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Navier-Stokes – Tristan Buckmaster [pdf]

cims.nyu.edu

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Re: Navier-Stokes – Tristan Buckmaster [pdf]

#491

Can somebody explain: do singularities / blow-ups in solutions have any relation to physical phenomena in fluid dynamics or are they purely artifacts of how the N-S equations may not accurately describe what actually happens in the physical world?

the latter (ish; it may not make a difference in any practical case)

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#493

From OpenAI: > 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. The fact that this is…

Playing the devil's advocate here. Suppose I use model A to do all heavy lifting (e.g. generating a bunch of good ideas) and then I go to the model B to complete the formalization. Accoring to a weird (unfair) tradition in math, the honors are attributed to the "last guy", which in this case is model B. That might have been a scenario OpenAI tried to avert. (Just a speculation)

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#494
post #451

Earlier quoted context omitted.

> if we just let OpenAI steal any good idea they can get their hands on if they think it is profitable I have terrible news about how literally every leading AI model was trained

That doesn't make it fine. We should not excuse this behaviour just because its rampant already, especially when it comes to such a serious prize

You're getting a massive discount because you're helping to train the model. If you want to have ZDR, you have to pay API rates.

This is well-known to anyone in the industry.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#495
post #83

Drama/accusation summary: - Aug 15th: Tristan Buckmaster & Levent Alpöge make progress on a few important math problems, "finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler." - they do NOT have a proof for the $1,000,000 Millenium Prize problem. BUT, they do claim to have a proof for a similar (non-Millenium) Navier Stokes problem that could help le…

> OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic well that sounds like an asshole move.

That's not quite right - Levent and Buckmaster did not actually have the Millennium Prize qualifying NS solution but something more limited. OAI invited Buckmaster to join and help rewrite the full solution paper but did not feel it was appropriate to invite an Anthropic employee to join as well - particularly given they were using internal unreleased models.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#496
post #467

Earlier quoted context omitted.

I think this might be a red herring. All it takes is someone to get an inkling that someone is working on a new approach and seeing some success for OpenAI to fire the AI cannon at the problem. The community seems fairly small (from this outsider's point of view). The idea that the data made it into the training set and that's how the bot figured it out is definitely possible, but I would want to rule out the simpler…

Terence Tao said the same[1] > In fact, it is now the identification of a promising problem which is the scarce and precious resource. We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any…

Could you just start engineering "leaks" of new proofs so that Anthropic or OpenAI just start burning $10million in compute

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#497

Earlier quoted context omitted.

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”.

These responses seem to me to make it abundantly clear who's telling the truth here. I wonder who this fools. It would be extraordinarily easy to simply say, this model was not trained on your work, if that were the case. It's telling that they refuse to acknowledge the root issue here, and are attempting to shift the conversation elsewhere.

I'm not sure it's so easy to tell whether a given piece of data was in a training run at their scale. It's entirely possible they think the answer is no, but on the off-chance that it could be, they'd rather not say no and then later it turns out they did and then they're claimed to be lying. If you were them, unless you could 100% rule it out, you'd hedge and say you can't.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#498
post #485

From OpenAI: > 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. The fact that this is…

> did Tristan opt out That “opt-out” thing is a dark pattern. It’s not a reliable and definitive way of protecting your data. Sometimes they flip on automatically when you accept a seemingly unrelated dialog box. Maybe you click it by mistake. You can’t take back what you’ve already shared. Also I don’t think it covers all the cases that they use your data. It’s really an opt-in button for voluntarily giving away you…

Business plans are specifically used for ZDR. If you're working on something that matters, you should be doing this.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#499
post #429
post #403

Earlier quoted context omitted.

it's very possible they only had to use the massive compute budget because they were trying to plagiarize his work before he published it though, e.g. autonomously do things in ~7 days what he had likely been thinking about for ~1 year.

This doesn't really make sense. You don't need massive amounts of computing to plagiarize something. The most nefarious explanation seems to be that they got wind it was possible to solve NS via LLMs and perhaps a small nudge in the right direction.

Of course you do if you're a) only given a partial solution b) racing against someone else using a competing AI.

The open question was whether their LLM got the nudge in the right direction because it got access to the chat somehow (e.g. automated training that scraped his chat logs) or just a high level "Navier stokes can be solved through LLM". It sounds like the former may have happened although right now we just have an accusation and a weak denial.

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