Fig. 6: Nonlinear information and choice correlations in a variance discrimination task, for neural data from two monkeys.

a Example oriented grating and saccade targets. b The orientations of the gratings were drawn from a narrow or wide distribution, and the monkey had to guess which by saccading to the appropriate target. c Neurons contain linear and nonlinear information about the task variable. This is revealed by the Normalized Average Conditional Choice Correlations (NACCC, Eq. (17)) predicted for optimal decoding, which are proportional to the measured signal-to-noise ratios (Eq. (7)) for each neural response pattern (blue r_i, green \(\delta {r}_{i}^{2}\), red δr_iδr_j). Color saturation indicates statistical significance (see the “Methods” subsection “Application to neural data”). d These neurons also contain significant information about the animal’s choice, as computed by the measured NACCC. e The measured and optimal NACCCs are highly correlated, with a proportionality near 1 (lines). The coefficient of determination, R-squared is 0.50, 0.33, 0.12 for linear, square and cross terms for monkey 1; 0.61, 0.64, 0.40 for monkey 2. Each point represents one response pattern (e.g. δr_iδr_j) in one session. Top and bottom panels are data from two different monkeys. These two plotted quantities are strongly correlated (0.76, 0.65, 0.53 for linear, square and cross terms for monkey 1; 0.80, 0.83, 0.72 for monkey 2). f Shuffling internal noise correlations while preserving nuisance correlations maintains the relationship between prediction and nonlinear choice correlations, implying that internal noise is not responsible for the correlations. g Shuffling nuisance correlations across trials (see the “Methods” subsection “Application to neural data”) nearly eliminates the relationship between measured and predicted nonlinear choice correlations (0.76, 0.05, 0.04 for monkey 1; 0.80, 0.10, 0.11 for monkey 2), implying that nuisance variation creates the nonlinear code.