BCAM SMRNN Seminar | Exploring Recurrent Neural Network Dynamics through Non-equilibrium Statistical Mechanics

This is the first of a series of informal BCAM seminars —Statistical Mechanics of Recurrent Neural Networks (SMRNN)— exploring the dynamics of recurrent neural networks (RNNs) using non-equilibrium statistical mechanical methods. Unlike equilibrium methods, which are limited to stationary states, non-equilibrium approaches accommodate diverse neuron types and synaptic symmetries, making them suitable for biologically realistic scenarios or more general machine learning models. The lecture will outline a strategy to derive dynamical laws governing macroscopic quantities emerging from microscopic neuronal dynamics. We will progress through simple to complex network models, elucidating the behavior of RNNs and highlighting the distinction between different regimes. Despite limited resources on non-equilibrium dynamics in RNNs, we will present foundational concepts and techniques —paving the way for future research— and emphasize the importance of non-equilibrium statistical mechanics in analyzing RNN dynamics and offer insights into biologically realistic models.