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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#231

Post by fn-mote »

tedsanders wrote: post #181
lambda wrote: post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

[flagged]

Re: On the Navier–Stokes Millennium Prize Problem

#233

Post by 20k »

ameliaquining wrote: post #220
magicalist wrote: post #160

Earlier quoted context omitted.

> Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra. Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?

I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.

It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model

What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question

If OpenAI is training models on researchers' prompts, and then threatening them into staying quiet about it, who knows if anything that's been announced is genuine - or just theft?

Edit:

OpenAI have admitted they were training on prompts at the time they made their breakthrough

https://mastodon.social/@tristanbuckmaster/11723647135247030...

Re: On the Navier–Stokes Millennium Prize Problem

#234

Post by pbhjpbhj »

rfgplk wrote: post #156
lambda wrote: post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

> Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else. At OpenAI's scale their entire pipeline is likel…

Aye, but do they train on user data in these circumstances or not? If they do, then almost certainly the model was influenced by the input of the allegedly plagiarised material.

Re: On the Navier–Stokes Millennium Prize Problem

#236

Post by tedsanders »

contemporary343 wrote: post #132
tedsanders wrote: post #41

Earlier quoted context omitted.

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a num…

All of those statements sound true, based on what I've heard.

- "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input

- it's all true that a team worked on this, a bunch of compute was burned, and the problem was solved in stages and pieces

I'm not sure how any of this provides evidence that OpenAI took any of their work.

As evidence against, we never looked at any of their ChatGPT conversations and our model's proof is quite different from theirs.

(I work at OpenAI, but not on the team that did this proof.)

Re: On the Navier–Stokes Millennium Prize Problem

#237

Post by blake__dev »

arctic-true wrote: post #35

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Yeah I'm surprised they posted a chart, you would think they would keep specifics like that hidden until they're closer to launch

Re: On the Navier–Stokes Millennium Prize Problem

#238

Post by Kotlopou »

For now I think more or less the same thing as with all recent math announcements: This is in a range where human work still exists (see Terry Tao, (1)). I wonder whether the trend will extend into the problems that (as far as I can tell) are considered complete brick walls right now -- P vs. NP, Collatz, Goldbach, odd perfect numbers, problems that aren't part of any research program. (2) In other words, is the progress coming from putting together vast amounts of existing work and computational power, or is it more from RLVR and self-play and autonomous effort?

The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true?

A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today".

---

(1) https://mathstodon.xyz/@tao/117207849921390904

(2) I'm not sure whether this is a hard distinction -- e.g. Tao also has some partial results towards Collatz (https://terrytao.wordpress.com/2019/09/10/almost-all-collatz...).

(3) https://scottaaronson.blog/?p=690

Re: On the Navier–Stokes Millennium Prize Problem

#239

Post by liberian »

slibhb wrote: post #120
dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#240

Post by QuesnayJr »

cv5005 wrote: post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

Someone has to actually check this. I'm guessing OpenAI had someone check it internally, but it's possible to get it wrong.
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