Interpreting Dynamical Systems as Bayesian Reasoners
This work addresses a foundational issue in active inference for researchers in AI and cognitive science, but it is incremental as it builds on existing concepts without introducing new methods or data.
The paper tackles the problem of determining when the internal states of a dynamical system can be interpreted as Bayesian beliefs, focusing on systems performing Bayesian filtering or inference, and develops a general theory using category theory to provide formal definitions for such interpretations.
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.