by Jeff Beck and Maxwell J.D. Ramstead
28 February 2025, arXiv
ABSTRACT. The free energy principle (FEP), along with the associated constructs of Markov blankets and ontological potentials, have recently been presented as the core components of a generalized modeling method capable of mathematically describing arbitrary objects that persist in random dynamical systems; that is, a mathematical theory of ``every'' ``thing''. Here, we leverage the FEP to develop a mathematical physics approach to the identification of objects, object types, and the macroscopic, object-type-specific rules that govern their behavior. We take a generative modeling approach and use variational Bayesian expectation maximization to develop a dynamic Markov blanket detection algorithm that is capable of identifying and classifying macroscopic objects, given partial observation of microscopic dynamics. This unsupervised algorithm uses Bayesian attention to explicitly label observable microscopic elements according to their current role in a given system, as either the internal or boundary elements of a given macroscopic object; and it identifies macroscopic physical laws that govern how the object interacts with its environment. Because these labels are dynamic or evolve over time, the algorithm is capable of identifying complex objects that travel through fixed media or exchange matter with their environment. This approach leads directly to a flexible class of structured, unsupervised algorithms that sensibly partition complex many-particle or many-component systems into collections of interacting macroscopic subsystems, namely, ``objects'' or ``things''. We derive a few examples of this kind of macroscopic physics discovery algorithm and demonstrate its utility with simple numerical experiments, in which the algorithm correctly labels the components of Newton's cradle, a burning fuse, the Lorenz attractor, and a simulated cell.