How pairwise correlations affect the redundancy in large populations of neurons

Simultaneously recorded neurons often exhibit correlations in their spiking activity. These correlations shape the statistical structure of the population activity, and can lead to substantial redundancy across neurons. Knowing the amount of redundancy in neural responses is critical for our understanding of the neural code. Here, we study the effect of pairwise correlations on the statistical structure of population activity. We model correlated activity as arising from common Gaussian inputs into simple threshold neurons. In population models with exchangeable correlation structure, one can analytically calculate the distribution of synchronous events across the whole population, and the joint entropy (and thus the redundancy) of the neural responses. We investigate the scaling of the redundancy as the population size is increased, and characterize its phase transitions for increasing correlation strengths. We compare the asymptotic redundancy in our models to the corresponding maximum- and minimum entropy models. Although this model must exhibit more redundancy than the maximum entropy model, we find that its joint entropy increases linearly with population size