Invariant errors reveal limitations in motor correction rather than constraints on error sensitivity

Abstract

Implicit sensorimotor adaptation is traditionally described as a process of error reduction, whereby a fraction of the error is corrected for with each movement. Here, in our study of healthy human participants, we characterize two constraints on this learning process: the size of adaptive corrections is only related to error size when errors are smaller than 6°, and learning functions converge to a similar level of asymptotic learning over a wide range of error sizes. These findings are problematic for current models of sensorimotor adaptation, and point to a new theoretical perspective in which learning is constrained by the size of the error correction, rather than sensitivity to error.

Fig. 1

Initial adaptation rates scale with error size, yet saturate to an invariant response magnitude. a Illustration of experimental apparatus and task structure for Exp. 1. b Schematic view of clamped visual feedback paradigm, in which the angular path of the cursor is independent of hand movement direction. c, d Behavior for all groups (n = 12 per group), divided into two panels for visualization purposes. The small clamp groups (c) demonstrate adaptation rates which scale with error size, whereas the large clamp groups (d) show saturated responses. e Segmented regression indicates that the initial adaptation rate scales between 0° and 4.4° before saturating for all errors above this break point (dashed vertical lines represent 95% CI). f Sensorimotor aftereffects, measured during the first cycle following the clamp block. Dots are individuals; shading and error bars denote SEM. Gray shading denotes cycles without visual feedback

Fig. 2

Implicit adaptation converges on a common asymptote. a The 1.75°, 3.5°, and 15° clamp groups in Exp. 2 (n = 10 per group) adapted at markedly different rates (bar graphs depict mean of cycles 3–7). However, there was convergence of all three learning functions by the end of 160 cycles, and (b) no difference between groups in the size of the final aftereffects. Asterisk in a denotes significant differences between groups early in the clamp phase. Dots are individuals; shading and error bars denote SEM

Fig. 3

Adaptation assessed in terms of error sensitivity (left) or error correction (right). Here we plot data from several different studies^,,, including the present one, using two ways to consider trial-by-trial changes in hand angle as a function of error size (Methods section). a Error sensitivity, operationalized as the change in hand angle divided by error size, starts at an early maximum and quickly decays as errors increase in size. b The same data, plotted in terms of the untransformed error correction, shows a function that starts small and then saturates, suggesting that the motor system continues to produce a robust, invariant response over a wide range of error sizes. Plotting the aftereffect data in terms of a sensitivity function (c) also fails to capture the relative invariance of these data within a given experimental context (d). Note the one discrepant point from Exp. 1 in panels C and D from the 1° clamp condition; we suspect this is due to an insufficient number of trials to approximate asymptotic performance. Error bars denote SEM.