When does a dynamical system implement a statistical inference?

I had a wonderful time speaking to the Brains Minds and Machines group at the Swinburne University of Technology. I thank the attendees for their interest and Oscar Schmidt for inviting me.

(Consider also looking at this previous lecture for a preliminary account of the story told here.)

Abstract:

We will trace through the logic of a certain variational free energy principle for non-equilibria and show how one arrives at the statement “a random process with a non-equilibrium steady state density looks as if it minimises variational free energy”. We will then discuss how this principle could be used to relate the physics of non-equilibrium systems with notions of reservoir computation by considering the connection between variational free energy minimisation and the maintenance of certain fluxes of energy in and out of a system. Some discussion of what a representation means in this context will follow. We will propose a minimalist account of representation as synchronisation in coupled random dynamical systems.

Slides (lightly edited to provide more references): BMMS slides June 2026.

Recording: to follow.

 

Some useful data are contained in the final four slides.