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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#451

Post by root_axis »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

It's incredible to me that every single time there's a new model people scream "singularity" from the rooftops and every time they are wrong.

This is an impressive result, but there is absolutely zero evidence of "the singularity".

Re: On the Navier–Stokes Millennium Prize Problem

#452

Post by anon48293 »

int32_64 wrote: post #413
igleria wrote: post #322

Earlier quoted context omitted.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

Could they say they don't retain, but do something "transformative" like use their own AI to summarize and paraphrase user sessions?

Yes, and that’s exactly what I believe they are doing

Re: On the Navier–Stokes Millennium Prize Problem

#453

Post by andrepd »

tedsanders wrote: post #181
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…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.

The _gall_ to say something like this. Do you perhaps think we are all stupid?? This very blogpost claims not to know if their work was used as input for this model. I don't even understand how that is possible, surely you can know if something is part of the training data, even if you are in the dark about what impact it actually made, qualitatively. The moon....

> Knowing most of the recipes we use, there's really no reason to think such contamination happened.

Yeah sorry but I don't trust you. I don't trust people or companies that have shown themselves to be dishonest before. Especially when the previous paragraph is comparing plagiarism and training data contamination with, _the phases of the moon_.

Might even be you're actually telling the truth, but the boy that cried wolf and all that.

-----

As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.

Re: On the Navier–Stokes Millennium Prize Problem

#454

Post by curt15 »

charm137 wrote: post #298
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…

It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that! Progress in humanity's knowledge now has to…

The scientist allegedly making that request comes from a machine learning background. Perhaps he's not familiar with the culture in mathematics regarding authorship. That sort of squabbling over author priority would be unconscionable to mathematicians.

Re: On the Navier–Stokes Millennium Prize Problem

#455

Post by dfdydx »

pfisch wrote: post #46
nehan wrote: post #15

"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.

If they could then it wouldn't be de-identified data...

Well you could search for elements similar to the proof / problem in the training data, even if it's de-identified, right? OpenAI can probably do better than Ctrl-f "Navier Stokes".

Re: On the Navier–Stokes Millennium Prize Problem

#456

Post by 3m4r »

This is a great day to re-read Ken Thompson's "Reflections on Trusting Trust":

>To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software.

https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_Ref...

Re: On the Navier–Stokes Millennium Prize Problem

#457

Post by azan_ »

rfgplk wrote: post #326
Aboutplants wrote: post #244

Earlier quoted context omitted.

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…

We are very likely at the begging of the next industrial revolution.

This one won’t create significant amount of new jobs though.

Re: On the Navier–Stokes Millennium Prize Problem

#458

Post by tkamat29 »

viccis wrote: post #386
hkmaxpro wrote: post #301

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”.

Kinda weird because the pure math world doesn't have this concept of "lead authors" like other STEM areas do. Authors are alphabetically listed and there isn't generally this kind of hierarchy.

From what I understand they aren't comfortable with the Anthropic employee being an author at all, not just lead author.

Re: On the Navier–Stokes Millennium Prize Problem

#459

Post by mrbungie »

Maxious wrote: post #205
igleria wrote: post #184

Earlier quoted context omitted.

I´m waiting on the other side version, because I know there is no justifiable way to talk to a person like they did. Sociopathic behaviour.

OpenAI version of events conceed some of the words alleged to have been used may have been used https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310

In what world a tweet and a screenshot of a private convo are evidence of good faith? Plain sociopathic behavior.

Re: On the Navier–Stokes Millennium Prize Problem

#460

Post by dermacentor »

tedsanders wrote: post #181
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…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

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