Posit: the problem of cognition has almost no overlap with supervised learning, what we're currently good at -- learning to map space x to space y given a dense sampling of x-cross-y
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They are capable of generalization, but it is necessarily local generalization, i.e. pattern recognition.
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I don't see why using a convnet should imply the need for a dense sampling of the input-output mapping. Do you have any links to papers where I could see it justified?
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