Computational strategies used by the brain strongly depend on the amount of information that can be stored in population activity, which in turn strongly depends on the pattern of noise correlations. In vivo, noise correlations tend to be positive and proportional to the similarity in tuning properties. Such correlations are thought to limit information, which has led to the suggestion that decorrelation increases information. In contrast, we found, analytically and numerically, that decorrelation does not imply an increase in information. Instead, the only information-limiting correlations are what we refer to as differential correlations: correlations proportional to the product of the derivatives of the tuning curves. Unfortunately, differential correlations are likely to be very small and buried under correlations that do not limit information, making them particularly difficult to detect. We found, however, that the effect of differential correlations on information can be detected with relatively simple decoders.

Behavior varies from trial to trial even when the stimulus is maintained as constant as possible. In many models, this variability is attributed to noise in the brain. Here, we propose that there is another major source of variability: suboptimal inference. Importantly, we argue that in most tasks of interest, and particularly complex ones, suboptimal inference is likely to be the dominant component of behavioral variability. This perspective explains a variety of intriguing observations, including why variability appears to be larger on the sensory than on the motor side, and why our sensors are sometimes surprisingly unreliable.

An influential theory of visual processing asserts that retinal center-surround receptive fields remove spatial correlations in the visual world, producing ganglion cell spike trains that are less redundant than the corresponding image pixels. For bright, high-contrast images, this decorrelation would enhance coding efficiency in optic nerve fibers of limited capacity. Here we test the central prediction of the theory and demonstrate that the spike trains of retinal ganglion cells are indeed decorrelated compared to the visual input. However, most of the decorrelation is accomplished not by the receptive fields, but by nonlinear processing in the retina. We show that a steep response threshold enhances efficient coding by noisy spike trains, and the effect of this nonlinearity is near optimal in both salamander and macaque retina. These results offer an explanation for the sparseness of retinal spike trains, and highlight the importance of treating the full nonlinear character of neural codes.