Response nonlinearities in networks of spiking neurons

Combining information from multiple sources is a fundamental operation performed by networks of neurons in the brain, whose general principles are still largely unknown. Experimental evidence suggests that combination of inputs in cortex relies on nonlinear summation. Such nonlinearities are thought to be fundamental to perform complex computations. However, these non-linearities are inconsistent with the balanced-state model, one of the most popular models of cortical dynamics, which predicts networks have a linear response. This linearity is obtained in the limit of very large recurrent coupling strength. We investigate the stationary response of networks of spiking neurons as a function of coupling strength. We show that, while a linear transfer function emerges at strong coupling, nonlinearities are prominent at finite coupling, both at response onset and close to saturation. We derive a general framework to classify nonlinear responses in these networks and discuss which of them can be captured by rate models. This framework could help to understand the diversity of non-linearities observed in cortical networks.Author summary: Models of cortical networks are often studied in the strong coupling limit, where the so-called balanced state emerges. Across a wide range of parameters, balanced state models explain a number of ubiquitous properties of cortex, such as irregular neural firing. However, in the strong coupling limit, balanced state models show an unrealistic linear network transfer function. We examined, in networks of spiking neurons, how nonlinearities arise as network coupling strength is reduced to realistic levels. We examine closed-form solutions that arise from mean-field analysis, and confirm results with numerical simulations, to show that nonlinearities at response onset and saturation emerge as coupling strength is reduced. Critically, for realistic parameter values, both types of nonlinearities are observed at experimentally-observed firing rates. Thus, cortical network models with moderate coupling strength can account for experimentally observed cortical response nonlinearities.