Abstract:
Large networks of sparsely coupled, excitatory and inhibitory cells occur
throughout the brain. For many models of these networks, a striking feature
is that their dynamics are chaotic and thus, are sensitive to small
perturbations. How does this chaos manifest in the neural code?
Specifically, how variable are the spike patterns that such a network
produces in response to an input signal?

To answer this, we derive a bound for a general measure of variability --
spike-train entropy. This leads to important insights on the variability of
multi-cell spike pattern distributions in large recurrent networks of
spiking neurons responding to fluctuating inputs. The analysis is based on
results from random dynamical systems theory and is complimented by
detailed numerical simulations. We find that the spike pattern entropy is
an order of magnitude lower than what would be extrapolated from single
cells.  This holds despite the fact that network coupling becomes
vanishingly sparse as network size grows -- a phenomenon that depends on
"extensive chaos", as previously discovered for balanced networks without
stimulus drive. Moreover, we show how spike pattern entropy is controlled
by temporal features of the inputs. Our findings provide insight into how
neural networks may encode stimuli in the presence of inherently chaotic
dynamics.