Fig. 4: Decoder learning rate influences interface performance and user learning.
a, Model predictions. All panels show the gradient field of the user and decoder cost functions. The purple (user) and orange (decoder) curves show nullclines (where the agent’s cost gradient equals 0) that intersect at stationary points (black stars). The slow (middle) and fast (right) panels zoom in on one stationary point and illustrate changes in the decoder (shades of orange) and encoder (purple) for different decoder learning rates. b, Average error as a function of time within the five-minute trial for fast (dashed dark orange) and slow (solid light orange) decoder learning rates (N = 14, median; shading shows the 25th–75th percentile). c, Percentage change in error from the start of the trial (first 30 s) to the end of the trial (last 30 s), separated by fast (dashed black) and slow (solid grey) learning rates (N = 14, centre shows the median; box shows the 25th–75th percentiles; whiskers extend to 1.5× the interquartile range; two-sided Wilcoxon signed-rank test, **P = 6.1 × 10−5). d, Average change in the user’s encoder within trials (∥Ef − Ei∥) for the slow and fast decoder learning rate conditions (N = 14, centre shows the median; box shows the 25th–75th percentiles; whiskers extend to 1.5× the interquartile range; two-sided Wilcoxon signed-rank test, **P = 1.8 × 10−4). e, Product of the decoder matrix with first-order feed-forward (F1) contributions of the encoder matrix (N = 14, median; shading shows the 25th–75th percentile) for fast (dashed dark pink) and slow (solid light pink) decoder learning rates. The black dashed lines represent values that yield perfect trajectory tracking. f, Product of the decoder matrix with first-order feedback (B1) contributions of the encoder matrix (N = 14, median; shading shows the 25th–75th percentile) for fast (dashed dark blue) and slow (solid light blue) decoder learning rates. The black dashed lines represent values that yield closed-loop stability.
