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Deep learning and the renormalization group · Around

2013

Deep learning and the renormalization group

Bény, Cédric

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Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics.

We compare the ideas behind the RG on the one hand and deep machine learning on the other, where depth and scale play a similar role.
In order to illustrate this connection, we review a recent numerical method based on the RG---the multiscale entanglement renormalization ansatz (MERA)---and show how it can be converted into a learning algorithm based on a generative hierarchical Bayesian network model.
Under the assumption---common in physics---that the distribution to be learned is fully characterized by local correlations, this algorithm involves only explicit evaluation of probabilities, hence doing away with sampling.

Built on

The renormalization group and critical phenomena
K.G. Wilson · 1983
Earlier work this paper cites.
ArXiv:quant-ph/0608197
D. Perez-Garcia, F. Verstraete, M.M. Wolf, and J.I. Cirac · 2006
Earlier work this paper cites.
Criticality, the area law, and the computational power of projected entangled pair states
F. Verstraete, M.M. Wolf, D. Perez-Garcia, and J.I. Cirac · 2006
Earlier work this paper cites.

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