Storage capacity of correlated perceptrons

Details Storage capacity of correlated perceptrons Storage capacity of correlated perceptrons

1996-10-22

arxiv.org/abs/cond-mat/9610160v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, Latex2e

Scientific paper

10.1103/PhysRevE.55.7369

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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