Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-07-14
Europhysics Letters (45)6, 739-744 (1999)
Physics
Condensed Matter
Statistical Mechanics
6 pages, 8 figures, LaTeX file
Scientific paper
10.1209/epl/i1999-00230-6
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 $\alpha$.
Ciria Jose C.
Dominguez D. R. C.
Maravall M.
Parga Nestor
Turiel Antonio
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