Robust sequential retrieval of memories in interaction-modulated neural networks

Associative memory networks are capable of storing a set of neural configurations and retrieving one of these memories given an initial state, a classic example being the Hopfield network. Such networks have been generalized to perform sequential retrieval, i.e., to dynamically retrieve a prescribed sequence of memories. We identify three requirements for sequential retrieval: a destabilization of the present memory, a directional bias towards the next memory in the sequence, and a separation of timescales. Earlier works have utilized time-delayed nodes to satisfy these requirements. We demonstrate that these models belong to a class where the delayed nodes exert an external input on the nodes of the original network. In contrast, we explore a class of models in which the delayed nodes modulate the interactions between the original nodes. We give several examples of such interaction-modulated networks capable of sequential retrieval. Further, we examine the phase space of sequential retrieval to compare the robustness of input-modulated and interaction-modulated networks within a unifying framework.