Metastable states in asymmetrically diluted Hopfield networks

A count of the number of metastable states is employed to obtain indications on the retrieval and spin-glass properties of asymmetrically diluted neural networks. It is found that the main effect is on the retrieval states. Their position, distribution and number depend essentially on the normalised storage parameter alpha , the ratio of the number of memories to the mean connectivity. The effect of asymmetrical dilution on metastable states uncorrelated with the memories depends on the dilution mode; the number of such states, however, still grows exponentially with system size, even for completely asymmetrical networks. To the extent that asymmetry destabilises this spin-glass phase it must be doing it by modifying the dynamics and not by eliminating metastable states. It is also shown that there are no individual retrieval states with significant basins of attraction, for the symmetric as well as the asymmetric neural network.