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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#951

Post by HarHarVeryFunny »

pama wrote: post #183
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.

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

With 10,000 agents and $20M of compute this is just brute force search.

It's a bit like telling 10,000 kids there's an easter egg hidden over there, pointing to one corner of your yard (or having "heard a rumor" it was hidden in that corner).

If you have $20M to spend on your problem, then yes, AI brute force search is an option, but unless you know a solution is possible (as OpenAI did here), you may still be wasting your money.

Re: On the Navier–Stokes Millennium Prize Problem

#952

Post by famouswaffles »

HarHarVeryFunny wrote: post #938
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.

If there is any truth to this timeline, then presumably it just means an additional 2 weeks of RL training on Astra. "Twice as capable in mathematics" just means they found some problems that Astra couldn't solve, or make progress on (who knows how they chose to define "capable", or "twice as" for that matter), then put those 2 weeks of training in to focus on those gaps. At this point, focused on their IPO, the best…

>If there is any truth to this timeline, then presumably it just means an additional 2 weeks of RL training on Astra

OpenAI finished a larger pre-train (rumors are it's the largest since GPT 4.5) in late August (not Astra). Presumably, this is post training on top of that since it lines up.

>They are not shy - if there was a more impressive claim they could make, they would have made it.

What claim would that be ?

Re: On the Navier–Stokes Millennium Prize Problem

#953

Post by lackoftactics »

user43928 wrote: post #565
20k wrote: post #233

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…

All that I have seen OpenAI employees "admit" is that if you press the Thumbs up button on a response, this can be used as a signal for training. That's it. The rest appears to be wild speculation.

do you even needs thumbs up? I've been long suspecting that code models get better because they use our data and our results from feedback, status codes, green tests for reinforcement learning

Re: On the Navier–Stokes Millennium Prize Problem

#954

Post by d_silin »

lbreakjai wrote: post #891
d_silin wrote: post #77

Earlier quoted context omitted.

...absolutely nothing will change short-term. Long-term, you still have to pay all the bills, but you won't be able to find a job (all taken by AIs).

Who is the AI doing the job for if no one is able to afford anything?

This is the question I don't have a satisfactory answer for. But neither does Sam and Dario.

Re: On the Navier–Stokes Millennium Prize Problem

#955

Post by Yizahi »

anthonypasq wrote: post #192
QuesnayJr wrote: post #158

Earlier quoted context omitted.

Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)

the goalposts are on Pluto at this point.

Is there any reference to a current goalpost position? Since you are claiming they had been moved, it's interesting from where exactly.

Re: On the Navier–Stokes Millennium Prize Problem

#956

Post by HarHarVeryFunny »

famouswaffles wrote: post #952
HarHarVeryFunny wrote: post #938

Earlier quoted context omitted.

If there is any truth to this timeline, then presumably it just means an additional 2 weeks of RL training on Astra. "Twice as capable in mathematics" just means they found some problems that Astra couldn't solve, or make progress on (who knows how they chose to define "capable", or "twice as" for that matter), then put those 2 weeks of training in to focus on those gaps. At this point, focused on their IPO, the best…

>If there is any truth to this timeline, then presumably it just means an additional 2 weeks of RL training on Astra OpenAI finished a larger pre-train (rumors are it's the largest since GPT 4.5) in late August (not Astra). Presumably, this is post training on top of that since it lines up. >They are not shy - if there was a more impressive claim they could make, they would have made it. What claim would that be ?

> What claim would that be ?

Huh? I'm saying there isn't one.

Re: On the Navier–Stokes Millennium Prize Problem

#957

Post by famouswaffles »

HarHarVeryFunny wrote: post #956
famouswaffles wrote: post #952

Earlier quoted context omitted.

>If there is any truth to this timeline, then presumably it just means an additional 2 weeks of RL training on Astra OpenAI finished a larger pre-train (rumors are it's the largest since GPT 4.5) in late August (not Astra). Presumably, this is post training on top of that since it lines up. >They are not shy - if there was a more impressive claim they could make, they would have made it. What claim would that be ?

> What claim would that be ? Huh? I'm saying there isn't one.

Okay. I was just confused.

Re: On the Navier–Stokes Millennium Prize Problem

#958

Post by redwood »

webcoon wrote: post #915

"Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens." At a conservative estimate of GPT 6 Astra pricing, this would have cost upwards of 15 Million dollars for anyone using the OpenAI API! To me this is the one silver lining. Yes, they can solve millennium prize problems, but it still costs a fortune.

The Millenium Prize awards are going to need to be raised!

Re: On the Navier–Stokes Millennium Prize Problem

#959

Post by peter_d_sherman »

>"The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics. The technical challenge is for the equations to develop the breakdown through the motion of the fluid itself, rather than, for example, us putting in an infinite force by hand. More mathematically, the terms in the Navier–Stokes equations that describe the motion—acceleration, pressure gradients, momentum transfer, viscosity—must both become big yet cancel in a precise way. This detailed balance leaves a smooth external force even as the velocity of the fluid grows without bound.

Diagram of a swirling vortex illustrating inward spiral and axial stretching. A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching."

Hmmm, isn't that interesting!

(Side note: Apparently we can't "compress" something, but apparently we can move more units of that thing over a specific space in a specific time... hmmm, I wonder what the difference between those two concepts could be...)

Main Observation: The image on OpenAI's web page above, looks sort of like the one for the Hopf Fibration:

https://en.wikipedia.org/wiki/Hopf_fibration

https://www.google.com/search?q=hopf+fibration&udm=2

Re: On the Navier–Stokes Millennium Prize Problem

#960

Post by brigandish »

Dlemlo wrote: post #930
noir_lord wrote: post #775

Earlier quoted context omitted.

Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.

I tried to build a procedural 3d asset pipeline for a specific use case. Before the Opus upgrade in November it was basically no way of doing this. I gave up very quickly. After November i tried again, and no model could build me anything relevant. Now it just works. Took me an hour to progress to a point were i'm happy. Whatever they do, progress is still real, still way faster than I assumed The list of Ubuntus 240…

What would being prepared look like? A house in the woods with a store of food? Knowing how to pick door locks and set up a militia in the desert?
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