14h: Jonathan Touboul, CIRB et INRIA. " Dynamics of Heterogeneous Networks: Insights from Random Matrix Theory."

Résumé: Since the seminal works of Sompolinsky, Crisanti and Sommers 25 years ago, where was shown a phase transition as a
function of the variance of the synaptic weights, the question of the link between the spectrum of random connectivity matrix and
macroscopic behaviors of random neural networks has remained largely open. In this talk, I will expose some recent works on the
analysis of the dynamics of large scale randomly coupled neural networks, and the link with the spectral properties of the underlying
random matrix. We will explore what happens at the phase transition in the classical Sompolinsky model, but also the dynamics of
networks with specific bio-inspired topologies both satisfying Dale's principle and balance conditions. I will conclude on the
characterization of rare events in the spectrum of the Ginibre ensemble motivated by the understanding of the index of the trivial state
in the random neural network. These topics are the result of a collaboration with Gilles Wainrib, Khashayar Pakdaman, Romain Allez
and Luis-Carlos Garcia del Molino.