Related papers: Multiscale Normalizing Flows for Gauge Theories
This paper introduces Tensor Gauge Flow Models, a new class of Generative Flow Models that generalize Gauge Flow Models and Higher Gauge Flow Models by incorporating higher-order Tensor Gauge Fields into the Flow Equation. This extension…
Normalizing flows are a class of machine learning models used to construct a complex distribution through a bijective mapping of a simple base distribution. We demonstrate that normalizing flows are particularly well suited as a Monte Carlo…
We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an $SU(N)$ variable (or on a $U(N)$ variable by a simple…
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…
The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not…
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example,…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed…
We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of…
Stochastic normalizing flows are a class of deep generative models that combine normalizing flows with Monte Carlo updates and can be used in lattice field theory to sample from Boltzmann distributions. In this proceeding, we outline the…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…
Many-body perturbation theory provides a powerful framework to study the ground state and thermodynamic properties of nuclear matter as well as associated single-particle potentials and response functions within a systematic order-by-order…
In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting…
The standard model of particle physics is generalized so as to be furnished with a horizontal symmetry generated by an intermediary algebra between simple Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(3)$. Above a certain high energy…
An SU(2) gauge theory is broken to U(1) by an adjoint scalar to produce magnetic monopoles. At a lower scale, this U(1) is further broken by a fundamental scalar to produce tubes of magnetic flux. We dualize the resulting theory to write an…
We discuss the renormalization group flow, duality, and supersymmetry breaking in N = 1 supersymmetric SU(N)xSU(M) gauge theories.