English

Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy

Category Theory 2023-08-03 v1 Artificial Intelligence Logic in Computer Science Adaptation and Self-Organizing Systems

Abstract

We present a categorical formulation of the cognitive frameworks of Predictive Processing and Active Inference, expressed in terms of string diagrams interpreted in a monoidal category with copying and discarding. This includes diagrammatic accounts of generative models, Bayesian updating, perception, planning, active inference, and free energy. In particular we present a diagrammatic derivation of the formula for active inference via free energy minimisation, and establish a compositionality property for free energy, allowing free energy to be applied at all levels of an agent's generative model. Aside from aiming to provide a helpful graphical language for those familiar with active inference, we conversely hope that this article may provide a concise formulation and introduction to the framework.

Keywords

Cite

@article{arxiv.2308.00861,
  title  = {Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy},
  author = {Sean Tull and Johannes Kleiner and Toby St Clere Smithe},
  journal= {arXiv preprint arXiv:2308.00861},
  year   = {2023}
}