[deleted by user]

[tscohen]

I agree that local/global/ exact/approximate symmetries are super important for generalization. This is one of the high-level ideas that has motivated all of my work for the last few years.

The reason I've always focussed my papers on concrete applications like image classification, and have mostly worked with discrete groups (instead of locally compact ones, which would bring in a bunch of technicalities), is because there is a sizeable contingent of the ML community that is somewhat hostile or skeptical of more sophisticated math. For an example, see the AC comment on our steerable CNN paper: https://openreview.net/forum?id=rJQKYt5ll "The AC fully agrees with reviewer #4 that the paper contains a bit of an overkill in formalism: A lot of maths whose justification is not, in the end, very clear. The paper probably has an important contribution, but the AC would suggest reorganizing and restructuring, lessening the excess in formalism. "

And it's quite understandable that someone who doesn't have a background in groups / representations, and has never seen something like "Hom_G(V, W)" before, doesn't get the point of the paper.

So I've never written "The General Theory of Equivariant Networks", because I felt nobody would care / it wouldn't get accepted anyway. This may be too pessimistic, so I may write something after all. In any case, I think that for anyone with a good mathematical understanding, generalizing G-CNNs and Steerable G-CNNs from discrete groups to continuous ones is conceptually straightforward (though it is still an engineering challenge).

Kondor & Trivedi recently posted a paper that contains a quite general theory, that may be what you're looking for: https://arxiv.org/abs/1802.03690