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 illustrating the theory on action selection. In the appendix the more subtle mathematical details are discussed. This part is aimed at readers who have already studied the active inference literature but struggle to make sense of the mathematical details and derivations. Throughout the whole manuscript, special attention has been paid to adopting notation that is both precise and in line with standard mathematical texts. All equations and derivations are linked to specific equation numbers in other popular text on the topic. Furthermore, Python code is provided that implements the action selection mechanism described in this paper and is compatible with pymdp environments.

翻译：本文提出了一种离散时间主动推理的简明数学描述。论文主体部分作为该主题的基础性导论，包含一个详细示例以阐明行动选择的相关理论。附录部分则探讨了更为精微的数学细节，主要面向已研读主动推理文献但难以理解数学细节与推导过程的读者。全文特别注重采用既精确又符合标准数学文献规范的符号体系，所有方程和推导均与相关经典文献中的特定方程编号建立对应关系。此外，本文提供了与pymdp环境兼容的Python代码，实现了所述行动选择机制。