Theories on random recurrent neural networks: a brief review

Random recurrent neural networks (RNNs) serve as one of the cornerstones in theoretical neuroscience. We survey theoretical approaches to analyzing the dynamics of these networks, including dynamical mean-field theory, population density methods for spiking networks, and techniques beyond mean-field approximations. We then explore quantitative measures that characterize the complex dynamics of RNNs. As an application, we discuss the computational properties of random RNNs and how chaotic dynamics can be suppressed. We conclude by outlining directions and open questions for future research.