RG inspired Machine Learning for lattice field theory

Abstract

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.

Talk given by Yannick Meurice at the conference Lattice 2017, Granada, Spain

References in corpus (4)

• Machine learning phases of matter
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Detection of phase transition via convolutional neural network
• Accurate exponents from approximate tensor renormalizations

Cited by in corpus (8)

• Thermodynamics and Feature Extraction by Machine Learning
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Deep learning black hole metrics from shear viscosity
• Neural Network flows of low q-state Potts and clock Models
• Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data
• Examples of renormalization group transformations for image sets
• Correlations in the shear flow of athermal amorphous solids: A principal component analysis
• Logical Reasoning for Revealing the Critical Temperature through Deep Learning of Configuration Ensemble of Statistical Systems