I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.
Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLMs similarly. It is just fancy autocomplete, but look what we can do with it!
Said differently, what is prediction but composition projected forward through time/ideas?
I'm not sure what the point of this exercise is. My prompt to ChatGPT: "Create a new English word with a reasonably sounding definition. That word must not come up in a Google search." Two attempts did come up in a search, the third was "Thaleniq (noun)". Definition: The brief feeling that a conversation has permanently changed your opinion of someone, even if nothing dramatic was said. Nothing in Google. There, a new word, not sure it proves or disproves anything. Or is it time to move the goal posts?
Definition: That highly specific, short-lived burst of nervous energy that makes you accidentally drop a small object (like a pen, a guitar pick, or a piece of LEGO) immediately after picking it up.
"Predicting the next token" is meaningless. Every process that has any sort of behavior, including a human writing, can be modeled by some function from past behavior to probability distribution of next action. Viewed this way, literally everything is just "predicting" the next action to be taken according to that probability distribution.
The most likely series of next tokens when a competent mathematician has written half of a correct proof is the correct next half of the proof. I've never seen anyone who claims "LLMs just predict the next token" give any definition of what that means that would include LLMs, but exclude the mathematician.
Nice smug attitude, but LLMs fall flat on their face over and over and over again at tasks no human would fail. They can't even reason out things that literal children succeed at. It's ludicrous to claim that they have some kind of reasoning ability.
> It's ludicrous to claim that they have some kind of reasoning ability.
Did you read the post that you're commenting on?
It seems wholly believable to me that they are narrow intelligences that are great at some kinds of reasoning and worse at other kinds. Obviously they can reason through problems that most adult humans can't solve
Said differently, what is prediction but composition projected forward through time/ideas?