And even if it were a justifiable analogy for LLMs, it does not follow that it applies to Turing-equivalent devices in general. A hash table is unequivocally not a Turing-equivalent device, even though it can be implemented by one.
In fact, the more one argues that LLMs are ordinary technology, the greater the challenge they present to the notion that things like conversational language use are beyond such technologies. The most interesting thing about these models, in my opinion, lies in figuring out what their conceptual simplicity says about us.
LLMs do not just return a probability distribution (and their prompts are not questions about probability distributions.) It would be a category error to conflate something that is part of how they work for the totality of what they do.
When you say "GPT, for all its clever responses, could be replaced with that hashtable with no loss of fidelity", where does one get all the prompts that will be given to it, in advance? A hash table does not respond to any input for which it has not already been given a response to return.
By exhaustive enumeration.
I never said it was going to be quick
Update: it is a significant difference that you don't have to do that with an LLM.
That hashtable would be ridiculously larger than the weighted model that constitutes GPT itself. But it at least theoretically could exist.
GPT, for all its clever responses, could be replaced with that hashtable with no loss of fidelity. So it is not ‘better’ than a hashtable.
It is much better than a hashtable of equivalent size.