Stability of the replica symmetric solution in diluted perceptron learning

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 $\alpha$ between the number of patterns M and the dimension N of the perceptron ($\alpha =M/N$), there exists a critical dilution field $h_c$ above which the replica symmetric ansatz becomes unstable.

Stability of the solution in arXiv:0907.3241, 13 pages, (some typos corrected)

References in corpus (3)

• Statistical physics-based reconstruction in compressed sensing
• Inference algorithms for gene networks: a statistical mechanics analysis
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Cited by in corpus (1)

• Expectation propagation on the diluted Bayesian classifier