Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution
Departamento de Física Teórica,
Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain
Accepted: 6 January 1999
The mutual information of a single-layer perceptron with N Gaussian inputs and P deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, , and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to . The most relevant results are: 1) the simulation supports the validity of the analytical prediction, and 2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of α.
PACS: 87.10.+e – Biological and medical physics: General theory and mathematical aspects / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems
© EDP Sciences, 1999