[2308.00861] Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy

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.

Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy Sean Tull1,2 , Johannes Kleiner2,3,4 , and Toby St Clere Smithe5,6 1 Quantinuum arXiv:2308.00861v1 [math.CT] 1 Aug 2023 2…

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