Towards a Neuronal Gauge Theory

TLDR

Gauge theory has been proposed to characterize brain and other self‑organized systems as entities resolving environmental uncertainty through internal state changes or environmental interactions. The paper aims to present the technical framework that enables variational inference on manifolds. It introduces an algorithm that employs Schild’s ladder for parallel transport of sufficient statistics on a statistical manifold to perform this inference. Formal arguments show that this approximate Bayesian inference–based neuronal gauge theory can illuminate previously unformalized phenomena such as attention and the action‑perception link.

Abstract

In a published paper [Sengupta, 2016], we have proposed that the brain (and other self-organized biological and artificial systems) can be characterized via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we have shown that a gauge theory for neuronal dynamics -- based on approximate Bayesian inference -- has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception. Here, we describe the technical apparatus that enables such a variational inference on manifolds. Particularly, the novel contribution of this paper is an algorithm that utlizes a Schild's ladder for parallel transport of sufficient statistics (means, covariances, etc.) on a statistical manifold.