Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory

• URL: http://arxiv.org/abs/2412.00200v1
• Date: Fri, 29 Nov 2024 19:01:05 GMT
• Title: Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Authors: Andrea Bulgarelli, Elia Cellini, Alessandro Nada,
• Abstract summary: Non-equilibrium Markov Chain Monte Carlo simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Normalizing Flows (SNFs) We present the first implementation of SNFs for $mathrmSU(3)$ lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates.
• Score: 44.99833362998488
• License:
• Abstract: Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Stochastic Normalizing Flows (SNFs). In this work we present the first implementation of SNFs for $\mathrm{SU}(3)$ lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times.

Related papers

• Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance [0.0]
  We present a novel framework for analyzing convergence in Score-based Generative Models (SGMs) We show that weak log-concavity of the data distribution evolves into log-concavity over time. Our approach circumvents the need for stringent regularity conditions on the score function and its regularity.
  arXiv  Detail & Related papers  (2025-01-04T14:33:27Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Stochastic normalizing flows as non-equilibrium transformations [62.997667081978825]
  We show that normalizing flows provide a route to sample lattice field theories more efficiently than conventional MonteCarlo simulations. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.
  arXiv  Detail & Related papers  (2022-01-21T19:00:18Z)
• Information Theoretic Structured Generative Modeling [13.117829542251188]
  A novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible. The implementation employs a single neural network driven by an orthonormal input to a single white noise source adapted to learn an infinite Gaussian mixture model. Preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as for training adversarial networks.
  arXiv  Detail & Related papers  (2021-10-12T07:44:18Z)
• Machine Learning and Variational Algorithms for Lattice Field Theory [1.198562319289569]
  In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. We introduce an approach to "deform" Monte Carlo estimators based on contour deformations applied to the domain of the path integral. We demonstrate that flow-based MCMC can mitigate critical slowing down and observifolds can exponentially reduce variance in proof-of-principle applications.
  arXiv  Detail & Related papers  (2021-06-03T16:37:05Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)
• Stochastic Normalizing Flows [2.323220706791067]
  We show that normalizing flows can be used to learn the transformation of a simple prior distribution. We derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end. We illustrate the representational power, sampling efficiency and correctness of SNFs on several benchmarks including applications to molecular sampling systems in equilibrium.
  arXiv  Detail & Related papers  (2020-02-16T23:29:32Z)
• Semi-Supervised Learning with Normalizing Flows [54.376602201489995]
  FlowGMM is an end-to-end approach to generative semi supervised learning with normalizing flows. We show promising results on a wide range of applications, including AG-News and Yahoo Answers text data.
  arXiv  Detail & Related papers  (2019-12-30T17:36:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.