BCAM SMRNN Seminar | Disordered neural networks in and out of equilibrium

This is the second 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. This seminar will present the dynamics of disordered neural networks both in and out of equilibrium. Focusing on systems with large number of attractors,we will explore the theoretical and mathematical methods necessary to understand such complex systems. Advanced tools from disordered systems theory, including replica theory for statics and generating functional analysis for dynamics, will be presented for tackling recurrent neural network models with extensively many attractors. We will also investigate how synaptic asymmetry fundamentally alters the landscape, ruling out microscopic equilibrium and requiring the study of their nonequilibrium dynamical regimes, even for a steady state. In the case out-of-equilibrium thermodynamics, we will study the stochastic thermodynamics of the system and analytically calculate its entropy production. Such methods can illustrate how to derive an exact analytical theory of the nonequilibrium thermodynamics of large-scale physical and biological systems and their phase transitions.