CrushItNerds519

Nope.

If you were to consider carefully enough the language example that I gave, you would see that it already refutes your speculation.

Another way would be to apply your argument to humans, who have managed to be useful despite having been trained only on (a broader class of) semantics (i.e., the sum of all qualia) and the logical imperfections that this entails (cf. your comments).

Happy new year!

This comment and many others speculate on the limits of ChatGPT based on assumptions about what ChatGPT does that are not quite accurate. In particular, ChatGPT does not simply output the “most semantically popular result”. That description applies only to the base model, before instruction tuning and RLHF.

As for the speculation itself, e.g., “as soon as you merge two subjects, you are right back to gambling semantics as logic”, it may be suggestive to consider that such models have learned to translate between English and French after having only trained on the two languages separately.

There may be some linguistic benefits to the "epsilon" formulation when discussing subconvexity rather than Lindelof. For instance, I think "the output is eventually bounded by 24% of the input" sounds more natural than "the limsup of output/input approaches something less than 24%".

As you say, we now know that each standard L-function satisfies a subconvex estimate as its argument varies. This falls short of "solving the subconvexity problem" in two respects.

The first, pointed out already by gavagai691, is that it is not known that "every L-function" is "standard" (this is a major open problem in the Langlands program).

The second is that the general "subconvexity problem" asks for a nontrivial estimate not only for each fixed L-function as its argument varies, but more generally as the L-function itself varies. The general case of the problem remains open.