  We evaluate the mutual information between the input and the output of a two
layer network in the case of a noisy and non-linear analogue channel. In the
case where the non-linearity 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 non-linear 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
non-linearities to the information transmission and in general to the neuronal
dynamics.
