Comment by red75prime

As with all the works that use too broad a definition of an LLM they prove too much. This work defines an "LLM" as a computable function obtained by applying a finite number of steps of a generic algorithm to an initial computable function.

What they really prove is that it's impossible to extrapolate unconstrained non-continuous function from a finite subset of its values. Good for them, I guess.

It's like saying that the no free lunch theorems proves that LLMs can't be the best optimizers, while it proves (roughly) that the best optimizers don't exists. That is, even people aren't the best optimizers, but we manage somehow, so LLMs can too.