A memory of errors in sensorimotor learning

Abstract

The current view of motor learning suggests that when we revisit a task, the brain recalls the motor commands it previously learned. In this view, motor memory is a memory of motor commands, acquired through trial-and-error and reinforcement. Here we show that the brain controls how much it is willing to learn from the current error through a principled mechanism that depends on the history of past errors. This suggests that the brain stores a previously unknown form of memory, a memory of errors. A mathematical formulation of this idea provides insights into a host of puzzling experimental data, including savings and meta-learning, demonstrating that when we are better at a motor task, it is partly because the brain recognizes the errors it experienced before.

Fig. 1

History of error alters error-sensitivity. A. Reaching paradigm with force field perturbations. The yellow circles note a perturbations state, and z indicates probability of remaining in that state. The slow, medium and rapidly switching environments are shown. One group of subjects was trained in each environment. We measured error-sensitivity via probe trials in which subjects experienced a constant perturbation, sandwiched between two error-clamp trials. B. Movement trajectories in the perturbation trial of the probe trials. Trajectories were averaged over 5 successive presentations of the probe. The errors in probe trials did not differ between groups. C. Learning from error in the probe trials, measured as the change in force from the trial prior to the trial after the perturbation. D. Learning from error in the probe trials, plotted as a percentage of the ideal force (left). Error-sensitivity η was measured as the trial-to-trial change in the percentage of ideal force divided by error (right). E. Change in error-sensitivity between the baseline block and the last 5 error-clamp triplets. Data are mean ± SEM.

Fig. 2

Error-sensitivity is a local function of experienced errors. A. Paradigm with visuomotor gain perturbations. B. Perturbation schedule. Dashed lines indicate changes in the statistics of the environment. C. Error-sensitivity averaged over all error-sizes measured over each environment block. D. Learning from error measured at various error sizes. E. Error-sensitivity as a function of error magnitude. F. Probability of error.

Fig. 3

Theoretical model and Experiment 3. A. On trial n−1, the motor command u⁽ⁿ⁻¹⁾ is generated, resulting in error e⁽ⁿ⁻¹⁾=−1. If the error in trial n is of the same sign as e⁽ⁿ⁻¹⁾, then error-sensitivity should increase (top). However, if the error experienced in trial n has a different sign than e⁽ⁿ⁻¹⁾ then error-sensitivity should decrease (bottom). B. Learning from error following experience of two consecutive errors from (A).. Error sensitivity around e⁽ⁿ⁻¹⁾ increases if sign (e⁽ⁿ⁻¹⁾e⁽ⁿ⁾)=1 and decreases otherwise. C. Model performance for slow, medium, and rapidly switching environments (gray line represents x̂⁽ⁿ⁾). However, learning from error (D) is increased in the slow switching environment and decreased in the rapidly switching environment. E. Experiment 3 perturbation protocol. F. Single-trial learning from a +8N perturbation and a −4N perturbation in Probes 1 and 2. Learning is increased for the −4N perturbation, while simultaneously decreased for a +8N perturbation. G. Learning from error normalized by the perturbation magnitude (4 or 8N) in the first trial of each repetition of the rapid (blue) and slowly switching (red) environments. Learning increased in the slowly switching (4N) environment but decreased when the perturbation was rapidly switching (8N). Error bars are SEM.

Fig. 4

Saving occurs only when previously experienced errors are re-visited. A. A visuomotor perturbation experiment. Gray arrows indicate 1–2 minute set-breaks. B. Performance in the final +30° perturbation. ANA and BNA groups show savings, i.e., faster learning of the perturbation compared to control (naive). Exponential fits are shown for the group data. C. The B_waitNA group does not exhibit savings. D. Exponential time constants are compared to controls (*p < 0.05, **p < 0.01). A lower time constant indicates faster learning. E. Comparison of the errors (i.e., after-effects) experienced by the BNA and B_waitNA groups. The B_waitNA group experienced smaller errors due to the presence of the set-break.