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

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

2000-10-18

arxiv.org/abs/cond-mat/0010249v1

Physics

Condensed Matter

Statistical Mechanics

Accepted as a preprint of ICTP, Trieste

Scientific paper

10.1142/S0217979201004496

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.

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