In this new paper, published by Miguel Aguilera, Amin Moosavi and Hideaki Shimazaki in Nature Communications, we study and unify different kinetic mean-field methods in Ising models with the objective of developing tools for studying large data-sets from networks of neurons in non-equilibrium conditions and near critical and maximally fluctuating regimes. We propose a framework that integrates previous methods under an information geometric perspective. This framework also also allows us to propose new methods under atypical assuptions for mean-field methods.
The University of Sussex’s Media Relations team has been so kind to write this nice piece on our paper, describing the importance developing methods for studying and modelling the activity of neurons in non-equilibrium conditions and near the edge of chaos.
Aguilera, M, Moosavi, SA & Shimazaki H (2021). A unifying framework for mean-field theories of asymmetric kinetic Ising systems. Nature Communications 12:1197; https://doi.org/10.1038/s41467-021-20890
Abstract
Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system’s temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system’s correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.