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Register a new userNumerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution
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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, $alpha = P/N$, 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 $alpha sim O(1)$. 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 $alpha$.
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