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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#151

Post by pred_ »

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…

> we did not read any private chats

Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically.

But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then making fun of them on social media? Does the entire company run on that toxic culture, or did those people run off of some kind of outrageous tangent?

Re: On the Navier–Stokes Millennium Prize Problem

#152

Post by chilmers »

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/

Re: On the Navier–Stokes Millennium Prize Problem

#153

Post by thorum »

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

It reminds me of the Cognitive Dark Forest hypotheses recently shared here:

> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you. So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”

https://ryelang.org/blog/posts/cognitive-dark-forest/

https://news.ycombinator.com/item?id=47566442

Re: On the Navier–Stokes Millennium Prize Problem

#154

Post by Betelbuddy »

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

[1] - https://cims.nyu.edu/%7Etristanb/statement.pdf

[1] - "...I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used. I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers.

I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”..."

Re: On the Navier–Stokes Millennium Prize Problem

#155

Post by jsw97 »

railgunmerlin wrote: post #25

Does seem like they gloss over Alpöge and Buckmaster's work with the following > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Which seems a bit irresponsible/rash?

Would that be more or less unlikely than accidentally hacking another company? More or less unlikely than colonizing an obscure wiki?

Highly persistent agents + vibe-coded security seems like a problem.

Re: On the Navier–Stokes Millennium Prize Problem

#156

Post by rfgplk »

lambda wrote: post #130
peri-cl wrote: post #58

Earlier quoted context omitted.

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

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…

> Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data?

Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else.

At OpenAI's scale their entire pipeline is likely 100% automated.

Re: On the Navier–Stokes Millennium Prize Problem

#158

Post by QuesnayJr »

jrflo wrote: post #111
chinathrow wrote: post #82

Earlier quoted context omitted.

Pre-IPO marketing?

I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?

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.)

Re: On the Navier–Stokes Millennium Prize Problem

#159

Post by sheafification »

recitedropper wrote: post #10

Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..

I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.

Re: On the Navier–Stokes Millennium Prize Problem

#160

Post by magicalist »

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.

> 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.

Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?

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