Phase diagrams and the instability of the spin glass states for the diluted Hopfield neural network model

Andrew Canning , Jean-Pierre Naef

The replica-symmetric order parameter equations derived in [2, 4] for the symmetrically diluted Hopfield neural network model [1] are solved for different degrees of dilution. The dilution is random but symmetric. Phase diagrams are presented for c=1, 0.1, 0.001 and c↦0, where c is the fractional connectivity. The line Tc where the memory states become global minima (having lower free energy than the spin glass states) is also found for different values of c. It is found that the effect of dilution is to destabilize the spin glass states and the line Tc is driven rapidly towards the line TM; the phase transition line where the memory states first stabilize. All the results are derived in the context of replica symmetry so are expected to be incorrect in certain parts of the phase diagram (the error increasing the further below the replica symmetry breaking lines we are) but our results do suggest in a general way that dilution, even in small quantities, increases the stability of the memory states with respect to the spin glass states.

Domaines: Articles anciens

Andrew Canning, Jean-Pierre Naef. Phase diagrams and the instability of the spin glass states for the diluted Hopfield neural network model. Journal de Physique I, 1992, 2 (9), pp.1791-1801. ⟨10.1051/jp1:1992245⟩. ⟨jpa-00246660⟩