> The function being approximated in an LLM is the mental process required to write like a human.
Quibble: That can be read as "it's approximating the process humans use to make data", which I think is a bit reaching compared to "it's approximating the data humans emit... using its own process which might turn out to be extremely alien."
Good point.
Then again, whatever process we're using, evolution found it in the solution space, using even more constrained search than we did, in that every intermediary step had to be non-negative on the margin in terms of organism survival. Yet find it did, so one has to wonder: if it was so easy for a blind, greedy optimizer to random-walk into human intelligence, perhaps there are attractors in this solution space. If that's the case, then LLMs may be approximating more than merely outcomes - perhaps the process, too.