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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#411

For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915 Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees

And even this version contains the line

> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .

Re: On the Navier–Stokes Millennium Prize Problem

#412

Earlier quoted context omitted.

Had no idea this was what lean looked like- that's mind blowing. I'm not even sure how someone would critique this if they wanted to

The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true. It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.

Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.

Re: On the Navier–Stokes Millennium Prize Problem

#413
post #119

OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.

> they trained the model on the prompts of the other mathematicians they were competing with

How would they have gotten that mathematician's progress though? Did that guy also use OpenAI?

If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.

Re: On the Navier–Stokes Millennium Prize Problem

#414
post #173
post #58

Earlier quoted context omitted.

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . That’s a bizarre statement. Their website says: > Services for individuals, such as ChatGPT and Codex > When you use our services for individuals such as ChatGPT and Codex, we may use your content to train our models. > You can opt out of training through our privacy portal by clicking on…

Do we have a first-hand confirmation that Buckmaster and/or Alpoge opted out? At this point it seems important information.

Re: On the Navier–Stokes Millennium Prize Problem

#415

Earlier quoted context omitted.

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

Could they say they don't retain, but do something "transformative" like use their own AI to summarize and paraphrase user sessions?

Re: On the Navier–Stokes Millennium Prize Problem

#416

the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side. https://x.com/rynorhn/status/2097223532438487463

The researchers are pretty directly accusing OpenAI of plagiarism

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

Re: On the Navier–Stokes Millennium Prize Problem

#417
post #58

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

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

You selected "do not train on my prompts" in your settings, the answer from OpenAI cannot be "While unlikely, we cannot rule out..." ???? What am I missing?

Re: On the Navier–Stokes Millennium Prize Problem

#418
post #310
post #52

People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.

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 . . .

Re: On the Navier–Stokes Millennium Prize Problem

#420
post #351

Earlier quoted context omitted.

Playing the devil's advocate here but it's true that OpenAI didn't have to make those offers.

They kind of did though, they were hoping to keep the fact that they may well have plagiarised these researchers unpublished work quiet. They did not want this to turn into a scandal about the fact that they appear to be training on prompts without consent It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people fee…

OpenAI claims the data contamination issue only surfaced after they proactively reached out to Buckmaster and Alpöge to coordinate a joint release. They also say that even if there was some contamination, the underlying proofs diverge substantially:

> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.

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