Comment by hodgehog11
18 hours ago
This argument, that LLMs can develop new crazy strategies using RLVR on math problems (like what happened with Chess), turns out to be false without a serious paradigm shift. Essentially, the search space is far too large, and the model will need help to explore better, probably with human feedback.
The search space for the game of Go was also thought to be too large for computers to manage.
It still is [1].
[1] https://www.vice.com/en/article/a-human-amateur-beat-a-top-g...
The blind spot exploiting strategy you link to was found by an adverserial ML model...
Yes and making a horse drawn cart drive itself was thought to be impossible so why don't we have faster than light travel yet...
Yes but "the search space is too large" is something that has been said about innumerable AI-problems that were then solved. So it's not unreasonable that one doubts the merit of the statement when it's said for the umpteenth time.
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I agree that LLMs are a bad fit for mathematical reasoning, but it's very hard for me to buy that humans are a better fit than a computational approach. Search will always beat our intuition.
Yes and no. I think we have vastly underestimated the extent of the search space for math problems. I also think we underestimate the degree to which our worldview influences the directions with which we attempt proofs. Problems are derived from constructions that we can relate to, often physically. Consequently, the technique in the solution often involves a construction that is similarly physical in its form. I think measure theory is a prime example of this, and it effectively unlocked solutions to a lot of long-standing statistical problems.