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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#931

Post by recursivecaveat »

tristanj wrote: post #770
biophysboy wrote: post #109

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…

Anonymized doesn't mean there's no way to know whether it is in there. My ballot is anonymized, but it's known to be in the box because a checkmark was put next to my name when my ID was verified. OpenAI can trivially check their account settings to know what happened to their chats. The fact that they are being vague about this likely indicates that they have already done so and discovered that the data did go into the training set.

Further, given that this is all in the open now, they can search the training data. No way somebody is using some specific unique cutting edge mathematical approach to solve a fluid dynamic problem 99.9% of people have never heard of and it's not locatable. Considering they spent $15,000,000 already on this, they could afford to grep around to be able to state that their hands are clean.

Re: On the Navier–Stokes Millennium Prize Problem

#932

Post by alansaber »

nullbio wrote: post #894
mewse-hn wrote: post #78

"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?

I've been saying it for a while now, but no one gives a fuck. Let me repeat it again. THE BIG LABS CLEAN ROOM YOUR DATA (CREATE SYNTHETIC DATASETS ON IT), EVEN IF YOU OPT OUT, SO THEY CAN BYPASS COPYRIGHT LAWS AND THEIR OWN LOOSELY WORDED TERMS OF SERVICE. "TOS: We don't train on your data" -> Correct. They train on the synthetic version of your data. I guess we're just going to ignore this forever though. Who cares…

For sure. Even if it wasn't a measure to avoid copyright, you pre-process LLM training data to remove errors, characters that can't be tokenized, etc etc. Doing so with another LLM has been standard for a while.

Re: On the Navier–Stokes Millennium Prize Problem

#933

Post by Kotlopou »

Kotlopou wrote: post #758
rybosworld wrote: post #691

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…

Elsewhere in this thread somebody claimed that at some point OpenAI pointed their new model at all the millennium problems and this is where they got some progress. We probably won't see proof of this, but it seems plausible to me -- I assume there's a list of problems that each new model is tested on, and you might as well put the big stuff on the list, if only to see how the model behaves when faced with a problem…

Okay, from the actual linked article it seems that their partial result was finding blowup in Euler equations, which seems pretty big. I wonder how the other attempts went. Did they get nothing at all, or something true but unimpressive?

Re: On the Navier–Stokes Millennium Prize Problem

#934

Post by carlailab2025 »

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.

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#935

Post by pickleRick243 »

throwaway81ag81 wrote: post #827
jampekka wrote: post #448

Earlier quoted context omitted.

> WOW This. I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still. If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.

I dislike both AI oligarchs as much as people who do this kind of deflection. People are not complaining about problems being solved or advancement in technology. They are complaining about terrible people doing terrible things.

I think the point is that one of the biggest problems in the field has been solved and yet the excitement from this is nearly nil. Can you imagine if say breast cancer were cured under similar circumstances, or even worse (say OpenAI openly admitting it basically stole a bunch of other researcher's chatGPT conversations)? No one would care about these petty bickerings- or at least the headline "CURE FOR BREAST CANCER FOUND" would completely swamp anything else. This is embarrassing: it tells you almost no one- not even mathematicians themselves really care about their own problems- if they're not careful people will get the impression it's all a form of bean counting in a carefully constructed "safe space" where making sure people get the credit is more important than the work itself. That only happens in fields/problems where no one actually really cares about the output.

Re: On the Navier–Stokes Millennium Prize Problem

#936

Post by Mr_Minderbinder »

WarmWash wrote: post #230
simianwords wrote: post #136

Earlier quoted context omitted.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief t…

Will history look back at comments like these as people being dumb, or people trying to cope?

The present looks back at such comments made in the past in that manner.

Re: On the Navier–Stokes Millennium Prize Problem

#937

Post by shaky-carrousel »

jdm2212 wrote: post #731
nozzlegear wrote: post #675

Earlier quoted context omitted.

> If you need privacy, then you are going to have to pay full price for those tokens (API). At this point, how can we even trust that they aren't accidentally training on those tokens too?

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.

Not long ago it'd have been corporate suicide being caught massively torrenting pirated media. Yet here we are.

Re: On the Navier–Stokes Millennium Prize Problem

#938

Post by pama »

topaz0 wrote: post #849
pama wrote: post #183

Earlier quoted context omitted.

Not only that, but it used 10k agents coherently over 88 hours to come up with the proof. This is a significant advance.

What makes you think they were coherent?

They managed to solve a problem that was beyond current human ability.

Re: On the Navier–Stokes Millennium Prize Problem

#939

Post by 0xDEAFBEAD »

root_axis wrote: post #455
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…

It's incredible to me that every single time there's a new model people scream "singularity" from the rooftops and every time they are wrong. This is an impressive result, but there is absolutely zero evidence of "the singularity".

I suggest this article as background reading, "Losing control of AI is actually the plan"

https://substack.com/home/post/p-214653853

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