Recognition ability of the fully connected Hopfield neural network under a persistent stimulus field

We investigate the pattern recognition ability of the fully connected Hopfield model of a neural network under the influence of a persistent stimulus field. The model considers a biased training with a stronger contribution to the synaptic connections coming from a particular stimulated pattern. Within a mean-field approach, we computed the recognition order parameter and the full phase diagram as a function of the stimulus field strength h, the network charge α and a thermal-like noise T. The stimulus field improves the network capacity in recognizing the stimulated pattern while weakening the first-order character of the transition to the non-recognition phase. We further present simulation results for the zero temperature case. A finite-size scaling analysis provides estimates of the transition point which are very close to the mean-field prediction.