Fig. 7: Decoding accuracy from simulated mixed and pure selectivity populations.

a Schematic of simulated population. The number of spikes generated by each cell follows a Poisson distribution with the mean λ. Each cell responds to a preferred cue (or a preferred combination of cues) with the mean of λ_pref and to an unpreferred cue with the mean of λ_unpref. The minimum unit population size is a set of four cells (rounded rectangle). Each cell preferentially responds to a specific trial type in the mixed selectivity population, or to a specific sample cue or test cue identity in the pure selectivity population. The population size increases by including N sets of the unit population with the same selectivity pattern. b Decoding accuracy for the sample cue (or test cue) in simulated population activity under a various combination of the mean activity (λ_pref and λ_unpref). The SNR in the population increases with higher λ_pref and lower λ_unpref under Poisson noise. The population activity was simulated on 10,000 trials and repeated 10,000 times, separately in mixed selectivity population (solid lines) and pure selectivity population (dashed lines). Shading indicates mean ± s.e.m. and is equal or smaller than the line widths. The population activity was simulated with 8 cells and noise correlation (ρ_noise = 0.1) in panels (b, d, f). c Similar to panel (b), but under various combinations of the population size and noise correlation level. The SNR in the population increases with a larger population size and lower noise correlation. The population activity was simulated with λ_pref = 2.0 and λ_unpref = 1.0 in panels (c, e, g). d Similar to panel (b), but with the decoding accuracy for the reward direction (XOR). For a pure selectivity population, the decoding accuracy of XOR (p_XOR, dashed line in panels d, e) can be predicted by decoding accuracy for the sample cue (or test cue) (p, dashed line in panels b, c). Open circles show \({\hat{p}}_{{{{{{\rm{XOR}}}}}}}\) predicted by p² + (1–p)²: the sum of probabilities that both sample and test cues decoded correctly (p²) or incorrectly (1–p)². See Supplementary Fig. 10 for reasoning. e Similar to panel (c), but with the decoding accuracy for the reward direction (XOR). f Similar to panel (d), but with XOR mutual information divided by the total number of expected spikes in a population. g Similar to panel (e), but with XOR mutual information divided by the total number of expected spikes in a population. Source data are provided as a Source Data file.