The Hopfield model of a neural network is studied for p = αN, where p is the number of memorized patterns and N the number of neurons. The averaging over the quenched randomness is performed with the replica method, with replica symmetry broken once. It is shown that the critical value of α increases from 0.138 to 0.144, in excellent agreement with simulation results. For 0.138 < α ≤ 0.144 retrieval states exist only with replica symmetry breaking. Wherever the difference between the replica symmetric solution and the broken symmetry solution is numerically detectable, symmetry breaking improves the retrieval. At αc the number of errors decreases from 1.5% to 0.9%.

SATURATION LEVEL OF THE HOPFIELD MODEL FOR NEURAL NETWORK / Crisanti, Andrea; D. J., Amit; H., Gutfreund. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - STAMPA. - 2:(1986), pp. 337-341. [10.1209/0295-5075/2/4/012]

SATURATION LEVEL OF THE HOPFIELD MODEL FOR NEURAL NETWORK

CRISANTI, Andrea;
1986

Abstract

The Hopfield model of a neural network is studied for p = αN, where p is the number of memorized patterns and N the number of neurons. The averaging over the quenched randomness is performed with the replica method, with replica symmetry broken once. It is shown that the critical value of α increases from 0.138 to 0.144, in excellent agreement with simulation results. For 0.138 < α ≤ 0.144 retrieval states exist only with replica symmetry breaking. Wherever the difference between the replica symmetric solution and the broken symmetry solution is numerically detectable, symmetry breaking improves the retrieval. At αc the number of errors decreases from 1.5% to 0.9%.
1986
01 Pubblicazione su rivista::01a Articolo in rivista
SATURATION LEVEL OF THE HOPFIELD MODEL FOR NEURAL NETWORK / Crisanti, Andrea; D. J., Amit; H., Gutfreund. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - STAMPA. - 2:(1986), pp. 337-341. [10.1209/0295-5075/2/4/012]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/68913
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