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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#531

Post by sebzim4500 »

apical_dendrite wrote: post #270
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > 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…

Their own tweets are also pretty eyebrow-raising: > One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Why would you offer another researcher the lead authorship on your g…

IIRC that happened with evolution. In the initial presentation of Darwin and Wallace's work on evolution (presented with their consent by someone else) Wallace was described as the primary author since he was planning to publish first.

Of course, no one understood that presentation so it was Darwin's later book that everyone remembers

Re: On the Navier–Stokes Millennium Prize Problem

#532

Post by piker »

"... The point remains that there is a substantial opportunity cost in converting a historically productive and motivating problem (such as Navier-Stokes regularity) into a mere viral social media post advertising some benchmark progress, rather than actually advancing the field and developing the next generation of both problems to ask, and people to work on them."

https://mathstodon.xyz/@tao/117219101339291693

Re: On the Navier–Stokes Millennium Prize Problem

#534

Post by fkarakurt3 »

hkmaxpro wrote: post #303
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > 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…

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

They are missing a great marketing stunt: "Our models are so good that our competitors are using it for leading research".

Re: On the Navier–Stokes Millennium Prize Problem

#535

Post by 20k »

simianwords wrote: post #425
20k wrote: post #310

Earlier quoted context omitted.

Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it Edit: OpenAI have now admitted they were training on prompts at the time they made their breakthrough: https://mastodon.social/@tristanbuckmaster/11723647135247030...

what's there to admit? they always said they do it and there's a way to opt out. you are making it sound more dramatic than it is.

This is textbook plagiarism, scooping their result knowing that the research was part of the training data

Re: On the Navier–Stokes Millennium Prize Problem

#536

Post by professoretc »

rfgplk wrote: post #138
imbusy111 wrote: post #83

Earlier quoted context omitted.

I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.

Skill issue. Also lean is meant to be executed, not read.

A proof is not like a program. The goal of a program is to "do the thing", thus you can make the argument that it doesn't matter what the code looks like as long as its works right. But the goal of a proof isn't to "do the thing" (where "the thing" is just to print Yes or No), it's to communicate. An unintelligible proof is really just a first draft.

Re: On the Navier–Stokes Millennium Prize Problem

#537

Post by hgoel »

10xDev wrote: post #190
chilmers wrote: post #152

Earlier quoted context omitted.

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/

Compute will always be the bottleneck even if this were true.

As a statement of fact divorced from context, this is of course true, but it's worth putting it in context of what small-medium scale models have been achieving recently. Many of the most recent releases from Chinese labs are almost on par with trillion parameter models from less than a year ago (edit: despite being small enough to usably run on prosumer hardware). It seems clear parameter efficiency can still be improved dramatically.

In which case, maybe we don't need as much compute as we might expect. I hesitate to say "to reach a singularity" because it's kind of hard to define how that works out. Even intelligence probably hits some scaling limits eventually (e.g. speed of light related restrictions on how far it can scale, or how quickly it can expand).

Re: On the Navier–Stokes Millennium Prize Problem

#538

Post by _fizz_buzz_ »

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.

Can someone explain if i understand this correctly: Are they saying that they started training this new model on August 28th and then started using it on September 1st? Does training a new model only take 3 days?

Re: On the Navier–Stokes Millennium Prize Problem

#539

Post by StatsAreFun »

aborsy wrote: post #364

Questions: can new research like this be done using publicly available models? Or will access to internal frontier models provide a big boost?

Publicly available models are pretty good but seemingly cannot compete with these Astra++ internal-only models.

Re: On the Navier–Stokes Millennium Prize Problem

#540

Post by MichaelDickens »

highfrequency wrote: post #427

> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool. But there is one huge question: di…

> But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game.

Just because something is legal and permitted by terms of service doesn't mean it's morally right.

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