Memory cycling in asymmetric neural networks is enhanced under nonequilibrium conditions

The Hopfield neural network is a paradigmatic model for associative memory. In the standard model, only one memory can be recalled for a given initial state of the network. However, when asymmetric coupling between neurons is included, sequences and cycles of multiple memories can be recalled. For a symmetric Hopfield network experiencing thermal fluctuations, it has been shown that the recall of a single memory is improved by replacing the associated white noise with colored noise, which keeps the system out of equilibrium. Here, we show that this nonequilibrium condition also enhances the recall of a memory cycle in an asymmetric Hopfield network.