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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#731

Post by Kotlopou »

HDThoreaun wrote: post #640
Kotlopou wrote: post #386

Earlier quoted context omitted.

Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490 But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904 We will have to see whether any other millennium problems fall. I guess that in a year th…

Nuts that Tao literally predicted the exact strategy openAI seems to have used not even a week ago

Since he wrote this five days ago, when these efforts were already underway, if he was not Terence Tao I would suspect he had inside access. But since he said he did not and was speaking hypothetically, and he seems to be an honest person as far as I can judge, I guess some people are just on another level.

Re: On the Navier–Stokes Millennium Prize Problem

#734

Post by olalonde »

hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

> I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.

This is sort of what OpenAI was supposed to be. I'll never understand how it was legal for them to turn it into a for profit corporation.

Re: On the Navier–Stokes Millennium Prize Problem

#735

Post by qlte »

bibimsz wrote: post #315
armchairhacker wrote: post #216

Earlier quoted context omitted.

Let's wait until AI solves a longstanding practical problem before "dawn of the singularity" (which could be tomorrow, but still).

feels like moving the goalpost. is the achievement impressive or isn't it?

The question being posed isn't whether AI is impressive but whether we're at the "dawn of the singularity"

Re: On the Navier–Stokes Millennium Prize Problem

#736

Post by sebzim4500 »

mucha wrote: post #686
tedsanders wrote: post #624

Earlier quoted context omitted.

If they opted out of training, then we definitely did not train on them. If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof. Reasons for my doubt: - I know…

That's not what your Chief Research Officer, Mark Chen, says on X: "Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company." https://x.com/markchen90/status/2097400166554993041

Can you explain what part of his post you believe is inconsistent with that quote?

Re: On the Navier–Stokes Millennium Prize Problem

#737

Post by hansvm »

intenex wrote: post #440

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Not a counterpoint per se, but I burned $50k recently on a much more modest math problem (result already known, just thought I had a sketch of a more interesting proof), and the LLM thought it had proved it within those bounds but had instead subtly fucked up the Lean definition. Take from that what you will.

Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or sniped the important details from the researchers it was spying on.

Re: On the Navier–Stokes Millennium Prize Problem

#738

Post by HarHarVeryFunny »

technotony wrote: post #653
HarHarVeryFunny wrote: post #600

Earlier quoted context omitted.

Yes there is - that OpenAI PR says that it was Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU.

They appear to have solved sub-problems (Euler problem) not this one...

The NYU professor, Tristan Buckmaster, has now released a statement on this.

https://cims.nyu.edu/~tristanb/statement.pdf

Re: On the Navier–Stokes Millennium Prize Problem

#739

Post by sebzim4500 »

caughtinthought wrote: post #721
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…

The fact that you're even here commenting on this is... a choice

AI companies seem much more relaxed than most about their employees posting on twitter/HN about this stuff. I'm not sure if it's about building hype or if it's about retaining talent. Probably both.

Re: On the Navier–Stokes Millennium Prize Problem

#740

Post by Imnimo »

tedsanders wrote: post #624
Imnimo wrote: post #254

Earlier quoted context omitted.

>we did not read any private chats The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?

If they opted out of training, then we definitely did not train on them. If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof. Reasons for my doubt: - I know…

I don't think you'd lie about it, I don't think you'd train on them if they opted out, and it seems very plausible that this wouldn't have been decisive in whether the model could solve the problem. That said, it also seems at least possible that a key idea or a particular step found its way into training data. It wouldn't mean OpenAI stole their proof - clearly the model developed its own approach.

Either way, it seems worth having clarity, and I'm a bit surprised OpenAI's stance is just "we can't rule this out, but don't worry about it". OpenAI is, apparently, very happy to use unreleased models to try to scoop big results if they get a whiff that someone else is close (which strikes me as pretty scummy regardless of any issues of training contamination). It seems like people who might want to use OpenAI's models as part of their research would want to be very clear about whether doing so can make them, even in principle, more likely to fall victim to this.

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