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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#262

Earlier quoted context omitted.

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…

So you definitely did train on their data, you just think it is unlikely that it impacted the final model significantly?

That’s also what I understand. If true yet another disgusting behavior from the company

Re: On the Navier–Stokes Millennium Prize Problem

#263
post #126

Earlier quoted context omitted.

right, surely they could've waited or even reached out? It reads as desperation to get there for marketing purposes

They did reach out. > Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our resul…

We've heard from Buckmaster, who says that they demanded a condition of cutting Alpöge of all credit. If true, it doesn't make them look too good.

Re: On the Navier–Stokes Millennium Prize Problem

#264
post #53

> 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…

Next month is going to be insane. Month ...

Re: On the Navier–Stokes Millennium Prize Problem

#265
post #156
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…

> 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 likel…

The question is not "does OpenAI know", it's "can OpenAI attest that the usage of their products for confidential data is not going to cause that sensitive data to become known to their models". And right now the answer I'm reading is that OpenAI can't attest to that.

Re: On the Navier–Stokes Millennium Prize Problem

#266
post #234

Earlier quoted context omitted.

I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.

It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question If OpenAI is training mode…

If you're alleging that they don't actually have a highly capable model and the work they're attributing to it was actually plagiarized from human mathematicians, well, that would be big if true, but I'd be inclined to take the other side of that bet. With most previous splashy AI results, others have subsequently used the model to do other things around the same difficulty level. Also, it would still be necessary to explain why all these famous open problems are suddenly falling like dominoes, if it's not AI solving them.

If you're saying that the question of whether they actually have a highly capable model is less important than the question of whether there's a plagiarism scandal, I continue to disagree.

Re: On the Navier–Stokes Millennium Prize Problem

#267

Earlier quoted context omitted.

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…

[flagged]

How sure are you that the phase of the moon is not an input to the system somewhere? http://www.catb.org/jargon/html/P/phase-of-the-moon.html

Re: On the Navier–Stokes Millennium Prize Problem

#268

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 singularity happening under trump? We could have had star trek, instead we're getting the combine.

Re: On the Navier–Stokes Millennium Prize Problem

#269
post #37

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?

What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.

> What else can they declare really?

Oh I don't know, maybe something like this?

"Given how seriously this would violate the most fundamental of academic standards, as well as taint the claimed capability behind this result, we take this issue very seriously, and we're launching a probe into identifying whether any of their research artifacts have entered our training set. We have further begun making changes to our UI/UX on all our surfaces, so that it is always clear whether any particular chat, or other user artifact, is eligible for being trained on."

Re: On the Navier–Stokes Millennium Prize Problem

#270
post #53

Earlier quoted context omitted.

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…

2) We are witnessing the intelligence explosion from the first row, wherever this takes us 3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms. But apart from A…

To be quite clear, the solution to the _Navier Stokes problem_ is one in which you get a finite time blow up (i.e. infinite pressure). This is more meant to suggest that Navier Stokes is unphysical in some way which is not necessarily unexpected.

There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can also drive pressure in other ways.

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