Asymmetric Sherrington-Kirkpatrick model of neural networks with random neuronal threshold
Yu‐qiang Ma, Chang-De Gong · Physical review. B, Condensed matter · 1992
The random asymmetric Sherrington-Kirkpatrick model of neural networks with random neuronal thresholds has been investigated by a Langevin-dynamics approach. It is shown that in the presence of Gaussian random ``external'' fields with zero mean and variance \ensuremath{\Delta}, the spin-glass transition disappears and the Edwards-Anderson order parameter remains finite at all temperatures T. The replica-symmetric phase is separated from the symmetry-breaking phase by a line of instability in the (T,\ensuremath{\Delta}) plane. The ferromagnetic phase, or the equivalent ``retrieval'' states in neural networks, is affected only slightly by weak random asymmetry and destroyed completely by random-field-induced fluctuations with sufficiently large values of \ensuremath{\Delta}. They can also be suppressed by a modest amount of stochastic synaptic noise T or synaptic-coupling-induced fluctuations.