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Storage capacity of correlated perceptrons

D. Malzahn·A. Engel·I. Kanter
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Abstract

We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A general formalism is introduced using a multi-perceptron costfunction that allows to determine the maximal number of random inputs as a function of the desired values of the correlations. Replica-symmetric results for $K=2$ and $K=3$ are compared with properties of two-layer networks of tree-structure and fixed Boolean function between hidden units and output. The results show which correlations in the hidden layer of multi-layer neural networks are crucial for the value of the storage capacity.

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BibTeXRIS

D. Malzahn, A. Engel, I. Kanter. 1996-10-22. Storage capacity of correlated perceptrons. https://doi.org/10.1103/physreve.55.7369

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