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Dynamical mean-field theory is a powerful physics tool used to analyze thetypical behavior of neural networks, where neurons can be recurrentlyconnected, or multiple layers of neurons can be stacked. However, it is noteasy for beginners to access the essence of this tool and the underlyingphysics. Here, we give a pedagogical introduction of this method in aparticular example of random neural networks, where neurons are randomly andfully connected by correlated synapses and therefore the network exhibits richemergent collective dynamics. We also review related past and recent importantworks applying this tool. In addition, a physically transparent and alternativemethod, namely the dynamical cavity method, is also introduced to deriveexactly the same results. The numerical implementation of solving theintegro-differential mean-field equations is also detailed, with anillustration of exploring the fluctuation dissipation theorem.

Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings