Biological networks have so many possible states that exhaustive sampling isimpossible. Successful analysis thus depends on simplifying hypotheses, butexperiments on many systems hint that complicated, higher order interactionsamong large groups of elements play an important role. In the vertebrateretina, we show that weak correlations between pairs of neurons coexist withstrongly collective behavior in the responses of ten or more neurons.Surprisingly, we find that this collective behavior is described quantitativelyby models that capture the observed pairwise correlations but assume no higherorder interactions. These maximum entropy models are equivalent to Isingmodels, and predict that larger networks are completely dominated bycorrelation effects. This suggests that the neural code has associative orerror-correcting properties, and we provide preliminary evidence for suchbehavior. As a first test for the generality of these ideas, we show thatsimilar results are obtained from networks of cultured cortical neurons.
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