The authors consider synaptic neural networks which minimise the output error of the stored patterns when the input patterns are ensembles of their noisy versions with overlap m_t with the clean patterns. When m_t is infinitesimally less than 1, the network automatically attains maximal stability, confirming the usefulness of training noises in enhancing memory associativity. When m_t drops below 1, the field distribution has two bands for large m_t, and one continuous band for small m_t. Errorless retrieval is impossible for training noises of the order N⁰. With the increase in training noise, the retrieval overlap deteriorates, although memory associativity does increase for sufficiently low storage.