Year: 2021
Type: article
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 ${\ensuremath{\phi}}^{4}$ 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 ${\ensuremath{\phi}}^{4}$ 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 ${\ensuremath{\phi}}^{4}$ 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.
Authors: Dimitrios Bachtis, Gert Aarts, Biagio Lucini
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1683282926, G2243907913, G31774293, G434337789, G4960855876, G5230481169, G5506003204, European network for Particle physics, Lattice field theory and Extreme computing, Fields, Strings and Lattices: From the Inflationary Universe to High-Energy Colliders, G6579576845, G6617361796, G7319073122
OpenAlex ID: W3131202180