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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 datsci_est_2015 »

hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

E.g. the concepts of “keystone species”, or even just the concept of a “species” in general is a lot more gray and continuous than something computationally tractable.

Re: On the Navier–Stokes Millennium Prize Problem

#952

Post by sensitivekt9q3 »

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/

Is it? The first article says they’re on-track to building an automated AI researcher by March 2028. So they haven’t achieved RSI yet, I would think?

Re: On the Navier–Stokes Millennium Prize Problem

#953

Post by wanderingpixel »

Aboutplants wrote: post #245
rfgplk wrote: post #107

Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at fronten…

So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “gene…

> I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster.

I'm curious how you intend to do that ?

Re: On the Navier–Stokes Millennium Prize Problem

#954

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

#955

Post by famouswaffles »

HarHarVeryFunny wrote: post #941
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

#956

Post by lackoftactics »

user43928 wrote: post #567
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

#957

Post by d_silin »

lbreakjai wrote: post #894
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

#958

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

#959

Post by HarHarVeryFunny »

famouswaffles wrote: post #955
HarHarVeryFunny wrote: post #941

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

#960

Post by famouswaffles »

HarHarVeryFunny wrote: post #959
famouswaffles wrote: post #955

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.
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