Report on scipost_202305_00028v1
Wenxuan Zou, Haiping Huang · 2023
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 generic 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 meanfield equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem. C Stability analysis for the ReLU transfer function 20 D Derivation of fluctuation-dissipation theorem in equilibrium 21References 23