Machine learning with quantum field theories

TL;DR

This paper explores the connection between quantum field theories and machine learning by demonstrating how scalar field theories can be reformulated as Markov random fields, leading to novel neural network architectures and algorithms.

Contribution

It establishes a formal link between $\,\phi^{4}$ scalar field theory and Markov random fields, deriving new machine learning algorithms from quantum field theoretical principles.

Findings

Recasting $\,\phi^{4}$ theory as a Markov random field.

Derivation of new neural network architectures from quantum field theory.

Applications using probability distribution minimization.

Abstract

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the $\phi^{4}$ scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the $\phi^{4}$ theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the $\phi^{4}$ machine learning algorithms and target probability distributions.