What frustrates me about Bayesian NNs is that talking about "priors" doesn't make nearly as much sense as it does in a regression context. A prior over parameter weights has no interpretation in the way that a prior over a regression coefficient, or even a spline smoothness, does. What you really want -- and what natural intelligence probably has -- are priors over aspects of the world.

Francois Chollet's paper on measuring intelligence was really informative for me on this front; the "priors" you should have about the world are not half-cauchys over certain hyperparameters or whatever, but priors about agent-ness, object-ness, goal-oriented-ness, and so on. How to encode that in a network...well, that's the real trick, right?