Computer Science > Machine Learning
[Submitted on 12 Jun 2019 (v1), last revised 10 Jun 2020 (this version, v2)]
Title:Is Deep Learning a Renormalization Group Flow?
View PDFAbstract:Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. Deep learning performs a sophisticated coarse graining. Since coarse graining is a key ingredient of the renormalization group (RG), RG may provide a useful theoretical framework directly relevant to deep learning. In this study we pursue this possibility. A statistical mechanics model for a magnet, the Ising model, is used to train an unsupervised restricted Boltzmann machine (RBM). The patterns generated by the trained RBM are compared to the configurations generated through an RG treatment of the Ising model. Although we are motivated by the connection between deep learning and RG flow, in this study we focus mainly on comparing a single layer of a deep network to a single step in the RG flow. We argue that correlation functions between hidden and visible neurons are capable of diagnosing RG-like coarse graining. Numerical experiments show the presence of RG-like patterns in correlators computed using the trained RBMs. The observables we consider are also able to exhibit important differences between RG and deep learning.
Submission history
From: Ellen de Mello Koch Ms [view email][v1] Wed, 12 Jun 2019 15:33:43 UTC (7,639 KB)
[v2] Wed, 10 Jun 2020 07:51:51 UTC (3,154 KB)
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