Extended Data Fig. 4: Control analyses for subspace decomposition.

a, b. Movement-null and movement-potent subspaces estimated as in Fig. 5g–l using DR and WC trials. a. Variance explained (R²) of motion energy by the sum squared magnitude of activity in the movement-null and movement-potent subspaces on single trials. Each point is the mean across trials for a session. b. Left, motion energy on single trials for an example session. Middle, sum-squared magnitude of activity in the movement-potent subspace. Right, sum-squared magnitude of activity in the movement-null subspace. Trials sorted by average delay epoch motion energy. c. Selectivity (left vs. right) of the neural population during WC trials. Mean and 95% CI across sessions shown. d, e. Same as (a,b) but estimating movement-null and movement-potent subspaces using WC trials only. f. Normalized magnitude of activity in the movement-null subspace (left) movement-potent subspace (right) when estimated using DR and WC trials as in (a,b), versus when estimated using WC trials only as in (d,e). Circles are average activity per trial for an example session. g, h. Same as (a,b), but estimating movement-null and movement-potent subspaces using data restricted to the response epoch of DR and WC trials. i. Magnitude of activity in the movement-null subspace (left) or movement-potent subspace (right) when estimated using DR and WC trials as in (a,b) versus when estimated using data from only the response epoch of DR and WC trials as in (g,h). Circles are average activity per trial for an example session. j, k. Same as (a,b), but estimating the movement-null and movement-potent subspaces using a two-stage PCA approach (see Methods). This approach is conservative in avoiding the mis-assignment of cognitive dynamics that correlate in time with movement to the movement-potent subspace. l. Magnitude of activity in the movement-null subspace (left) or movement-potent subspace (right) when estimated using DR and WC trials as in (a,b) versus when estimated using the two-stage PCA approach as in (j,k). Circles are average activity per trial for an example session.