Interpreting Dynamical Systems as Bayesian Reasoners

TL;DR

This paper develops a formal framework using category theory to determine when dynamical systems can be interpreted as Bayesian reasoners performing filtering or inference, bridging physical systems and probabilistic models.

Contribution

It introduces a general theoretical approach to interpret dynamical systems as Bayesian agents, formalizing conditions for such interpretations using category theory.

Findings

Provides formal definitions for Bayesian interpretability of systems

Establishes criteria for when systems can be seen as Bayesian filters or inferencers

Lays groundwork for connecting physical dynamics with probabilistic reasoning

Abstract

A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior. Here we begin the development of a general theory that would tell us when it is appropriate to interpret states as representing beliefs in this way. We focus on the case in which a system can be interpreted as performing either Bayesian filtering or Bayesian inference. We provide formal definitions of what it means for such an interpretation to exist, using techniques from category theory.