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Mathematical exploration and discovery at scale

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Re: Mathematical exploration and discovery at scale

#11

Post by tux3 »

nsoonhui wrote: post #8
qsort wrote: post #6

Earlier quoted context omitted.

I'm not claiming to be an expert, but more or less what the article says is this: - Context: Terence Tao is one of the best mathematician alive. - Context: AlphaEvolve is an optimization tool from Google. It differs from traditional tools because the search is guided by an LLM, whose job is to mutate a program written in a normal programming language (they used Python). Hallucinations are not a problem because the LL…

>> If the LLM fucks up, that branch is cut. Can you explain more on this? How on earth are we supposed to know LLM is hallucinating?

In this case AlphaEvolve doesn't write proofs, it uses the LLM to write Python code (or any language, really) that produces some numerical inputs to a problem.

They just try out the inputs on the problem they care about. If the code gives better results, they keep it around. They actually keep a few of the previous versions that worked well as inspiration for the LLM.

If the LLM is hallucinating nonsense, it will just produce broken code that gives horrible results, and that idea will be thrown away.

Re: Mathematical exploration and discovery at scale

#13

Post by qsort »

nsoonhui wrote: post #8
qsort wrote: post #6

Earlier quoted context omitted.

I'm not claiming to be an expert, but more or less what the article says is this: - Context: Terence Tao is one of the best mathematician alive. - Context: AlphaEvolve is an optimization tool from Google. It differs from traditional tools because the search is guided by an LLM, whose job is to mutate a program written in a normal programming language (they used Python). Hallucinations are not a problem because the LL…

>> If the LLM fucks up, that branch is cut. Can you explain more on this? How on earth are we supposed to know LLM is hallucinating?

We don't, but the point is that it's only one part of the entire system. If you have a (human-supplied) scoring function, then even completely random mutations can serve as a mechanism to optimize: you generate a bunch, keep the better ones according to the scoring function and repeat. That would be a very basic genetic algorithm.

The LLM serves to guide the search more "intelligently" so that mutations aren't actually random but can instead draw from what the LLM "knows".

Re: Mathematical exploration and discovery at scale

#15

Post by energy123 »

nsoonhui wrote: post #8
qsort wrote: post #6

Earlier quoted context omitted.

I'm not claiming to be an expert, but more or less what the article says is this: - Context: Terence Tao is one of the best mathematician alive. - Context: AlphaEvolve is an optimization tool from Google. It differs from traditional tools because the search is guided by an LLM, whose job is to mutate a program written in a normal programming language (they used Python). Hallucinations are not a problem because the LL…

>> If the LLM fucks up, that branch is cut. Can you explain more on this? How on earth are we supposed to know LLM is hallucinating?

Google's system is like any other optimizer, where you have a scoring function, and you keep altering the function's inputs to make the scoring function return a big number.

The difference here is the function's inputs are code instead of numbers, which makes LLMs useful because LLMs are good at altering code. So the LLM will try different candidate solutions, then Google's system will keep working on the good ones and throw away the bad ones (colloquially, "branch is cut").

Re: Mathematical exploration and discovery at scale

#16

Post by tornikeo »

I love this. I think of mathematics as writing programs but for brains. Not all programs are useful and to use AI for writing less useful programs would generally save humans our limited time. Maybe someday AI will help make even more impactful discoveries?

Exciting times!

Re: Mathematical exploration and discovery at scale

#18

Post by nl »

Hopefully this will finally stop the continuing claims[1] that LLMs can only solve problems they have seen before!

If you listen carefully to the people who build LLMs it is clear that post-training RL forces them to develop a world-model that goes well beyond a "fancy Markov chain" that some seem to believe. Next step is building similar capabilities on top of models like Genie 3[2]

[1] eg https://news.ycombinator.com/item?id=45769971#45771146

[2] https://deepmind.google/discover/blog/genie-3-a-new-frontier...

Re: Mathematical exploration and discovery at scale

#19

Post by mariusor »

nl wrote: post #18

Hopefully this will finally stop the continuing claims[1] that LLMs can only solve problems they have seen before! If you listen carefully to the people who build LLMs it is clear that post-training RL forces them to develop a world-model that goes well beyond a "fancy Markov chain" that some seem to believe. Next step is building similar capabilities on top of models like Genie 3[2] [1] eg https://news.ycombinator.c…

For the less mathematically inclined of us, what is in that discussion that qualifies as a problem that has not been seen before? (I don't mean this combatively, I'd like to have a more mundane explanation)

Re: Mathematical exploration and discovery at scale

#20

Post by SkiFire13 »

nsoonhui wrote: post #8
qsort wrote: post #6

Earlier quoted context omitted.

I'm not claiming to be an expert, but more or less what the article says is this: - Context: Terence Tao is one of the best mathematician alive. - Context: AlphaEvolve is an optimization tool from Google. It differs from traditional tools because the search is guided by an LLM, whose job is to mutate a program written in a normal programming language (they used Python). Hallucinations are not a problem because the LL…

>> If the LLM fucks up, that branch is cut. Can you explain more on this? How on earth are we supposed to know LLM is hallucinating?

The final evaluation is performed with a deterministic tool that's specialized for the current domain. It doesn't care that it's getting its input from a LLM that may be allucinating.

The catch however is that this approach can only be applied to areas where you can have such an automated verification tool.

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