  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.
