# A Concise Mathematical Description of Active Inference in Discrete Time

arXiv: https://arxiv.org/abs/2406.07726 · HTML: https://mlsanity.com/paper/2406.07726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Whence the Expected Free Energy?](https://mlsanity.com/paper/2004.08128/) (2020)
- [pymdp: A Python library for active inference in discrete state spaces](https://mlsanity.com/paper/2201.03904/) (2022)
- [Active Inference as a Model of Agency](https://mlsanity.com/paper/2401.12917/) (2024)

## Abstract (arXiv)

In this paper we present a concise mathematical description of active inference in discrete time. The main part of the paper serves as a basic introduction to the topic, including a detailed example of the action selection mechanism. The appendix discusses the more subtle mathematical details, targeting readers who have already studied the active inference literature but struggle to make sense of the mathematical details and derivations. Throughout, we emphasize precise and standard mathematical notation, ensuring consistency with existing texts and linking all equations to widely used references on active inference. Additionally, we provide Python code that implements the action selection and learning mechanisms described in this paper and is compatible with pymdp environments.