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Large networks of sparsely coupled, excitatory and inhibitory cells occurthroughout the brain. A striking feature of these networks is that they arechaotic. How does this chaos manifest in the neural code? Specifically, howvariable are the spike patterns that such a network produces in response to aninput signal? To answer this, we derive a bound for the entropy of multi-cellspike pattern distributions in large recurrent networks of spiking neuronsresponding to fluctuating inputs. The analysis is based on results from randomdynamical systems theory and is complimented by detailed numerical simulations.We find that the spike pattern entropy is an order of magnitude lower than whatwould be extrapolated from single cells. This holds despite the fact thatnetwork coupling becomes vanishingly sparse as network size grows -- aphenomenon that depends on ``extensive chaos," as previously discovered forbalanced networks without stimulus drive. Moreover, we show how spike patternentropy is controlled by temporal features of the inputs. Our findings provideinsight into how neural networks may encode stimuli in the presence ofinherently chaotic dynamics.

Structured chaos shapes spike-response noise entropy in balanced neural networks