Dynamic Markov Blanket Detection for Macroscopic Physics Discovery

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'' orthings''. 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.

Overview of Dynamic Markov Blanket Detection for Macroscopic Physics Discovery

The paper "Dynamic Markov Blanket Detection for Macroscopic Physics Discovery" by Jeff Beck and Maxwell J. D. Ramstead leverages the framework of the Free Energy Principle (FEP) to propose an innovative approach to system identification and macroscopic physics discovery. This work situates itself at the intersection of various disciplines, integrating the statistics of Markov blankets with reinforcement learning, systems identification theory, and macroscopic physics to build a comprehensive, generative modeling framework. The authors derive and demonstrate algorithms capable of partitioning complex systems into interacting macroscopic subsystems, which are labeled as "objects" or "things."

The central thesis of the paper is the operationalization of Markov blankets in dynamic environments to define and detect object types through their interactions with the environment, rather than relying on static conditions. The authors propose a dynamic Markov blanket detection algorithm built on variational Bayesian expectation maximization. This algorithm identifies and classifies macroscopic objects by evaluating the statistics of observable microscopic dynamics, partitioning the system into internal, boundary, and external elements.

Key Contributions

Due to the inherent complexity of many systems, traditional system identification methods often impose arbitrary boundaries to externalize the subsystem interactions. The authors advance the field by reframing subsystem identification as detecting and characterizing dynamic Markov blankets that evolve over time, addressing earlier limitations of static models. This reframing allows for modeling objects with transient or porous boundaries, such as flames or organisms with material turnover.

Numerical Results: The proposed method's efficacy is presented through several illustrative examples, including Newton’s cradle, a burning fuse, a Lorenz attractor, and a simulated cell. These cases demonstrate that the algorithm effectively identifies and labels macroscopic components, recognizing dynamic subsystems and macroscopically relevant interaction laws.

Theoretical Implications: This work extends the applicability of the FEP to non-stationary phenomena, accommodating systems with dynamic and wandering boundaries. It provides a theoretical foundation for ontological potential functions, defining object types via boundary statistics and dynamics. By situating this within the context of systems that display non-equilibrium and stochastic behaviors, the method positions itself to formalize the ontological potentials as free energy functionals.

Broader Theoretical Context

Critically, this paper addresses several longstanding questions and critiques of the FEP, especially concerning its applicability to systems with dynamic, interacting subsystems. The authors adeptly address doubts about the FEP's use for systems with strong environmental interaction. Through path-based formulations and maximum caliber modeling, the study extends the FEP toolbox to embrace these more complex scenarios.

Macroscopic Physics Discovery: By integrating Markov blanket statistics with principles from systems theory and thermodynamics, the authors propose a cohesive approach to physics discovery at macroscopic scales. This spans both conceptual and methodological innovations, enabling robust subsystem typifications, even in entropic-dominated conditions.

Future Directions: The proposed approach encourages further investigations into more sophisticated models and inference techniques, promising enhancements in predictive capabilities and deeper integrations with dynamic systems theory frameworks, particularly for systems exhibiting emergent and downward causation phenomena.

In conclusion, Beck and Ramstead make a significant contribution to the understanding and practical application of the FEP, providing a robust framework for dynamic systems modeling. Their work simplifies complexity while embracing the intrinsic variability of macroscopic phenomena, extending the frontier of known modeling capabilities. Their contributions suggest promising pathways for future research in autonomous system identification and the broader implications of Markov blanket theory in modeling biological and physical systems.