A perturbative approach to non-linearities in the information carried by a two layer neural network

Abstract

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.

Accepted as a preprint of ICTP, Trieste

Cited by in corpus (3)

• Recurrent biological neural networks: The weak and noisy limit
• Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous and discrete stimuli
• A diagrammatic approach to study the information transfer in weakly non-linear channels