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That is not how any of this works. This is not even close to why its hard to make a machine like that (and very much possible to do so, in theory).

The model does not produce statistically indistinguishable from human outputs, but the outputs that satisfy its training rewards system most strongly. Those are very different things. And the rest of the argument is less logically.

How would a machine capable of detecting that difference be usable to train a 'better' model? Only _if_ the goal was to make it indistinguishable from human, which it is not, the goal is to make it succeed at a set of training tasks! Tasks that in fact don't lead to it being all that human like.

And if we assume that was possible, and that such a detector could be used to train better models, which in turn would lead to better detectors, that would not break any laws of information theory of thermodynamics either! That would still require immersive amounts of compute!

And compute, famously, cost energy! Which is why this doesn't break thermodynamics. It also doesn't break information theory, because we already know what human text looks like, and are just extracting out the patterns that make it look like so via computation.

Also, the thing is that, a text or any other thing, that has all the average values of a large diverse population, is very strange! A text that is statistically closest to the overall dataset average of all human text, is not very human look at all!

One example is that you can analyze the usage of location specific slang or terminology. People have accents, and not just in their speech! As a result, with enough text, it is very much possible to specifically identify the author of something!

The thing that makes LLM detection hard now, is not some inherent impossibility, but the models tendencies to change this linguistic 'profile' based on user input. So if you throw a prompt at it, like 'write in x style' it will often adopt another, distinct 'voice.'

The actual technical question with LLM detection feasibility now is if those profiles share certain properties that human profiles do not. The answer is, probably yes for old models, and absolutely for most new ones, because AI labs intentionally fine tune them for it.