[unlikelymordant]

this is exactly what happens in transfer learning. A recent paper by google ( https://research.googleblog.com/2017/07/revisiting-unreasona... ) shows that pre-training on a very large image database leads to improvements in state of the art for several different image problems. This is because the weights required for one image problem are not necessarily all that different from another image problem, especially in the early layers. There may not be as much common ground beteen images and e.g. NLP. Perhaps at much higher abstraction levels, but we aren't there yet.

[webmaven]

Transfer learning has been shown to improve training times in other modes (such using an image classification model to initialize an NLP model) over randomly initialized values.