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.

翻译：本文提出预测处理与主动推理认知框架的范畴化表述，该表述以弦图解形式呈现，并在一类具有复制与舍弃操作的幺半范畴中进行解释。具体包含生成模型、贝叶斯更新、感知、规划、主动推理及自由能的图解化诠释。我们特别通过自由能最小化推导出主动推理公式的图解化表达，并建立自由能的组合性特性，使得自由能可应用于智能体生成模型的各个层级。除为熟悉主动推理的研究者提供直观图形语言外，本文亦期望为该框架提供简洁的表述形式与入门导引。