Quantum field-theoretic machine learning

TL;DR

This paper introduces a novel approach to machine learning by deriving algorithms from discretized quantum field theories, specifically using the $^{4}$ scalar field theory, bridging quantum field theory and neural network design.

Contribution

It demonstrates that $^{4}$ scalar field theory can be formulated as a Markov random field, enabling the development of quantum field-theoretic machine learning algorithms and neural network architectures.

Findings

Successfully recast $^{4}$ theory as a Markov random field

Developed neural network architectures from quantum field theory

Applied the framework to minimize distributional distances

Abstract

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the $\phi^{4}$ theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the $\phi^{4}$ theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.