Top left: Cumulative distribution across all pairs of neurons of the correlation coefficient between coupling filters fit to baseline trials and manipulated trials. Black curve shows the baseline distribution computed using odd and even baseline trials. Gray curves show the null distribution constructed by shuffling the neuronal pairs. Shaded regions denote 1 SEM estimated by bootstrapping ( n =25,805/20,798/22,506 neuron pairs for sensory/latent/motor manipulation). Top right: Cumulative distribution of the correlation coefficient between tuning function to sensory variables (the two sensory variables - linear and angular velocity - were concatenated) fit to baseline trials and manipulated trials across all neurons. Bottom left: Similar to top right, but computed using tuning to latent variables. Bottom right: Similar to top right, but computed using motor tuning.