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. More generally, we discuss the relationship between PCA and observables in Monte Carlo simulations and the possibility of reducing the number of learning parameters in supervised learning based on RG inspired hierarchical ansatzes.
Highlights
Machine learning has been a fast growing field of research in several areas dealing with large datasets and should be useful in the context of lattice field theory [1]
Results for the leading principal components analysis (PCA) eigenvalue and specific heat for blocked configurations were found qualitatively similar to the unblocked results
Direct use of tensor renormalization group (RG) methods are being used for the machine learning (ML) treatment of worm configurations of the 2D Ising model near criticality and will be presented elsewhere [8]
Summary
Machine learning has been a fast growing field of research in several areas dealing with large datasets and should be useful in the context of lattice field theory [1]. In these proceedings, we briefly introduce the concept of machine learning. We discussed work in progress relating the coarse graining of the worm images to an approximate procedure in the tensor renormalization group (TRG) treatment of the Ising model [5,6,7]. We briefly mention an upcoming preprint about this question [8]
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