Towards a geometry and analysis for Bayesian mechanics

I returned to UCL’s Theoretical Neurobiology seminar to speak about my recent work on gauge symmetries in inference.

Abstract:

This talk gives some geometric intuitions for a functional-analytic and gauge-theoretic rewriting of variational inference in the free energy principle. We will sketch out a proof, at a mostly conceptual level, of how maximising entropy over the degrees of freedom of a random dynamical system arises from a gauge force acting on the state space of a stochastic process. We will then connect this to the free energy principle explicitly, showing how a particular constraint on the dynamics of the system can be taken as one such gauge force, maintaining the non-equilibrium steady state density we identify with ‘thing-ness.’ Aside from new geometric principles for complex systems theory and the analysis of random functions, the idea of a gauge force keeping a Markov blanket in place has a rich interpretation as a field theory of life(-like dynamics).

Talk: link to recording

Slides: TNB March 2022.pdf