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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#581

Post by madrox »

dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

Statements from OpenAI about it:

https://x.com/SebastienBubeck/status/2097379411691516310

https://x.com/sama/status/2097385167002415140

I tend to believe OpenAI on this. Their stated desires seem rational, and Buckmaster's account makes them sound like cartoon villains. It sounds like there may have been some things lost in translation along with some bruised egos. Seems like the most plausible explanation for what Buckmaster is claiming.

Re: On the Navier–Stokes Millennium Prize Problem

#584

Post by dfdydx »

keeda wrote: post #559
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…

At the scale at which these models are now, regardless of whether they are proprietary or open weight or list their training datasets, there are hundreds of billions of works that have gone into trillions of parameters, each one providing tiny perturbations in some tiny fraction of the weights. It is probably impossible to attribute provenance to any specific input (which is also why the courts' finding of Fair Use i…

There are two different things:

- was item X in the training data

- did the inclusion of X in the training data lead to Y

I understand why the second is hard, but why is the first one hard?

Re: On the Navier–Stokes Millennium Prize Problem

#585

Post by anon109 »

jijijijij wrote: post #485
DudleyBluffles wrote: post #436

Not a great time to be starting sophmore year in cs & math. Should I just say fuck it, and go hitchhiking across Europe with some friends?

> Should I just say fuck it, and go hitchhiking across Europe with some friends? Yes. Assuming you are young and haven't had such experience. The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career persp…

Have you people gone insane?

Re: On the Navier–Stokes Millennium Prize Problem

#587

Post by nerevarthelame »

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…

My employer would be rightfully outraged if I commented publicly on a sensitive, nuanced, and controversial issue like this based on my second-hand understanding of the matter.

Re: On the Navier–Stokes Millennium Prize Problem

#589

Post by tristanj »

thomascountz wrote: post #572

At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. Maybe just don't mention that bit, OpenAI.

They have to, otherwise people will accuse the OpenAI model of hacking into people's chat logs and stealing the data there. Which is a claim people are already making.

Re: On the Navier–Stokes Millennium Prize Problem

#590

Post by danielmarkbruce »

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.

With Lean, math has become a really well suited problem for LLMs. We will likely see large gains for many years from here, just doing more and more rlvr, like continuously, non stop. No need to train from scratch. It really doesn't speak to the general intelligence of models though. It does speak to how good these things can become when a problem space has verifiable rewards, especially when you can verify one step at a time like Lean enables.
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