Fig. 3. Contribution of individual units to low-dimensional representations.

a, c The pairwise relationship between regression coefficients for task-relevant variables (abscissa and ordinate labels) are shown for each unit (open circles; point estimates derived from all trials) with standard deviations (horizontal and vertical error bars; computed by resampling trial-level responses, N = 700 resampled data sets per unit, see “Methods”), for monkeys N (a) and K (c). If units generally encoded a solitary variable, circles would cluster on the horizontal and vertical meridians (dashed lines), which was not observed, consistent with mixed selectivity. If estimates of the regression coefficients were unreliable, then apparent mixed selectivity could arise spuriously from imprecise estimates and error bars would consistently overlap the meridians, which was not observed. b, d The Pearson’s correlation coefficient between pairs of representations (i.e., sRAs) of different (open bars) or same (filled bars) variable(s) are shown for monkeys N (b) and K (d). For between-sRA correlations, the coefficient (bar height) was measured from the full data set; dashed horizontal line and shading indicate the mean and 95% confidence interval (CI), respectively, of the hypothetical correlation between two perfectly correlated (or anti-correlated) representations corrupted by independent noise (i.e., low precision of the individual-unit coefficients). Observed correlations were significantly closer to zero than these hypothetical values, defining the representations as separable. For within-sRA correlations, the coefficient mean (bar height) and 95% CI (error bars) were measured from the resampled data sets. The resampled data for both between- and within-sRA analyses included 700 resampled data sets generating N = 244,650 pairwise correlations. See full distributions in Supplementary Fig. 7 and summary statistics in Supplementary Table 2. For present figure, all regression coefficients pertain to non-orthogonalized sRAs, which most closely reflected the population encoding and permitted meaningful comparison between representations (in contrast, the correlation between orthogonalized sRAs would necessarily be 0).