Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

On the Navier–Stokes Millennium Prize Problem

openai.com

Post reply on HN
Print view View original

291–300 of 1001 posts

Re: On the Navier–Stokes Millennium Prize Problem

#291

Post by lambda »

tedsanders wrote: post #181
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…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

So, one way to prove that the data played no part is to trace and show that it wasn't used in the training process at all. If the data was never used in training, then it couldn't have played a part in the training process.

You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.

This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.

It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."

Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.

But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.

Re: On the Navier–Stokes Millennium Prize Problem

#293

Post by Kotlopou »

diomedes wrote: post #61

madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert

No idea about which is more likely, but I'm rooting for Yang-Mills. It's absurd that fundamental physics has formulated its most precise currently known theory way back in the seventies and since then, even a tiny subset of it can't be proven to be actually well-defined. If we got out of that morass then something good would come out of this at least.

Of course, as with all of those, it's about the broader program, e.g. section 7 here (https://www.scottaaronson.com/papers/npcomplete.pdf), where Scott Aaronson wants to ask about whether quantum computers using quantum field theory could gain any speed advantage over regular quantum computers, but can't even formulate the question because quantum field theory is mathematically ill-defined.

Just solving Yang-Mills because that's what the prize is attached to would be useless.

Re: On the Navier–Stokes Millennium Prize Problem

#294

Post by 20k »

ameliaquining wrote: post #266
20k wrote: post #234

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…

If you're alleging that they don't actually have a highly capable model and the work they're attributing to it was actually plagiarized from human mathematicians, well, that would be big if true, but I'd be inclined to take the other side of that bet. With most previous splashy AI results, others have subsequently used the model to do other things around the same difficulty level. Also, it would still be necessary to…

The issue is that if OpenAI is training on prompts generally, what we really have is the first fully automated luxury plagiarism machine. In that it isn't able to genuinely solve problems, but merely steal the work that other mathematicians have been putting into prompts, and regurgitating that to other users as its own work. That makes them incredibly less useful as research tools

The fact that this plagiarism scandal exists underpins the idea that there's actually a mass theft going on, and that these models aren't nearly as capable as is it would seem

Re: On the Navier–Stokes Millennium Prize Problem

#296

Post by kzrdude »

famouswaffles wrote: post #29
mapmeld wrote: post #18

> Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result. Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?

>Does OpenAI have a policy of not claiming math prizes like this Wouldn't be surprising if they did. The prize money isn't worth the almost certainly negative PR.

I don't see how it would be negative PR. If anything, the love these breakthroughs and use it in their PR campaigns.

Re: On the Navier–Stokes Millennium Prize Problem

#298

Post by denverllc »

mrbungie wrote: post #178
slibhb wrote: post #120

Earlier quoted context omitted.

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.

Of course AI was involved, you'd expect most mathematicians and researchers to use AI nowadays. This drama is about AI achieving impressive outcomes with little to no human intervention, as that would be signalling AGI.

> This drama is about AI achieving impressive outcomes with little to no human intervention

That's not at all what the drama is.

Re: On the Navier–Stokes Millennium Prize Problem

#299

Post by credit_guy »

naveen99 wrote: post #81
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.

Astra was trained more than two weeks ago.

The internal model they mention is different from Astra.

Re: On the Navier–Stokes Millennium Prize Problem

#300

Post by igleria »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

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 goal here was not to scoop any particular individuals and we were looking at many problems beyond these)

That is your opinion, but the optics of that should raise for you some flags. OAI could have waited (how long is a task left to the ethics committee) to see how the rumors panned out. Right now the optics look a lot like "we don´t care there is a 1/7 chance we one-up a human researcher by reacting to this rumor immediately, might makes right"

Post reply on HN