We measured the fit quality (R2) of the motor cortex data to a linear dynamical system with different dimensionalities using leave-one-condition-out cross-validation. Model dimensionalities in the horizontal axis reflect the number of principal components retained in the population response before fitting the dynamical system. Colored traces show the R2 from different datasets from the motor cortex (nine datasets). Black dot is the highest cross-validated R2 value, which is used in Fig. 6a and Supplementary Fig. 9. Note that all test results are robust to this choice of dimensionality over a wide range (all but the smallest dimensionalities; see Fig. 6b).