Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings
This is an incremental tutorial for beginners in physics and neuroscience to understand complex neural network dynamics.
The paper provides a pedagogical introduction to dynamical mean-field theory for analyzing the collective dynamics of randomly connected neural networks with correlated synapses, and introduces an alternative dynamical cavity method to derive the same results.
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.