[PaulHoule]

Neural networks compose complex functions out of simple functions. A three layer network can approximate any function w/ multiple inputs and outputs. Now, a network has to be able to learn that approximation with a reasonable amount of time and computation and all of the innovations in network architectures are about making networks that actually do learn.

As for reasoning with uncertainty people do a lot of that. There was that time I went to my doc because I had rashes on on my arms and neck and my doc (e.g. like MYCIN) thought some of them looked allergic and some looked bacterial. Instead of overthinking it, he wrote me scripts for two different creams and I tried both.

My take is that rapid progress in neural networks is not about people having a lot of understanding or a general theory or even that the average work is of very good quality, but an awful lot of people are working on it and throwing a lot of resources at it. People are discovering things empirically that work.

One can consider many counterfactuals which would have sped up development a lot. If the Japanese had developed a 5th generation computer project around accelerating neural networks instead of accelerating logical inference, if people had tried ReLU in the 1980s, etc.