arXiv:1301.3124quant-ph
Deep learning and the renormalization group
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Abstract
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.
To establish in a semi-rigorous way the (btw obvious) relationship between coarsening in physics and in stacked neural networks, as was done long after the latter became a thing [1][2], is at the same level as observing the analogy between Black-Scholes and diffusion. It's cute…
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