Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy
This work provides a foundational mathematical account for cognitive science and AI researchers, offering a graphical language to simplify and unify complex frameworks, though it is incremental in its formalization approach.
The paper tackles the problem of formalizing Predictive Processing and Active Inference frameworks by presenting a categorical formulation using string diagrams in a monoidal category, resulting in a diagrammatic derivation of active inference via free energy minimization and establishing compositionality for free energy across an agent's generative model.
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.