摘要：Due to feedback connections, recurrent neural networks (RNNs) are dynamic models. RNNs can provide morecompact structure for approximating dynamic systems compared to feedforward neural networks (FNNs). For someRNN models such as the Hopfield model and the Boltzmann machine, the fixed-point property of the dynamic systemscan be used for optimization and associative memory. The Hopfield model is the most important RNN model, andthe Boltzmann machine as well as some other stochastic dynamic models are proposed as its generalization. Thesemodels are especially useful for dealing with combinatorial optimization problems (COPs), which are notorious NPcompleteproblems. In this paper, we provide a state-of-the-art introduction to these RNN models, their learningalgorithms as well as their analog implementations. Associative memory, COPs, simulated annealing (SA), chaoticneural networks and multilevel Hopfield models are also important topics treated in this paper.
