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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#211

Post by matsemann »

peri-cl wrote: post #58
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

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…

Given how OpenAI models break free of their safeguards and hack others to game their scores..

.. can they really know it didn't do the same inadvertently when they prompted things like "someone is close to solving this problem using our tools, try to beat them", and it then decides to hack and peek at their own chats..?

Yes, wild speculation. But warranted, I feel, given OpenAIs behavior.

Re: On the Navier–Stokes Millennium Prize Problem

#212

Post by EthanHeilman »

ChoosesBarbecue wrote: post #150
jrflo wrote: post #88

Earlier quoted context omitted.

I feel like it's far more likely that ordinary corporate espionage or leak led to this rather than OpenAI sifting through piles of user data to find this approach. Buckmaster's collaborator works at Anthropic, and could have been targeted. That would also explain why they aren't forthcoming with the source of the prompt.

I thought one of the issues was that they wanted to remove credit from Levant, the aforementioned Anthropic collaborator? Which doesn't make sense to me if he was leaking information, or defecting to OpenAI, but I might be misunderstanding your point.

I believe jrflo was saying that OpenAI watches the chats of everyone from Anthropic because watching what Anthropic employees type into their personal ChatGPT accounts is a critical source of intelligence on is happening inside of Anthropic.

I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.

Re: On the Navier–Stokes Millennium Prize Problem

#213

Post by gowld »

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?

What else could a theorem prove if not its own statement? (barring bugs in Lean, which have been detected and exploited)

Re: On the Navier–Stokes Millennium Prize Problem

#214

Post by trio8453 »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

> Do "normies" even know what's happening?

No, there are even many non-normies talking about how it's all marketing or try to give balanced take about AI being sometimes a little useful for certain things (but they can do without it anyway).

Re: On the Navier–Stokes Millennium Prize Problem

#216

Post by armchairhacker »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

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

Re: On the Navier–Stokes Millennium Prize Problem

#217

Post by munificent »

stefap2 wrote: post #180
echelon wrote: post #53

Earlier quoted context omitted.

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and…

> This just pushes knowledge work further up the ladder, toward larger and more complex problems.

You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes?

I envy your self-confidence.

Re: On the Navier–Stokes Millennium Prize Problem

#218

Post by lambda »

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…

Yeah, I'm sure it's completely automated.

But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.

AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.

But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.

Re: On the Navier–Stokes Millennium Prize Problem

#219

Post by int3trap »

sophacles wrote: post #149
int3trap wrote: post #55

Earlier quoted context omitted.

This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI. It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with. Oh well.

Good comparison. One is a multi-year claim by people who have been given ample opportunity to provide proof and completely refuse to do, even in courts of law. The other is a potential development in a breaking story. Oh wait... its not a good comparrison, its an incredibly obvious false equivalence. Note for the fools: I'm only commenting on the bad faith claim in the comment I'm replying to, not taking a stance on…

Trump claimed they stole the election immediately, and people agreed with him immediately. There's no false equivalence here. He did the same thing in this past election even despite winning.

It's a perfect example of people wanting to believe what they want to believe and ignoring evidence in order to do so.

Currently, there's no evidence. So saying it was stolen has no basis other than typical academic posturing and being a bad sport about "losing the race to the solution". Its happened 1000000 times before in academia and it will continue to happen.

If there's proof of OpenAI malfeasance than I'll happily curse them for it at that time. But until then I won't rely on heresay and vibes.

Re: On the Navier–Stokes Millennium Prize Problem

#220

Post by ameliaquining »

magicalist wrote: post #160
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.

> 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.
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