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https://doi.org/10.1103/physre...
Article . 2020 . Peer-reviewed
License: APS Licenses for Journal Article Re-use
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https://dx.doi.org/10.48550/ar...
Article . 2020
License: arXiv Non-Exclusive Distribution
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Short-sighted deep learning

Authors: Ellen de Mello Koch; Anita de Mello Koch; Nicholas Kastanos; Ling Cheng;

Short-sighted deep learning

Abstract

A theory explaining how deep learning works is yet to be developed. Previous work suggests that deep learning performs a coarse graining, similar in spirit to the renormalization group (RG). This idea has been explored in the setting of a local (nearest neighbor interactions) Ising spin lattice. We extend the discussion to the setting of a long range spin lattice. Markov Chain Monte Carlo (MCMC) simulations determine both the critical temperature and scaling dimensions of the system. The model is used to train both a single RBM (restricted Boltzmann machine) network, as well as a stacked RBM network. Following earlier Ising model studies, the trained weights of a single layer RBM network define a flow of lattice models. In contrast to results for nearest neighbor Ising, the RBM flow for the long ranged model does not converge to the correct values for the spin and energy scaling dimension. Further, correlation functions between visible and hidden nodes exhibit key differences between the stacked RBM and RG flows. The stacked RBM flow appears to move towards low temperatures whereas the RG flow moves towards high temperature. This again differs from results obtained for nearest neighbor Ising.

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Keywords

FOS: Computer and information sciences, Computer Science - Machine Learning, Statistical Mechanics (cond-mat.stat-mech), Statistics - Machine Learning, FOS: Physical sciences, Machine Learning (stat.ML), Computational Physics (physics.comp-ph), Physics - Computational Physics, Condensed Matter - Statistical Mechanics, Machine Learning (cs.LG)

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
Green