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تسجيل مستخدم جديدRG inspired Machine Learning for lattice field theory
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Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use Renormalization Group (RG) ideas in the context of machine learning. We examine coarse graining procedures for perceptron models designed to identify the digits of the MNIST data. We discuss the correspondence between principal components analysis (PCA) and RG flows across the transition for worm configurations of the 2D Ising model. Preliminary results regarding the logarithmic divergence of the leading PCA eigenvalue were presented at the conference and have been improved after. More generally, we discuss the relationship between PCA and observables in Monte Carlo simulations and the possibility of reduction of the number of learning parameters in supervised learning based on RG inspired hierarchical ansatzes.
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In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this limit, restr
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This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428,
and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree of freedo
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