Modelling Brain Dynamics with Recurrent Neural Networks

Recurrent Neural Networks (RNNs) are a powerful tool to shed light on how brain may work. RNNs can recapitulate different dynamical phases observed in cortical circuits, such as silent or chaotic state, and provide a simple explanation of asynchronous rate activity in neural systems and information processing capabilities. In this thesis, we will exploit advanced approaches in statistical physics to investigate emergent phases of RNNs with random coupling. Integrating tools from Dynamical Mean Field Theory and Random Matrix Theory with numerical simulations, we analyse the properties of the network with particular focus on its stability and the effect of quenched external inputs on the dynamical phases of the network. Finally, we will also study the equivalence of two frequently used forms of recurrent rate models with random interactions.