Theoretical limits on the speed of learning inverse models explain the rate of adaptation in arm reaching tasks.

An essential aspect of human motor learning is the formation of inverse models, which map desired actions to motor commands. Inverse models can be learned by adjusting parameters in neural circuits to minimize errors in the performance of motor tasks through gradient descent. However, the theory of gradient descent establishes limits on the learning speed. Specifically, the eigenvalues of the Hessian of the error surface around a minimum determine the maximum speed of learning in a task. Here, we use this theoretical framework to analyze the speed of learning in different inverse model learning architectures in a set of isometric arm-reaching tasks. We show theoretically that, in these tasks, the error surface and, thus the speed of learning, are determined by the shapes of the force manipulability ellipsoid of the arm and the distribution of targets in the task. In particular, rounder manipulability ellipsoids generate a rounder error surface, allowing for faster learning of the inverse model. Rounder target distributions have a similar effect. We tested these predictions experimentally in a quasi-isometric reaching task with a visuomotor transformation. The experimental results were consistent with our theoretical predictions. Furthermore, our analysis accounts for the speed of learning in previous experiments with incompatible and compatible virtual surgery tasks, and with visuomotor rotation tasks with different numbers of targets. By identifying aspects of a task that influence the speed of learning, our results provide theoretical principles for the design of motor tasks that allow for faster learning.

When 90% of the variance is not enough: residual EMG from muscle synergy extraction influences task performance.

Muscle synergies are usually identified via dimensionality reduction techniques, such that the identified synergies reconstruct the muscle activity to an accuracy level defined heuristically, often set to 90% of the variance. Here, we question the assumption that the residual muscle activity not explained by the synergies is due to noise. We hypothesize instead that the residual activity is not entirely random and can influence the execution of motor tasks. Young healthy subjects performed an isometric reaching task in which the surface electromyography of 10 arm muscles was mapped onto a two-dimensional force used to control a cursor. Three to five synergies explained 90% of the variance in muscle activity. We altered the muscle-force mapping via "hard" and "easy" virtual surgeries. Whereas in both surgeries the forces associated with synergies spanned the same dimension of the virtual environment, the muscle-force mapping was as close as possible to the initial mapping in the easy surgery; in contrast, it was as far as possible in the hard surgery. This design maximized potential differences in reaching errors attributable to residual activity. Results show that the easy surgery produced smaller directional errors than the hard surgery. Additionally, simulations of surgeries constructed with 1 to 10 synergies show that the errors in the easy and hard surgeries differ significantly for up to 8 synergies, which explains 98% of the variance on average. Our study thus indicates the need for cautious interpretations of results derived from synergy extraction techniques based on heuristics with lenient accuracy levels.NEW & NOTEWORTHY The muscle synergy hypothesis posits that the central nervous system simplifies motor control by grouping muscles into modules. Current techniques use dimensionality reduction, such that the identified synergies reconstruct 90% of the muscle activity. We show that residual muscle activity following such identification can have a large systematic effect on movements, even when the number of synergies approaches the number of muscles. Current synergy extraction techniques must therefore be updated to identify true physiological synergies.