I have no doubt that some day (soon?) neural networks will be able to explain themselves (using language). But the explanation they give will be less than satisfactory to our aesthetic criteria. Occam's razor is a great aesthetic rule, but it doesn't guarantee beauty. We will most likely find out that the computational vision of the past had managed to find some rules covering some cases, but it missed many more, most of which will be higher-order and not that elegant. And it may turn out denoising was a rather messy problem, as was probably speech recognition.
Drugs work but we don't know how a surprisingly large number of them work. Yet chemists don't complain about them. Theoreticians should not complain either. Deep nets give them a huge subject matter that probably hides many interesting insights in it. I mean, don't convolutional layers look like gabor filters?
The question of what can be understood from them can go deep, to the limits of the ability of language/math to express ideas.
I don't see a problem in splitting all these domains to an "applied" school, that focuses research into evolving solutions that currently seem effective in approximating answers for certain engineering problems, and a more theoretical school that has the potential to carve new revolutionary paths while pursuing some (abstract?) ideal such as mathematical elegance. One shouldn't exclude the other and apparently there are enough scientists around that are attracted to either one of the two approaches.
Drugs work but we don't know how a surprisingly large number of them work. Yet chemists don't complain about them. Theoreticians should not complain either. Deep nets give them a huge subject matter that probably hides many interesting insights in it. I mean, don't convolutional layers look like gabor filters?
The question of what can be understood from them can go deep, to the limits of the ability of language/math to express ideas.