A unifying framework for mean-field theories of asymmetric kinetic Ising systems

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. Many mean-field theories are proposed for studying the non-equilibrium dynamics of complex systems, each based on specific assumptions about the system's temporal evolution. Here, Aguilera et al. propose a unified framework for mean-field theories of asymmetric kinetic Ising systems to study non-equilibrium dynamics.We thank Yasser Roudi and Masanao Igarashi for valuable comments and discussions on this manuscript. This work was supported in part by the Cooperative Intelligence Joint Research between Kyoto University and Honda Research Institute Japan, MEXT/JSPS KAKENHI Grant Number JP 20K11709, and the grant of Joint Research by the National Institutes of Natural Sciences (NINS Program No. 01112005). M.A. was funded by the European Union's Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No 892715 and the University of the Basque Country UPV/EHU post-doctoral training program grant ESPDOC17/17, and supported in part by the Basque Government project IT 1228-19 and project Outonomy PID2019-104576GB-I00 by the Spanish Ministry of Science and Innovation