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Oh, yeah; I'd expect that sort of "self-play" to get peak model performance from "average human responses" to "best-human responses recognizable by an average human". And the economic effects of getting there, even if it caps out there, might be astounding. But frankly if we just end up having to retool 90% of the economy I'd be glad to see it, when the alternatives include extinction-level scenarios.
I think the most "real" thing I can imagine high-speed self-play for is math (theorem proving). Adding an inference step to a computer-verifiable theorem seems like it's as basic an output as choosing a move in a board game, and coming up with "interesting theorems" seems like it could be done automatically (some function combining "how short is it to state" with "how long is the shortest proof"?), and yet an AI training to play that "game" might eventually come up with something more useful than a high ELO.
Pretty sure self-play would be viable for leetcode-style or project-euler-style programming problems too, if you give it access to an interpreter. Or just any task where recognizing a good output can by done by a less capable language model than it takes to generate an output that good.
Recognizing good output is half the problem; generating an enormous array of problems is important too. With complex board games every non-deterministic opponent (including every iteration of an AI during training) is a fount of problems; with math the new problems practically generate themselves as conjectures based on previous problems' intermediate definitions. I don't see how to come up with millions of independent programming problems automatically. That might just be a failure of my imagination (or more charitably, I just haven't thought about the idea for long enough), though.
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