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arXiv · 1209.5941

Stability of the replica symmetric solution in diluted perceptron learning

Alejandro Lage-Castellanos·Andrea Pagnani·Gretel Quintero Angulo
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Abstract

We study the role played by the dilution in the average behavior of a perceptron model with continuous coupling with the replica method. We analyze the stability of the replica symmetric solution as a function of the dilution field for the generalization and memorization problems. Thanks to a Gardner like stability analysis we show that at any fixed ratio $α$ between the number of patterns M and the dimension N of the perceptron ($α=M/N$), there exists a critical dilution field $h_c$ above which the replica symmetric ansatz becomes unstable.

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Alejandro Lage-Castellanos, Andrea Pagnani, Gretel Quintero Angulo. 2012-10-05. Stability of the replica symmetric solution in diluted perceptron learning. https://doi.org/10.1088/1742-5468%2F2013%2F02%2Fl02002

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