Deep learning is useful because it enables us to create programs that we could not otherwise code by hand. But the space of programs you can learn via deep learning models is a minuscule slice of the space of programs that we may be interested in.
Most interesting processes cannot be learned by a stack of affine transforms (plus squashing functions) mapping one vector space to another point-by-point. Even given large amounts of data.
Perhaps more importantly, although human engineers can cover a dramatically larger section of the space of interesting programs (compared to deep learning models), many useful programs remain inaccessible even to humans -- we cannot develop them by hand.
It will be the job of future AI systems to give us access to these programs.
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