You have a problem with gradient descent?
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You can measure how well nearest-neighbor "extracts information from examples" by counting how many samples it needs to reach a given error level. Do the same with a neural net trained with gradient descent. The result will not support your statement.
If you use the dumbest possible form of nearest-neighbor and the smartest possible form of gradient descent, yes. If you're smart about how you map test examples to training ones, no. In any case, I was talking about the information extracted per step, where kNN blows GD away.
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In high-dimensions, kNN makes no sense at all, as we have no good distances a priori. So, in high-dimensions, GD works while kNN does not. It is as simple as that. I think we should improve Deep Learning rather than denying it as a major step in the right direction.
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kNN does not even create a "model of the world", as we need the "training" examples during inference. It is much far way from intelligence than GD. Our mind does not need to remember all dogs that we had seen before to know that a unseen dog is a dog.
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