Quantum field-theoretic machine learning

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 ${\varphi }^4$ 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 ${\varphi }^4$ 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 ${\varphi }^4$ 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.

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Cited by in corpus (18)

• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Stochastic normalizing flows as non-equilibrium transformations
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Nonperturbative renormalization for the neural network-QFT correspondence
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• Inverse Renormalization Group in Quantum Field Theory
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse
• p-Adic Statistical Field Theory and Deep Belief Networks
• p-Adic Statistical Field Theory and Convolutional Deep Boltzmann Machines
• On learning higher-order cumulants in diffusion models
• Quantum field theories, Markov random fields and machine learning
• Reducing finite-size effects with reweighted renormalization group transformations
• Bayesian RG Flow in Neural Network Field Theories
• Machine learning with quantum field theories
• Preserving gauge invariance in neural networks
• The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limit
• Applications of flow models to the generation of correlated lattice QCD ensembles
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes