Fig. 5: Decoder penalty affects user effort and cursor velocity but not performance.

a, Model predictions. The panels show the gradient fields of the user and decoder cost functions (format as that in Fig. 4a) when the decoder penalty term is equal to (left) or less than (right). The arrows depict the expected stationary points of the user (purple) and decoder (orange). b, Percentage change in error from the trial start (first 30 s) to end (last 30 s), separated by high (dark grey) and low (light grey) decoder penalty term conditions (N = 14, median; shading shows the 25th–75th percentile; two-sided Wilcoxon signed-rank test, ns = 0.17). c, Left: average magnitude of the decoder matrix (norm) over time in the trial for low (dashed light orange) and high (solid dark orange) decoder penalty terms (N = 14, median; shading shows the 25th–75th percentile). Right: box plots are average decoder efforts across the trial for each subject (N = 14, centre shows the median; box shows the 25th–75th percentiles; whiskers extend to 1.5× the interquartile range; one-sided Wilcoxon signed-rank test, **P = 6.1 × 10⁻⁵). d, Left: average magnitude of the user encoder matrix (norm) over time in the trial for low (dashed light purple) and high (solid dark purple) decoder penalty terms (N = 14, median; shading shows the 25th–75th percentile). Right: box plots are average effort for each subject across the trial (N = 14, centre shows the median; box shows the 25th–75th percentiles; whiskers extend to 1.5× the interquartile range; one-sided Wilcoxon signed-rank test, *P =0.018). e, Left: average cursor speed as a function of time in the trial for low (dashed light grey) and high (solid dark grey) decoder penalty terms (N = 14, median; shading shows the 25th–75th percentile). Right: box plots are the average cursor speed across the trial for each subject (N = 14, centre shows the median; box shows the 25th–75th percentiles; whiskers extend to 1.5× the interquartile range; one-sided Wilcoxon signed-rank test, **P = 6.1 × 10⁻⁵). f, Average difference in cursor speed between the low and high decoder penalty conditions plotted against the average difference in encoder efforts between the low and high decoder penalty conditions for each individual participant (black dots). The shading illustrates qualitatively identified groupings. g, Schematic illustrating the relationship between encoder effort and cursor speed when the decoder effort changes. The dots represent the encoder effort and velocity for high (dark orange) and low (light orange) decoder penalty terms. The arrows depict the potential scenarios of how the decoder penalty can shift the encoder effort and velocity.