Dynamics of selective recall in an associative memory model with one-to-many associations

The dynamics of selective recall in an associative memory model are analyzed in the scenario of one-to-many association. The present model, which can deal with one-to-many association, consists of a heteroassociative network and an autoassociative network. In the heteroassociative network, a mixture of associative items in one-to-many association is recalled by a key item. In the autoassociative network, the selective recall of one of the associative items is examined by providing a seed of a target item either to the heteroassociative network (Model 1) or to the autoassociative network (Model 2). We show that the critical similarity of Model 2 is not sensitive to the change in the dimension ratio of key vectors to associative vectors, and it has smaller critical similarity than Model 1 for a large initial overlap. On the other hand, we show that Model 1 has smaller critical similarity for a small initial overlap. We also show that unreachable equilibrium states exist in the proposed model.