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It appears that it's exactly the distinction between fixed and arbitrary precision that decides whether or not transformers are Turing Complete: https://openrev
by Tainnor 3y ago
It appears that it's exactly the distinction between fixed and arbitrary precision that decides whether or not transformers are Turing Complete: https://openreview.net/forum?id=HyGBdo0qFm¬eId=r1lxKiAJlV https://openreview.net/forum?id=HyGBdo0qFm¬eId=r1lxKiAJlV
I think the larger point though is that "is X Turing Complete?" depends on the exact assumptions made and that's a point that the authors of the paper IMHO failed to understand while reading the reviews.
- light_hue_1 3y agoThe arbitrary vs fixed precision people are also totally clueless. All of the arbitrary precision papers should have been rejected. This is CS theory 101. Any non-trivial architecture is not just Turing complete, it can perform hypercomputation (solving the halting problem), if it can use arbitrary precision numbers.
- Tainnor 3y ago> Any non-trivial architecture is not just Turing complete, it can perform hypercomputation (solving the halting problem), if it can use arbitrary precision numbers. Can you explain this part? (It doesn't seem like CS theory 101 to me - maybe 201). I suppose that I'm not entirely sure what you mean by "use arbitrary precision numbers". TMs can use arbitrary precision numbers (integers and rationals) and they can't solve the halting problem, so you must mean something different. If what you say is true (I don't really know anything about transformers), then that reflects rather poorly on the field that such wrong results would end up being published.