Retrieval phase diagrams in the asymmetric Sherrington-Kirkpatrick model and in the Little-Hopfield model

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Abstract
The effects of random external fields on the retrieval properties of neural networks are examined. Phase diagrams of the fully asymmetric Sherrington-Kirkpatrick model and Little-Hopfield model are obtained. It is shown that the ferromagnetic retrieval states are destroyed by fluctuations induced by random external fields. The probability at zero field determines the size of the basins of attraction. The basin boundary occurring in systems with a discrete random-field distribution cannot be observed in systems with a continuous Gaussian distribution, and are due to the peculiarities of the discrete distribution.

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