Figure 6.

Autocorrelation functions and the error-corrective learning model. a–c, Mean (and SE) autocorrelation functions of reach speed (a), direction (b), and neural activity (c), averaged across target and session for behavior and across targets, sessions, and neurons for neural activity. The data were fit to a linear dynamical learning model characterized by either one decay time constant (first-order model, Eq. 5a; gray lines) or two decay time constants (second-order model, Eq. 5b; colored lines). d, Comparison of fit decay time constants using the second-order model; fit errors are from the bootstrapping technique. These time constants are also compared with analogous time constants found in the 2011 MLB pitching data. (To reduce our sensitivity to noise, we only included the 64, of 160, pitcher games in which measured drift is found to be significant at p < 0.003, permutation test.) We also show motor learning time constants from Smith et al. (2006), who directly measured the time course of learning in response to external perturbations. (There, learning is described with a two-state learning model; we used Equation 3 to express their empirical parameters as autocorrelation time constants. We assumed that their stated measurement errors were independent but verified that this does not significantly affect the size of the errors on the time constants.)