I think the underlying assumption is that there is (an invariant) structure and distribution that becomes more resolved (q) as more data is incorporated. Traini

I think the underlying assumption is that there is (an invariant) structure and distribution that becomes more resolved (q) as more data is incorporated. Training LLMs also involves sequences of tokens by design so that is also implicit. The only venue left is to question whether this (n -> q) is a linear relationship or something else. That would only matter if we were looking at absolute measure (to compare say an LLM architecture to something else), but as a comparative measure for LLMs it works, whether it is o(n) or o(logn) or whatever, since more tokens means more sequences and more sequences mean greater ability.