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

arXiv: https://arxiv.org/abs/2002.04309 · HTML: https://mlsanity.com/paper/2002.04309/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [Dynamical Mean-Field Theory of Self-Attention Neural Networks](https://mlsanity.com/paper/2406.07247/) (2024)
- [Inferring entropy production in many-body systems using nonequilibrium maximum entropy](https://mlsanity.com/paper/2505.10444/) (2025)
- [Machine learning at the mesoscale: a computation-dissipation bottleneck](https://mlsanity.com/paper/2307.02379/) (2023)
- [Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks](https://mlsanity.com/paper/2602.14885/) (2026)

## Abstract (arXiv)

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.