Not really, I mean at it's core machine learning from an application perspective often seeks produce human level results, but there isn't any theorem describing human understanding of reality.
Like proving computer vision works well is essentially like proving you have a correct understanding of human perception.
It becomes somewhat circular, and while there exists proofs for certain qualities of data, none of them are true. I mean think about trying to describing reality, it exists on a lower dimensional manifold but analytically describing it? Don't think so.
Even proving robustness ends up being somewhat futile since even if you correctly eliminate advasarial examples this doesn't mean you CV application will produce correct results in general, only that the classification is robust(robust and correct are two different things).