Generalization in a Hopfield network with noise

The generalization ability of the Hopfield model of neural networks trained with examples is studied in mean-field theory in the presence of synaptic noise. Although the latter improves the generalization ability for a finite number of concepts, it does not for a macroscopic number of them. Nevertheless, the network performance is still robust against synaptic noise. Numerical simulations are performed to verify the mean-field theory predictions.