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.

我们提出了一种基于范畴的认知框架，使用具有复制和丢弃功能的范畴内解释的字符串图表达方式，其中包括生成模型、贝叶斯更新、感知、规划、主动推理和自由能量的图表表示。我们通过自由能量最小化的图表导出了主动推理的公式，并建立了自由能量的组合性属性，使得自由能量可以应用于代理模型的所有层次。除了为熟悉主动推理的人提供一个有用的图形语言外，我们也希望本文能够提供一个简洁的框架和介绍。