> Language models with a loop absolutely aren't Turing complete.
They absolutely are. It's trivial to test and verify that you can tell one to act as a suitably small Turing machine and give it instructions to use to manipulate the conversation as "the tape".
Anything else would be absolutely astounding given how simple it is to implement a minimal 2-state 3-symbol Turing machine.
> Assuming the model can even follow your instructions the output is probabilistic so in the limit you can guarantee failure.
The output is deterministic if you set the temperature to zero, at which point it is absolutely trivial to verify the correct output for each of the possible states of a minimal Turing machine.
If you'd care to actually implement what you describe, I'm sure the resulting blog post would make a popular submission here.
It's not very interesting - it's basically showing it can run one step of a very trivial state machine , and then add a loop to let it keep running with the conversation acting as the tape io.
It's pretty hard to make any kind of complex system that can't be coerced into being Turing complete once you add iteration.