You're not wrong, but the numbers are quite different if you have a strong search heuristic. And that is where neural nets excel. See AlphaGo and derivatives. So this isn't just some random gradient descent exploring the full space; a properly designed and trained neural net will effectively cordon off vast swaths of the search space, and suddenly the problem is probably many orders of magnitude more tractable.
That's really why deep learning shines in technical applications. Solution search heuristics were until recently solely within the domain of biological neural networks; now we have created technology which is capable of extracting superior heuristics over the course of learning. And it's already paying off in industrial science, despite the cries of naysayers, though the applications are still in infancy.
That's really why deep learning shines in technical applications. Solution search heuristics were until recently solely within the domain of biological neural networks; now we have created technology which is capable of extracting superior heuristics over the course of learning. And it's already paying off in industrial science, despite the cries of naysayers, though the applications are still in infancy.