2025/03/01 by Manuel Baltieri, Baltieri, Manuel, Martin Biehl +5 · 2 voices · 6 citations
Engineering · Mathematics · Neuroscience · Psychology · #A priori and a posteriori #Bayesian inference #Bayesian probability #Categorical variable #Child and Animal Learning Development #Class (philosophy) #Cognitive Science and Education Research #Cognitive model #Embodied and Extended Cognition #Internal model #Interpretation (philosophy) #Variable-order Bayesian network #eess.SY #math.CT #math.OC
paper · pdf · doi:10.48550/arxiv.2503.00511
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/08/05
The internal model principle, originally proposed in the theory of control of linear systems, nowadays represents a more general class of results in control theory and cybernetics. The central claim of these results is that, under suitable assumptions, if a system (a controller) can regulate against a class of external inputs (from the environment), it is because the system contains a model of the system causing these inputs, which can be used to generate signals counteracting them. Similar claims on the role of internal models appear also in cognitive science, especially in modern Bayesian treatments of cognitive agents, often suggesting that a system (a human subject, or some other agent) models its environment to adapt against disturbances and perform goal-directed behaviour. It is however unclear whether the Bayesian internal models discussed in cognitive science bear any formal relation to the internal models invoked in standard treatments of control theory. Here, we first review the internal model principle and present a precise formulation of it using concepts inspired by categorical systems theory. This leads to a formal definition of ``model'' generalising its use in the internal model principle. Although this notion of model is not a priori related to the notion of Bayesian reasoning, we show that it can be seen as a special case of possibilistic Bayesian filtering. This result is based on a recent line of work formalising, using Markov categories, a notion of ``interpretation'', describing when a system can be interpreted as performing Bayesian filtering on an outside world in a consistent way.