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My guess is that eventually fairly parallelizable matrix-based ML methods mostly subsume what we currently think of as general-purpose computation. But right now you're not going to replace your single-threaded C or Javascript code with anything that looks like a neural net...
It's a fun problem to think about - writing a web browser which is a neural net. (A friend of mine once taught his spam filter to play chess.)
It might be a easier problem than writing a new web rendering engine from scratch! Very fun to think about 
, lots of training data, probably faster and lower power too with the right Silicon 
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