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%.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
