That's the DL equivalent of cold fusion: it violates what we know on a fundamental level, and overwhelming evidence should be required
Every once in a while, a paper comes out claiming to get competitive results using only some form of greedy layer-wise training
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But these papers never provide much evidence or explanations, and seem to take their own claims in strides, unaware of their enormity
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On the other hand, partially updating a (possibly large) neural network seems useful for life-long learning, but that's another topic.
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