An Exact Mapping Between the Variational Renormalization Group and Deep Learning | Hacker News Reader

An Exact Mapping Between the Variational Renormalization Group and Deep Learning

arxiv.org

30 pointsevanb7 comments

There was some discussion of a blog post explaining this paper here a month ago: https://news.ycombinator.com/item?id=9833584

I have a question for OP @evanb, or anyone else who's knowledgeable on this: Are ideas from tensor networks (eg: how the relevant degrees of freedom are organized), or even neural networks for that matter, applied to lattice gauge theories? In the other direction, is it understood how to implement states of gauge theories as tensor networks?

I'm aware of Elitzur's theorem (that there is no local gauge invariant order parameter), but I'm afraid I do not know much about lattice gauge theories.

I don't know much about tensor networks, so I may not be the right person to answer your question. Maybe that's answer enough? I would guess that it would only be apparent how to do some kind of embedding like you're thinking about after fixing a gauge, so that there would be gauge configurations that are physically equivalent but not at all manifestly related to the network you're interested in.

I do know that people think about tensor networks seriously as toy models for quantum gravity. But that's quite outside my range of expertise.

How do you establish an exact mapping to sth that is not exact, but only a buzzword term under which different people collect different methods?

Well, not that important. It's only important that the buzzword appears in the title!

The problem with this comment is that it doesn't teach us anything. If the article is wrong, it would be valuable to explain how it is wrong in a way that readers here can understand. But a sarcastic dismissal that leaves out the substance merely adds negativity.

I think that, if a phrase is meaningless, it is enough to explain why it is meaningless (because it proposes to make an 'exact' connexion between something rigorously defined and something that is not) without having to explain in what way the argument for it fails to fulfil that meaningless goal.

Nonetheless, it's surely also true that it would be nice to suggest a constructive remedy; and, fortunately, one need not go farther than the abstract to find (a better approximation to) the precise statement that the authors are making:

> We construct an exact mapping from the variational renormalization group, first introduced by Kadanoff, [to] deep learning architectures based on Restricted Boltzmann Machines (RBMs).

That was a case of not reading the link rather than asserting meaninglessness. The abstract makes clear that deep learning as an umbrella term would even fit RG, a completely unrelated concept from physics.

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