Mean field theory for random recurrent spiking neural networks

Abstract—Recurrent spiking neural networks can provide biologically inspired model of robot controller. We study here the dynamics of large size randomly connected networks thanks to ”mean field theory”. Mean field theory allows to compute their dynamics under the assumption that the dynamics of individ-ual neuronsare stochastically independent. We restrict ourselves to the simple case of homogeneous centered gaussian independent synaptic weights. First a theo-retical study allows to derive the mean-field dynamics using a large deviation approach. This dynamics is characterized in function of an order parameter which is the normalized variance of the coupling. Then vari-ous applications are reviewed which show the applica-tive potentiality of the approach