Fig. 4: Information-limiting noise makes a network more robust to suboptimal decoding.

a A simulated optimal decoder produces measured choice correlations that match our optimal predictions (blue, on diagonal). In contrast, when a noise covariance Γ₀ permits the population to have extensive information, then a suboptimal decoder can exhibits a pattern of choice correlations that does not match the prediction of optimal decoding. Here we show two suboptimal decoders, one that is blind to higher-order correlations (\({{{{{{{\bf{w}}}}}}}}\propto {{{{{{{\bf{F}}}}}}}}^{\prime}\), red), and another ‘worse’ decoder that has the same weights but with 40% random sign flips (green). As in Fig. 5, horizontal axis shows optimal choice correlations (Eq. (7)) and vertical axis shows measured choice correlations (Eq. (5)). b When information is limited, the same decoding weights may be less detrimental, and thus exhibit a similar pattern of choice correlations as an optimal decoder (red), or if they are sufficiently bad they may retain a suboptimal pattern of choice correlations (green).