A PERTURBATIVE APPROACH TO NONLINEARITIES IN THE INFORMATION CARRIED BY A TWO LAYER NEURAL NETWORK

We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and nonlinear analogue channel. In the case where the nonlinearity is small with respect to the variability in the noise, we derive an exact expression for the contribution to the mutual information given by the nonlinear term in first order of perturbation theory. Finally we show how the calculation can be simplified by means of a diagrammatic expansion. Our results suggest that the use of perturbation theories applied to neural systems might give an insight on the contribution of nonlinearities to the information transmission and in general to the neuronal dynamics.