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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#771

Post by calf »

tedsanders wrote: post #623
Imnimo wrote: 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…

Your perspective is not helpful until you read and reflect on Tristan's letter stating serious grievances. Your remarks here have minimized his complaints and that is a sign of bias. Do not then pre-accuse HN commenters of being convinced when there reasonable skepticism such biased behavior showing itself in this very thread, saying things that amount to "my tribe/company would never be so egregious and if you think that then it is bad faith". That's the projection. If the word prejudice means anything to you then please do the work of attending to that instead of using the platform to reinforce such biases. If you are not a PhD yourself maybe your are not culturally qualified to assess and expound on the overall situation anyways.

Re: On the Navier–Stokes Millennium Prize Problem

#772

Post by mellosouls »

intenex wrote: post #439

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Here you go:

When you read the detail the compute they are throwing at it is incredible, tens of thousands of agents with different groups competing.

It's not like a single Gauss as you imply, "just" many, many mathematicians working tirelessly in a completely ego-less way, guided by other agents and ultimately humans, built - allegedly - on recent human insights.

Stunning, undoubtedly, but this is a "brilliant autistic herd" result, not that of a singular mind.

Re: On the Navier–Stokes Millennium Prize Problem

#773

Post by ImaCake »

trio8453 wrote: post #214
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…

> 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).

I am absolutely struggling to sell my workplace (which is entirely knowledge work) on the usefulness of LLMs for proofreading let alone on automation of hairy parts of our workflows. So yeah, even people who should be able to see what is coming are not looking.

Re: On the Navier–Stokes Millennium Prize Problem

#774

Post by kypro »

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 think OpenAI are correct that it's worth noting, but realistically any relevant usage data they have and used to improve their models would be very insignificant unless they were deliberately using logs from other researchers and training specifically on it (which they seem to deny).

The fact the proofs differ suggests that the models were not directed to be particularly focused on that avenue of research nor trained to converge in that direction.

I get the scepticism, but I feel some of the accusations here are bad faith.

Re: On the Navier–Stokes Millennium Prize Problem

#775

Post by bananzamba »

raincole wrote: post #86
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…

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. "People" are just misinformed and keep…

The accusation is that they stole his approach of solving it. If OpenAI didn't bruteforce it with dozens of agents, he would have solved Navier-Stokes eventually since he evidently had the right approach. So knowing which approach to take makes all the difference, if they didn't know the approach they couldn't have solved it.

It's like he had a treasure map and was about to find the treasure, but they copied his treasure map and scooped him with a faster boat and found the treasure first. But he would have found it if it weren't for them.

Re: On the Navier–Stokes Millennium Prize Problem

#776

Post by WarmWash »

nozzlegear wrote: post #765
jdm2212 wrote: post #726

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.

> It'd be corporate suicide for them to be caught violating zero-data-retention commitments. One would think getting caught asleep at the wheel while their bots are escaping containment and hacking third parties would be corporate suicide. One would think that potentially stealing their competitors' work on the Navier-Stokes problem would be corporate suicide. Alas we live in bizarro world where there are zero conseq…

Neither of those other two examples would stop corporations from giving you money. Bold faced lying to them would.

Boardrooms run businesses, not bookstore ethics clubs.

Re: On the Navier–Stokes Millennium Prize Problem

#777

Post by ImaCake »

elwell wrote: post #529
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?

Isn't this a proof that the usage data is truly "de-identified"? If OpenAI could prove that "their usage" influenced the finding, then it wouldn't be de-identified. (Also, it's a bit disingenuous to trim the "While unlikely," prefix.)

Yes. If they could prove where the de-identified data came from then it wouldn't be de-identified. There's a whole field of statistics dedicated to this problem and often applied to things like national census data.

Re: On the Navier–Stokes Millennium Prize Problem

#778

Post by noir_lord »

chilmers wrote: post #152
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.

The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/

Recursive self improvement of their upcoming IPO value maybe.

They are fluffy PR pieces otherwise.

Re: On the Navier–Stokes Millennium Prize Problem

#779

Post by calf »

semi-extrinsic wrote: post #707
sobellian wrote: post #668

Earlier quoted context omitted.

Whether or not ways exist to work around the singularities, that they exist is surely of note. Before von Neumann formalized QM people were still doing QM, okay fine. But it's wrong to then say von Neumann was doing no physics of note.

"Does there exist a pathological combination of smooth body forces and initial conditions for this set of PDEs, where singularities appear, which by the way is completely impossible to actually create in the real world unless you are a literal God?" is a question of math, not physics. This is a hill I will die on.

You realize that hill is a mathematical argument, not a physical hill.
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