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As far as I understand there's a parameter to make the output more "novel" (different/interesting/less predictable or generic) and that works by specifically not using the highest probability.

I suspect the probability of a statement being false (a confabulation) is unrelated to the probabilities of the words and grammar making up the statement.

That's certainly possible, but I'd want to hear from someone who'd actually tried it before dismissing the concept.

That's a pretty good idea, actually. It'll be a bitch and a half to tune the threshold so it's reliable, and doesn't mark normally generated text though.