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@karolherbst You can probably fairly trivially show that you can construct a neural net that can accurately and deterministically advance the state machine of a cpu and keep track of memory at the same time. As for current LLMs, they may not be 100% accurate but I'd be suprised if the following wouldn't work:
send an asm snippet toghether with text encoding cpu state and memory and ask it to advanve that sate.
It can probably do it fairly reliably. And yeah may not be 100% reliable (though it might also be) but I wouldn't write it off as not being turing complete for that (just like real machines are susceptible to noise) as it has little relevance practically.

@karolherbst why? Think of the embedding space as the memory strip and attention/matrix multiplication in general as being able to index and compute a function on it to get the next state. the only thing you need is some feedback to make sure you can keep the computation going indefinitely (which LLMs have).

@karolherbst It doesn't take much to be turing complete and I'd be surprised if they weren't honestly.