This paper provides a concise description of the free energy principle, starting from a
formulation of random dynamical systems in terms of a Langevin equation and ending with a …

This paper describes a path integral formulation of the free energy principle. The ensuing
account expresses the paths or trajectories that a particle takes as it evolves over time. The …

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the
interface between a system and its environment with a Markov blanket. This affords …

In this treatment of random dynamical systems, we consider the existence—and
identification—of conditional independencies at nonequilibrium steady-state. These …

In theoretical biology, we are often interested in random dynamical systems—like the brain—
that appear to model their environments. This can be formalized by appealing to the …

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown
central to a wide range of applications, including hypothesis testing, sampler selection …

The recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems
raises questions regarding how such models are to be understood and the principles …

In this chapter, we identify fundamental geometric structures that underlie the problems of
sampling, optimization, inference, and adaptive decision-making. Based on this …

Control variates are variance reduction tools for Monte Carlo estimators. They can provide
significant variance reduction, but usually require a large number of samples, which can be …

In this commentary, we respond to a technical analysis of the Free Energy Principle
(hereafter: FEP) presented in" How particular is the physics of the Free Energy Principle" by …