Synaptic noise in neural networks at finite temperatures

The authors investigate the effects of the synaptic noise in neural networks at finite temperatures. The analytic results are obtained through the use of the path-integral formulation which facilitates performing the quenched average over the random patterns and random noises. We consider the noise effects in the diluted Hopfield model, the fully-connected Hopfield model and the dynamic model, laying emphasis on the interplay with the temperature. In the phase diagrams drawn as functions of the temperature, the storage, and the noise strength, interesting features including re-entrance, first-order transitions as well as second-order transitions are found.