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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#681

Post by flir »

zem wrote: post #666
20k wrote: post #233

Earlier quoted context omitted.

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 mode…

even apart from the plagiarism issue, what sort of slimy company thinks "oh, here's someone using our models to work on a problem, let's throw more compute at it and scoop them"?

Training on prompts I can understand - that's kinda baked into the premise, and they've been explicit about it.

Publication, though? Slimy is right.

But the interesting question to me is: once they had a solution, what should they have done with it? I see two choices: bury it, or contact the mathematicians whose prompts they were listening in on.

Re: On the Navier–Stokes Millennium Prize Problem

#682

Post by futureshock »

I feel like something is being lost in the drama here.

First of all, there has been published work from Diego Cordoba and Luis Martinez-Zoroa that will be in every training set. It was suggestive of the pathway to solve Navier-Stokes.

Then Tristan Buckmaster and Levent Alpoge built on this work using LLMs from OpenAI and Anthropic. Possibly internal models were used from Anthropic. And of course Anthropic wants to credit for solving the first Millennium Problem just as bad as OpenAI. It seems they were getting close and were aware that they might get to Navier-Stokes.

OpenAI swoops in. At a minimum they are aware that Anthropic has either solved a Millennium problem or is close to it. At a maximum they may have Tristan and Levant’s unpublished proofs of related problems.

They then throw a truly staggering amount of compute at Navier-Stokes. They seem to be aware it is the best candidate problem. And they crack it. They are the first with a verified proof.

So the outcome here is that we have a solved Millennium Problem. It’s not the extremely simple narrative that would be easy to understand, “solve Navier-Stokes make no mistakes.” It was a messy race to finish against two unpublished frontier models, a whole bunch of brilliant mathematicians and enough compute to drain a lake. It’s kind of irrelevant which company got there first. They were both within a few months of being capable. I think the thing to remember here is that without LLMs, I don’t think we would have a proof to Navier-Stokes in hand today.

Re: On the Navier–Stokes Millennium Prize Problem

#683

Post by ccozan »

Bluestein wrote: post #441
mzhaase wrote: post #267

Earlier quoted context omitted.

The singularity happening under trump? We could have had star trek, instead we're getting the combine.

"I love Singularities. I am the best at Singularities. Everybody knows it ..."

Beautiful Singularities.

Re: On the Navier–Stokes Millennium Prize Problem

#684

Post by QuesnayJr »

matteoraso wrote: post #194

This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0] [0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.

I wouldn't call it "struggle", but it does seem better at proving "there exists" statements than proving "for all" statements.

Re: On the Navier–Stokes Millennium Prize Problem

#685

Post by mucha »

tedsanders wrote: post #623
Imnimo wrote: post #253

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…

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

Re: On the Navier–Stokes Millennium Prize Problem

#686

Post by swat535 »

biesnecker wrote: post #616
nerevarthelame wrote: post #587

Earlier quoted context omitted.

My employer would be rightfully outraged if I commented publicly on a sensitive, nuanced, and controversial issue like this based on my second-hand understanding of the matter.

I came here to say this, like... wow. I'm pretty sure at at least a few of the places I've worked that would be grounds for immediate termination.

They probably should have added the disclaimer: opinions are my own..

Re: On the Navier–Stokes Millennium Prize Problem

#687

Post by Lapra »

logancbrown wrote: post #418
20k wrote: post #310

Earlier quoted context omitted.

Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it Edit: OpenAI have now admitted they were training on prompts at the time they made their breakthrough: https://mastodon.social/@tristanbuckmaster/11723647135247030...

Steal someone elses work, whose work was also AI generated . . .

Whether that's relevant to the conversation depends on what their prompt was.

Re: On the Navier–Stokes Millennium Prize Problem

#688

Post by rybosworld »

In chess, a grandmaster just needs to know at what moment in a game there's a critical move to gain a significant advantage over their opponent. They don't need to know the move itself.

OpenAI got wind that a millenium problem was being solved. And that feels a bit like the critical move in chess. That is - it was a signal that AI advanced far enough that it would be worth spending a lot of time and resources solving a millenium problem.

Re: On the Navier–Stokes Millennium Prize Problem

#689

Post by nozzlegear »

Jtariiiii wrote: post #606
MichaelDickens wrote: post #540

Earlier quoted context omitted.

> But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. Just because something is legal and permitted by terms of service doesn't mean it's morally right.

>Just because something is legal and permitted by terms of service doesn't mean it's morally right. What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Are they supposed to manually review all their data to make sure competing mathematicians didn't accidentally leave the "submit prompts" toggle on? Or were they supposed to not try to so…

> What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data?

Personally, I would expect them to have a little class, to KYC, and to manually turn off training for known competitors using their service so as to avoid any unforced goofs like this.

Re: On the Navier–Stokes Millennium Prize Problem

#690

Post by whimsicalism »

tedsanders wrote: post #236
contemporary343 wrote: post #132

Earlier quoted context omitted.

"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…

I'm confused, your employer very directly stated that they are unable to confirm that the model was not trained on the conversations.
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