During extended motor adaptation, learning appears to saturate despite persistence of residual errors. This adaptation limit is not fixed but varies with perturbation variance; when variance is high, residual errors become larger. These changes in total adaptation could relate to either implicit or explicit learning systems. Here, we found that when adaptation relied solely on the explicit system, residual errors disappeared and learning was unaltered by perturbation variability. In contrast, when learning depended entirely, or in part, on implicit learning, residual errors reappeared. Total implicit adaptation decreased in the high-variance environment due to changes in error sensitivity, not in forgetting. These observations suggest a model in which the implicit system becomes more sensitive to errors when they occur in a consistent direction. Thus, residual errors in motor adaptation are at least in part caused by an implicit learning system that modulates its error sensitivity in response to the consistency of past errors.
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Code for the state–space memory of errors model is deposited in OSF and is available at https://osf.io/9hzmq/. Additional analysis codes are available on request from the corresponding author.
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This work was supported by the National Institutes of Health (grant nos R01NS078311, R01NS096083 and F32NS095706), the National Science Foundation (grant no. CNS-1714623), the Cambridge Trust, the Rutherford Foundation and a travel grant from the Boehringer Ingelheim Fonds. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. Additionally, we thank H. Fernandes and K. Kording for so graciously compiling and sharing their data with us. Finally, we recognize the Summer School in Computational Sensory-Motor Neuroscience (CoSMo) and its organizers (G. Blohm, K. Kording and P. Schrater) for giving us the opportunity to learn and develop the original idea for this work.
The authors declare no competing interests.
Peer review information Nature Human Behaviour thanks Masaki Abe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Primary Handling Editor: Marike Schiffer.
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Extended Data Fig. 1 Variance-dependent changes in error sensitivity are due to learning from error.
We applied our analysis in Fig. 4A to the numerator (a, learning from error) and denominator (b, error) of Eq. (8). For this analysis, we sorted pairs of movements into different bins according to the size of the error on the first movement. For each bin in a, we calculated the total change in reach angle between the trial pairs (discounted by the retention factor a as in Eq. (8)). For each bin in b, we calculated the mean error that occurred on the first trial in each pair. We performed these analyses separately for the zero-variance group (black) and high-variance group (red) in Experiments 1, 4 and 6 (experiments where the retention factor, a, was measured). For a and b, we used a mixed-ANOVA followed by post-hoc Bonferroni-corrected two-sample t-tests. We found a similar statistical pattern in both insets (left: learning from error, mixed-ANOVA, between-subjects effect of variance, F(1,84) = 13.7, P < 0.001, \(\eta _p^2\) = 0.14; post-hoc Bonferroni-corrected two-sample t-tests, t(71) = 3.77, P = 0.0011, d = 0.69, 95% CI = [0.54,2.3] for 5–14°; t(71) = 3.77, P = 0.001, d = 0.76, 95% CI = [0.9,3.38] for 14–22°; t(71) = 1.53, P = 0.45, d = 0.35, 95% CI = [−0.52,2.08] for 22–30°; right: error magnitude, mixed-ANOVA, between-subjects effect of variance, F(1,84) = 19.2, P < 0.001, \(\eta _p^2\) = 0.19; post-hoc Bonferroni-corrected two-sample t-tests, t(71) = 4.65, P < 0.001, d = 0.92, 95% CI = [0.23,0.63] for 5–14°; t(71) = 5.04, P < 0.001, d = 1.15, 95% CI = [0.37,0.81] for 14–22°; t(71) = 0.5, P = 1.0, d = 0.06, 95% CI = [−0.29,0.39] for 22–30°). Error bars are mean ± SEM.
a, Data were adapted from Robinson and colleagues3. Monkeys were adapted to a gain-down saccade perturbation. The error on each trial was fixed to −1° (top). Middle inset shows saccadic gain on each trial (black points). We fit the ‘decay’ and ‘no decay’ models to behaviour. Decay model is shown in blue. No decay model is shown in magenta. Time course of error sensitivity is shown at bottom. b, Data were adapted from Kojima and colleagues4. Monkeys adapted to a gain-up perturbation, followed by a gain-down perturbation, followed by a re-exposure to the gain-up perturbation. Paradigm is shown at top. Saccadic gain is shown in middle. Black and blue regression lines represent linear fit to first 150 trials during initial and re-exposure to the perturbation. Behaviour predicted by decay-free model shown in solid line at bottom. Dashed line is a copy of model prediction for Exposure 1 (provided for comparison). P1 refers to first gain-up perturbation. P2 refers to second gain-up perturbation. c, Data were adapted from Kojima and colleagues4. Monkeys adapted to a similar perturbation schedule as in a, only now gain-up perturbation periods were separated by a long washout period (top). Saccadic gain is shown in middle. Regression lines indicate the slope of a linear fit to the first 150 trials of initial exposure and re-exposure. The ‘zero-error’ period led to the loss of savings, as indicated by regression line slope. At bottom, we show the behaviour predicted by the ‘no decay’ model (solid magenta line). In addition, we simulated a ‘decay’ model, in which error sensitivity decayed during the zero-error period (shown in blue). d, We quantified the slope of adaptation in c by fitting a line to the behaviour of the ‘decay-free’ and ‘decay’ models over the periods labelled ‘i’, ‘ii’ and ‘iii’. At top, we show the percent change in slope from ‘i’ to ‘ii’ present in the actual data in b. At bottom, we show the percent change in slope from ‘i’ to ‘iii’ present in the actual data, the ‘decay’ model, and the ‘no decay’ model.
Here we consider data adapted from Neville and Cressman9. Participants in an uninstructed condition were placed into 3 groups, each defined by perturbation magnitude. a, At left, we show response of the 20° rotation group. At middle, we show response of the 40° rotation group. At right, we show response of the 60° rotation group. b, We calculated the total amount of learning in each group over the last 10 perturbation epochs (black points). Next, we simulated the total learning predicted by Eq. (6) (Eq. (S1) in Supplementary Information) reproduced at top of inset. Model prediction is shown in blue line. c, We calculated the total residual error (perturbation minus total learning) over the last 10 epochs of the perturbation period (black points). Next, we simulated the total residual error predicted by Eq. (S3), reproduced at top of inset. Model prediction is shown in blue line. Error bars are mean ± SEM.
Extended Data Fig. 4 Error consistency modulates error sensitivity, irrespective of perturbation variance.
Here we report data adapted from Experiment 1 of Herzfeld et al. (2014)2. a, Participants were placed into 3 different groups: low-switch (z = 0.9), medium-switch (z = 0.5), high-switch (z = 0.1). In each group, perturbations followed a Markov chain shown at top. The +1 state indicates a 13 N-s/m force field perturbation. The −1 state indicates a −13 N-s/m force field perturbation. At the end of each 30-trial perturbation mini-block, retention was measured in probe trials (green) and learning from error was measured in a probe-perturbation-probe sequence (purple). b, By design, each group experienced the same set of perturbations irrespective of perturbation statistics. Here we show the standard deviation of the perturbation in each mini-block. c, We considered pairs of trials during the perturbation period. Here we show reach trajectories for example trial pairs. We separated pairs into consistent errors (left, when the direction of error repeated) and inconsistent errors (right, when direction of error switched). d, We calculated the probability of experiencing an inconsistent error in each group (red shows z = 0.9, green shows z = 0.5 and blue shows z = 0.1). Switch probability increased the fraction of inconsistent errors (ANOVA, F(24,2) = 336, P < 0.001, \(\eta _p^2\) = 0.97; post-hoc Bonferroni-corrected two-sample t-tests, t(16) = 20.28, P < 0.001, d = 9.56, 95% CI = [0.39,0.42] for low-medium; t(16) = 21.49, P < 0.001, d = 10.13, 95% CI = [0.61,0.74] for low-high; t(16) = 11.11, P < 0.001, d = 5.24, 95% CI = [0.24,0.35] for medium-high) e, At left, the error sensitivity measured in each group is shown as a function of mini-block (25 mini-blocks in total). At right, the change in error sensitivity from the baseline block to the last 5 three-trial probe sequences is shown. Error bars are mean ± SEM.
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Albert, S.T., Jang, J., Sheahan, H.R. et al. An implicit memory of errors limits human sensorimotor adaptation. Nat Hum Behav 5, 920–934 (2021). https://doi.org/10.1038/s41562-020-01036-x