This is very much not my area of physics (I worked in condensed matter), but from what I know I'm not seeing anything which looks outrageously implausible. I t

This is very much not my area of physics (I worked in condensed matter), but from what I know I'm not seeing anything which looks outrageously implausible. I think the intuition is something like this, and I'm going to be really informal here so please indulge me while I have a go at the pop-science version (and experts, please correct me!) One of the ways deep learning is useful, compared to other feature extraction schemes, is that (in most formulations) it's a multi-scale method (it learns features at various length scales from very short to very long, specifically as you ascend/descend layers in the network). The renormalization group is a mathematical framework for reasoning about how physics changes between length scales. Very informally, the hardest unsolved problem in physics is building a single theory which works for both the very short and the very big – very big problems (astrophysics) have an effective theory in the form of general relativity, very very short length scales have effective theory in the form of quantum field theory (basically all of modern particle physics), and the rest of physics (e.g. quantum mechanics, which from a purely theoretical perspective just is the entirety of chemistry and materials science...) is likewise somewhere in between on the great cosmic measuring stick. So far so Powers of Ten, right? The challenge is building a mathematical structure for transforming between these length scales in such a way as to have a coherent single theory which works for all of them. This is what people mean when they talk about "unification" in physics. The best mathematical framework we have for that thus far is the renormalization group. So this paper – which I have no more than skimmed – purports to show that these two mathematical structures are (in some deep sense) more or less the same shape, which would make sense given that the problems they are solving are the same kind of shape (making sense of something at a range of length scales). So it could be wrong, but it's not obviously misguided. Is it useful? In terms of practical machine learning applications right now, probably not (and ditto, but more strongly, in terms of theoretical physics). But if it means a bunch of mathematical techniques worked out in one domain can be ported over to the other (in practice, from particle physics to analyzing deep neural networks), that'd be useful!