Box-and-whisker plot of MSEs for EM-based models and for rEFHs of various sizes.

<p>Each box corresponds to 20 networks trained <i>de novo</i> and tested on a common data set. Median MSE for each model is marked with a horizontal line; the box contains the interquartile range; whiskers extend to 1.5× the interquartile range, beyond which outliers are marked with plus signs. Performance among the EM-learned linear dynamical systems (the first two boxes, light red and blue) varies comparatively little, although large outliers are sometimes produced. In fact, the higher-order (best performing) models are all outliers. To facilitate comparison with the rEFHs, a line extends from the <i>best</i> EM-based models across the entire plot. The remaining twelve boxes (turquoise) are rEFHs with different numbers of hidden units, listed on the abscissae. All have the same number of recurrent units as hidden units, and have a fixed number of “sensory units”: (A) 15 proprioceptive, or (B) 15 proprioceptive and 15 efference-copy. (A) The uncontrolled dynamical system. Overall, MSEs decline with increasing number of hidden/recurrent units, but appear to asymptote by 180 hidden units (ratio = 180/15 = 12). (B) The controlled dynamical system. The optimal number of hidden units is about 180 (ratio = 180/30 = 6), after which mean and variance (across networks) of MSE increases.