You can prove the ANN works, but how do you check it conforms to any specification, other than by testing and accepting high probability of real world failure?

Eventually, you have a high level fuzzy requirement which is hard to even specify right. Just look at, say, latest YouTube guidelines about content they try to ML around to make tractable...

And that's a classifier, now try to do the same with a machine translation system.

There are papers that use SMT over RNNs to prove smoothness of the output functions. You can absolutely apply these techniques to ML.

So you have any links? I’m very curious, and a quick search did not turn up anything.

Clark Barrett's group at Stanford (previously NYU) is a leader here.

Thank you!