the critical target across 1,000 bootstrap resamples. In panels A–C, the x-axis shows the standard deviation of the endpoint hand angle relative to the critical target, reflecting the variability in participants’ reaching directions. (A) In Experiment 1, the Algorithmic group showed greater movement variability than the Retrieval group. Together with implicit recalibration arising from the non-critical targets, this increased variability likely contributed to a broader generalization function centered on the critical target. (B) In Experiment 2, the group difference in movement variability was even larger than in Experiment 1. Because implicit recalibration at the non-critical targets was minimal, variability around the critical target likely became the main factor underlying the broader generalization function. (C) In Experiment 3, implicit recalibration under error-clamp feedback was largely independent of aiming strategy. Although the Algorithmic group still showed somewhat greater movement variability, the implicit generalization functions were nearly identical across groups.