[mysterEFrank]

I think it's clear that there's a strong relationship between all of these methods. Papers proving that Neural Networks are GPs came out a year or two ago, for example. Deep learning is more useful in the end because kernel machines and gaussian processes (classically) store all samples in a dataset and require expensive pairwise comparison. Deep learning/gradient descent doesn't.

[rq1]

I don’t want to seem like minimising (if I may say) all these works and similar ones. This is not surprising at all and they’re not new results actually. Cf. Donsker-like theorems.