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The same is true about deep learning as well -- current limitations may be more about gradient descent than about deep neural networks themselves
I think something similar too--after all, a "deep neural network" these days is just a matrix based computer program format with certain restrictions on control flow over numeric representations--but, I put the blame on loss functions. SGD is a search strategy, true but
I think the limitations come more from how guidance is provided on how to navigate that space via loss & problem formulation. So if you replaced SGD, you'd more be changing navigation & replacement need not be strictly better.
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