  The beneficial role of noise-injection in learning is a consolidated concept
in the field of artificial neural networks, suggesting that even biological
systems might take advantage of similar mechanisms to optimize their
performance. The training-with-noise algorithm proposed by Gardner and
collaborators is an emblematic example of a noise-injection procedure in
recurrent networks, which can be used to model biological neural systems. We
show how adding structure to noisy training data can substantially improve the
algorithm performance, allowing the network to approach perfect retrieval of
the memories and wide basins of attraction, even in the scenario of maximal
injected noise. We also prove that the so-called Hebbian Unlearning rule
coincides with the training-with-noise algorithm when noise is maximal and data
are stable fixed points of the network dynamics.
