Could you comment on some of the claims in the abstract?
1. Deep learning is a broad set of techniques that uses multiple layers of representation...
Agreed- that's what "deep" implies.
Is multi-scale analysis a primary component of 'deep learning'?
This may be true in vision, but not in general (e.g. in linguistics tasks and in speech, there is usually not a natural notion of scale).
2. "relatively little is understood theoretically about why these techniques are so successful at feature learning and compression.
True... deep learning methods are not very easy to analyze (personally I am skeptical that there is much point in trying very hard to analyze them).
"We construct an exact mapping from the variational renormalization group..."
Is this not new, not correct, or is this simply not of much use to deep learning?
I think the closest is to say it's not of much use. I didn't read the paper super carefully (and I'm not a physicist so am not familiar with the renormalization group), but I imagine the analogy is not very close at all and only applies in specific cases, e.g. in convolutional nets or something like that.
The renormalization group theory is so general and powerful, it's had profound impacts on many areas of theoretical and mathematical physics. Do you think this can't or won't impact the field of deep learning? If deep learning has multi-scale analysis at its heart, it appears on the surface that RG should be a good treatment. Have there been attempts to use RG for deep learning aside from the present work?
If the connection is real, it would seem to suggest that perhaps deep learning may have something to offer physics, if it really is "employing a generalized RG-like scheme." Do you have any comment on this?
I haven't read the paper in detail but I just don't think it's plausible that there is a very interesting connection as they are such different things.
To pick a random example, imagine you are a botanist and someone told you there is a connection between hydroelectric dams and oranges. Even if there is a connection, it's probably not something that is going to help you very much, and you probably wouldn't be so excited to read the paper explaining the purported connection.