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A concise mathematical description of active inference in discrete time

Jesse van Oostrum et al.

Journal of Mathematical Psychology2025https://doi.org/10.1016/j.jmp.2025.102921article
AJG 3
Weight
0.37

What the paper says

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. • Language and notation that is in line with standard texts on probability theory. • Detailed example of the T-maze environment of active inference. • Precise derivations of the inference and learning rules of active inference.

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https://doi.org/https://doi.org/10.1016/j.jmp.2025.102921

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@article{jesse2025,
  title        = {{A concise mathematical description of active inference in discrete time}},
  author       = {Jesse van Oostrum et al.},
  journal      = {Journal of Mathematical Psychology},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1016/j.jmp.2025.102921},
}

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A concise mathematical description of active inference in discrete time

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Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.