A higher gauge theory for machine learning and inference

I submitted this account of some preliminary work to a poster session for ECRs at my institution.

Abstract:

We consider the mathematical theory underlying deep learning and machine learning, and attempt to motivate the success of such algorithms in finding solutions to dynamical problems. We use Jaynes’ Maximum Calibre, a form of Maximum Entropy, as a generalisation of machine learning-like inference. Borrowing from the principal bundle formalism underlying much of modern mathematical physics, we describe maximising calibre as a particular least action principle on the space of solutions of a dynamical system. We then prove an equivalence between the expressions for entropy maximisation under a constraint, and parallel transportation in the path space over a bundle. In doing so, we provide a theory justifying machine learning’s efficacy in solving arbitrarily complex data-generating processes.

Poster: A Higher Gauge Theory for Machine Learning and Inference