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> Deep models are important because without the extra “dimension” of depth/abstraction, there is no way to construct “shortcuts” between random variables that are separated by large amounts of time with short-range interactions; 1D models will be doomed to exponential decay.

From my non-professional perspective the above seems that it should have been very obvious - (and also that correlations between variables for natural languages would be better explained by multi-dimensional structure). That is if you told me that this were proved / formally supported as it is in this paper, my reaction would be a "that sounds like reasonable approximation" not - "that result sounds very surprising I must read the paper".



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