Catch trials induced short-term unlearning. A: Hand trajectories of single movements, averaged across all 40 subjects, during the first (labeled 1st), 38th (ct-1), 39th (ct), and 40th (ct+1) movements toward 90° (0° is at 3 o’clock). Intersection of error bars indicates parallel and perpendicular displacement (p.d.) 250 ms into the movement. B: Jumps in p.d. between before (ct-1) and after (ct+1) catch trials versus p.d. in catch trials (ct), averaged within target directions across subjects. C: Orientation of preferred direction of movement-initiating EMG in ct-1, ct, and ct+1. Asterisks indicate significant (p < 0.05) rotation of EMG preferred direction between ct-1 and ct+1. D: Errors in force field movements following ct. In all figures, error bars indicate 95% confidence intervals of the mean (CIM) across subjects.

Sensitivity to movement error across target directions. A: Errors in subjects’ reaches (·) (p.d. at 250 msec) toward 90°, averaged across subjects (n=40). Catch trials are the large negative spikes (one labeled ct). Lines are best fits of scalar (black) and vector (red) state-space models to the data (y in ). B: Average sensitivity of the IM to errors experienced in previous movements (b in ) as a function of angular distance ϕ. Error bars (95% CIM) calculated through bootstrapping. C: Average sensitivity b(ϕ) for simulated adaptive controllers that constructed an IM with Gaussians of width σ. b(ϕ) in simulations and subjects were averaged across target directions.

Movement characteristics of systems that learn an IM with velocity encoding Gaussians. A: Simulated adaptive controllers trained in a target set without catch trials. The 11th (left) and 21st (right) movements toward 90° are shown for each controller. Learning with wide Gaussians produced S-shaped movements. B: Adaptive controllers’ estimation of the force field after training for 100 movements in a target set without catch trials. Peak velocity of typical movements is 0.35 m/s. C: Time course of error (p.d. at 200 msec) for simulated controllers with various Gaussian widths, smoothed across a 13-movement window. Overcompensation (generation of S-shaped hand trajectories) occurs when p.d. becomes negative. D: Error (p.d.) averaged over the subset of movements 65-128 during which the force field was on. With narrow Gaussians, overcompensation never occurred, regardless of catch trial probability. With wide Gaussians, movements became S-shaped below critical probabilities (near 17%). E: Parallel and perpendicular displacements averaged across movements and subjects. E1: Subjects (n=24) trained in target sets without catch trials, resulting in S-shaped movements. E2: Subjects (n=40) trained in target sets with 17% catch trial probability and did not produce S-shaped movements. F: A controller relying upon wide Gaussians (σ=0.12 m/s) trained in target sets with 17% catch trial probability did not produce S-shaped trajectories.

Learning with wide Gaussians imposes limits on adaptation. A: Correlation between actual force field and IM acquired after 50 targets by adaptive controllers with various width Gaussians, versus the frequency of the nonlinear force field (m in ). B: A high spatial frequency field (m=4) in which subjects and a simulated controller trained. C: The IM learned by the controller with σ=0.12 m/s Gaussians after training for 50 movements. Note that for directions 22.5° and 157.5°, the controller predicts the field to be resistive, whereas actual forces are assistive. D: Hand velocities parallel to target direction of three subjects trained in the same high spatial frequency field in the same target set as the simulated controller. Plotted are velocities in baseline null field movements (mean ± standard deviation) and during catch trials in targets 51 and 58 toward 22.5° and 157.5°. In catch trials, the hand is moving significantly faster, consistent with an IM that expects a resistive field.