Linear-nonlinear(LN) model is a approximation method for linking the time trace of stimulus with the firing rate. However, this is only a approximation and we can actually have some intuitive understanding about when it will fail.

To do this, I(Peter) first introduced the intuitive idea about spike-time coding and firing rate coding according to Thibaud Taillefumier and Marcelo O. Magnasco 's PNAS paper. It showes that the sparseness of noise will affect the temporal coding strategy of a stochastic Integrate-and-fire neural. 

Then, I introduced how to do the LN approximation typically : 

1. Spike-triggered average (reverse correlation,STA) by applying white noise to the system
2. Fitting the nonlinear mapping function from the linear approximation with the firing rate in the real data

Also, I showed you how this method is applied in modeling primary visual system

At the end, by showing you Srdjan Ostojic and Nicolas Brunel paper, one can observe that when the system synchronized well, the LN model underestimate the firing rate. The failure is because this time the system encoding temporal information by spike-time !