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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#981

Earlier quoted context omitted.

The things you don’t care about are highly relevant to that claim

Elaborate?

If the model started from work that Tristan Buckmaster had already done, and was aided by an entire team of mathematicians as he alleged, then it's not as capable as you seem to be precluding

Re: On the Navier–Stokes Millennium Prize Problem

#982

Earlier quoted context omitted.

There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.

interesting, i haven't heard anything about that. i don't know much about the hodge conjecture, all i really know is that it's incredibly abstract and obtuse - not sure if that has any implication for solvability by an AI though. do you have any source for the hodge rumor? curious to learn more

So far it's just anonymous accounts on X and Reddit during the past few days, no "official leak" or anything like that. But the rumors about Navier-Stokes being solved started the same way. If somebody really solved it, the incentive is to come forward soon before being scooped by another team. We'll see.

Re: On the Navier–Stokes Millennium Prize Problem

#983
post #852

Earlier quoted context omitted.

We don't have any proof of that at all. Please stop rushing to judge without data.

> We don't have any proof of that It’s fair to give benefit of doubt to Buckmaster given OpenAI is currently being very credibly sued by Apple for openly stealing others’ original work in another context.

A prior of "one large company is current involved in an unrelated lawsuit with another large company" is pretty weak; the case is undecided and about an entirely different kind of IP theft.

In short I think a lot of people are jumping to conclusions without supporting evidence and that's really not helping the situation.

Re: On the Navier–Stokes Millennium Prize Problem

#984
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…

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Re: On the Navier–Stokes Millennium Prize Problem

#985

Earlier quoted context omitted.

It'd be corporate suicide for them to be caught violating zero-data-retention commitments. But also if you're really paranoid you can just use ChatGPT on Azure or AWS, where nothing is flowing back to OpenAI at all.

Zero data retention commitments? Technically generating synthetic data off of user data on the fly, counts as zero retention of user data! And it technically means they didn't lie either, because they didn't keep user data, they kept their own, synthetic data. That is what they already do with reasoning when they provide summaries/sanitized versions of it to prevent "distillation attacks" even via the API. They gener…

This is flatly false. ZDR means the customer request is processed and nothing about its content remains on the model provider's servers.

Re: On the Navier–Stokes Millennium Prize Problem

#987

Earlier quoted context omitted.

Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.

> OAI pushed a button and solved NS Not exactly... From here: https://cims.nyu.edu/~tristanb/statement.pdf "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 thei…

The evidence we have (not much) leaves the facts severely under-constrained. All the below are consistent with what we observe:

- OpenAI lying their face off for marketing purposes

- Buckmaster sore about getting beaten to NS, misrepresenting what was told

- Buckmaster not being an expert in ML, not understanding what he was told and hearing what he wanted to hear as it vindicated him

- Others...

OAI claimed that none of the people on their team were domain experts. So it's more akin to Deep Blue than Stockfish (actually slightly better than Deep Blue which did hire domain experts) but nevertheless represents a highly sophisticated automatic theorem prover.

Re: On the Navier–Stokes Millennium Prize Problem

#988
post #857

I've been working on this problem for what seems like for ever. Kudos to the OpenAI team. For those of you who don't care about the drama and want to see this distilled to 3 lines: https://x.com/nadermx/status/2097414953225310280

Any version with a bit more prose for a peasant like me to remotely pretend to grasp it

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Re: On the Navier–Stokes Millennium Prize Problem

#989

Earlier quoted context omitted.

Why is it unlikely?

Because the models are trained on hundreds of billions of user conversations, across more than a billion different humans. The conversations are anonymized and not easily traceable back to a specific user. It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes. We also don't know if the authors unintentionally provided data to OpenAI through alterna…

Not possible? You can remove all those conversations from training and see if it still solves the problem. That'll be expensive though.

Re: On the Navier–Stokes Millennium Prize Problem

#990

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…

Some millennium problems? Are there more coming?

Why would they stop trying?
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