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

TL;DR

This paper introduces a categorical, diagrammatic framework for modeling predictive processing and active inference, providing a compositional approach to free energy minimization in cognitive systems.

Contribution

It offers a novel categorical and diagrammatic formulation of active inference, including derivations and properties of free energy in a compositional setting.

Findings

Diagrammatic derivation of active inference formula

Establishment of compositionality property for free energy

Provides a graphical language for active inference modeling

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.