You are making a big assumption here, which is that LLMs are the main "algorithm" that the human brain uses. The human brain can easily be a Turing machine, that's "running" something that's not an LLM. If that's the case, we can say that the fact that humans can come up with novel concept does not imply that LLMs can do the same.

▲

vidarh a day ago | parent [-]

No, I am not assuming anything about the structure of the human brain.

The point of talking about Turing completeness is that any universal Turing machine can emulate any other (Turing equivalence). This is fundamental to the theory of computation.

And since we can easily show that both can be rigged up in ways that makes the system Turing complete, for humans to be "special", we would need to be able to be more than Turing complete.

There is no evidence to suggest we are, and no evidence to suggest that is even possible.

▲

Fargren a day ago | parent [-]

An LLM is not a universal Turing machine, though. It's a specific family of algorithms.

You can't build an LLM that will factorize arbitrarily large numbers, even in infinite time. But a Turing machine can.

▲

vidarh a day ago | parent [-]

To make a universal Turing machine out of an LLM only requires a loop and the ability to make a model that will look up a 2x3 matrix of operations based on context and output operations to the context on the basis of them (the smallest Turing machine has 2 states and 3 symbols or the inverse).

So, yes, you can.

Once you have a (2,3) Turing machine, you can from that build a model that models any larger Turing machine - it's just a question of allowing it enough computation and enough layers.

It is not guaranteed that any specific architecture can do it efficiently, but that is entirely besides the point.

	▲	Fargren a day ago \| parent \| next [-]
		LLMs cannot loop (unless you have a counterexample?), and I'm not even sure they can do a lookup in a table with 100% reliability. They also have finite context, while a Turing machine can have infinite state.
	▲	johnisgood a day ago \| parent \| prev [-]
		Are you saying that LLMs are Turing complete or did I misunderstand it?