We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the “balanced network”, which yields only linear behavior. We more exhaustively analyze the 2-dimensional case of 1 excitatory and 1 inhibitory population. We show that in this case dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for “supersaturation”, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing.

SummaryCorrelated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. Specifying the cortical operating regime is key to understanding the computations underlying perception.