Figure 2.

Measurements of planning and execution noise and adaptation rate in a visuomotor adaptation experiment. A, Setup. The projection screen displayed the location of the robotic handle (“the cursor”), start location of the movement (“the origin”), and target of the movement (“the target”) on a black background. The position of the origin on the screen was fixed throughout the experiment, while the target was placed 10 cm from the origin at an angle of –45°, 0°, or 45°. B, Trial types. The experiment included vision unperturbed and perturbed trials and no-vision trials. In vision unperturbed trials, the cursor was shown at the position of the handle during the movement. The cursor was also visible in vision perturbed trials, but at a predefined angle from the vector connecting the origin and the handle. In no-vision trials, the cursor was turned off when movement onset was detected and therefore only visible at the start of movement to help subjects keep the cursor at the origin. C, Experimental design. The baseline block consisted of 225 vision unperturbed trials and 225 no-vision trials (indicated by vertical red lines). The perturbation block had 50 no-vision trials and 400 vision trials, with every block of nine trials containing 1 no-vision trial. Most vision trials were perturbed vision trials whose perturbation magnitudes formed a staircase running from –9° to 9°. D, Simulation of planning noise ${\sigma }_{\eta }$ and standard deviation ${\sigma }_y$ of the movement angle. ${\sigma }_y$ increases with ${\sigma }_{\eta }$. Calculated for $A=0.98$ and ${\sigma }_{ϵ}=2°$ with $B=0.2$ for the solid line and $B=0$ for the dashed line. E, Simulation of planning noise ${\sigma }_{\eta }$ and lag-1 autocorrelation $R\left(1\right)$ of the movement angle. $R\left(1\right)$ increases with ${\sigma }_{\eta }$. Calculated for $A=0.98$ and ${\sigma }_{ϵ}=2°$ with $B=0.2$ for the solid line and $B=0$ for the dashed line. F, Simulation of execution noise ${\sigma }_{ϵ}$ and standard deviation ${\sigma }_y$ of the movement angle. ${\sigma }_y$ increases with ${\sigma }_{ϵ}$. Calculated for $A=0.98$ and ${\sigma }_{\eta }=0.2°$ with $B=0.2$ for the solid line and $B=0$ for the dashed line. G, Simulation of execution noise ${\sigma }_{ϵ}$ and lag-1 autocorrelation $R\left(1\right)$ of the movement angle. $R\left(1\right)$ decreases with ${\sigma }_{ϵ}$. Calculated for $A=0.98$ and ${\sigma }_{\eta }=0.2°$ with $B=0.2$ for the solid line and $B=0$ for the dashed line. H. Simulated learners without vision. The green and red traces show a single realization of two learners with either high planning noise (red learner ${\sigma }_{\eta }=0.4°$ and ${\sigma }_{ϵ}=0°$) or high execution noise (green learner ${\sigma }_{\eta }=0°$ and ${\sigma }_{ϵ}=2°$). Both sources increase the movement noise, but planning noise leads to correlated noise, whereas execution noise leads to uncorrelated noise. This property can be seen from the relation between sequential trials. For the red learner, sequential trials are often in the same (positive or negative) direction. For the green learner, sequential trials are in random directions. This is captured by the lag-1 autocorrelation. I, Simulation of ${\sigma }_{py}$ between the perturbation $p$ and movement angle $y$, and adaptation rate $B$. ${\sigma }_{py}$ gets more negative for increasing $B$ (simulated with $A=0.98$). J, Simulated learners with perturbation. The gray and blue lines show a simulated slow ($A=0.98$, $B=0.05$) and fast ($A=0.98$, $B=0.2$) learner. The fast learner tracks the perturbation signal more closely than the slow learner. This property is captured by the covariance between the perturbation and the movement angle.