Associative memory for complex dynamical attractors in reservoir computing*

Traditional neural network models of associative memories were mostly for storing and retrieving static patterns. We develop a class of reservoir-computing based models of memories for complex dynamical attractors, under two common recalling scenarios: location-addressable with an index channel and context-addressable without such a channel. We demonstrate that, for the location-addressable scenario, a single reservoir computing machine can memorize more than a dozen chaotic or periodic states, each retrievable with a specific index value. We articulate control strategies to achieve near-perfect switching among the memorized states. A scaling law is uncovered between the number of stored states and the reservoir network size. For context-addressable retrieval, we exploit multistability with cue signals, where the stored attractors coexist in the high-dimensional phase space of the reservoir neural network. As the length of the cue signal increases through a critical value, a near-perfect success rate can be achieved. Complicated basin structures unseen before can emerge in such extremely high-dimensional nonlinear dynamical systems with many attractors coexisting in one recurrent neural network. The work provides foundational insights into developing models of long-term memories for complex dynamical patterns.