  Neural correlations play a critical role in sensory information coding. They
are of two kinds: signal correlations, when neurons have overlapping
sensitivities, and noise correlations from network effects and shared noise. It
is commonly thought that stimulus and noise correlations should have opposite
signs to improve coding. However, experiments from early sensory systems and
cortex typically show the opposite effect, with many pairs of neurons showing
both types of correlations to be positive and large. Here, we develop a theory
of information coding by correlated neurons which resolves this paradox. We
show that noise correlations are always beneficial if they are strong enough.
Extensive tests on retinal recordings under different visual stimuli confirm
our predictions. Finally, using neuronal recordings and modeling, we show that
for high dimensional stimuli noise correlation benefits the encoding of
fine-grained details of visual stimuli, at the expense of large-scale features,
which are already well encoded.
