I skimmed through the article. It's very accessible and well-written, compared to my experience with some of the other literature in ML.

As a bit of an outsider I'd like to ask, how does this compare to the traditional analogue? In what scenarios is this superior to the classic BP NNs?

I understand that the point of the paper is to show that shared-weight training is possible, but the results look promising, hence the question.

There was a mention that one of the test cases achieved results competitive with current state of the art, but using 10 times less connections. That's pretty impressive.