Markov Blanket Density and Free Energy Minimization

TL;DR

This paper introduces Markov blanket density as a continuous measure to extend the Free Energy Principle, linking spatial gradients to active inference dynamics and providing a mathematical framework for new predictions.

Contribution

It develops a continuous, information-theoretic extension of the Free Energy Principle using Markov blanket density, connecting density gradients to active inference dynamics.

Findings

Markov blanket density quantifies conditional independence spatially.

Active inference dynamics emerge from spatial gradients in density.

Provides a mathematical framework linking density to free energy minimization.

Abstract

This paper presents a continuous, information-theoretic extension of the Free Energy Principle through the concept of Markov blanket density, i.e., a scalar field that quantifies the degree of conditional independence between internal and external states at each point in space (ranging from 0 for full coupling to 1 for full separation). It demonstrates that active inference dynamics, including the minimization of variational and expected free energy, naturally emerge from spatial gradients in this density, making Markov blanket density a necessary foundation for the Free Energy Principle. These ideas are developed through a mathematically framework that links density gradients to precise and testable dynamics, offering a foundation for novel predictions and simulation paradigms.