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.

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?