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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#191

Post by Turn_Trout »

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…

OAI could check whether those accounts enabled training data. If "yes", OAI could trace whether that data was used in any related training process. If either of those answers comes out to be "no", then that's sufficient to conclude training data independence.

We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.

Re: On the Navier–Stokes Millennium Prize Problem

#192

Post by anthonypasq »

QuesnayJr wrote: post #158
jrflo wrote: post #111

Earlier quoted context omitted.

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.)

the goalposts are on Pluto at this point.

Re: On the Navier–Stokes Millennium Prize Problem

#194

Post by matteoraso »

This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0]

[0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.

Re: On the Navier–Stokes Millennium Prize Problem

#195

Post by burkaman »

Yajirobe wrote: post #124
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 would Anthropic employee even use OpenAI's models? Cross-polination would have been avoided

> I should also emphasize that this is not an institutional effort. It is a strictly personal collaboration between the two of us, and there is no formal agreement behind it. I pay for the tools my group uses out of my own research funds, including footing a large bill to OpenAI.

The non-Anthropic employee, Tristan Buckmaster, is the one paying for OpenAI models and presumably the one who chose to use them. The Anthropic employee, Levent Alpöge, was collaborating in his personal capacity, and obviously it wouldn't make sense for him to cut off their work together just because his employer's competitor's tool was used.

Re: On the Navier–Stokes Millennium Prize Problem

#196

Post by quantumwoke »

simianwords wrote: post #136
aizk wrote: post #52

People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief t…

Some observations:

1. It seems at least possible that some of the proof of NS was contained in the training data, making it less novel.

2. The formalisation of mathematics into lean has been an underappreciated force multiplier on discovery.

Re: On the Navier–Stokes Millennium Prize Problem

#197

Post by WarmWash »

pu_pe wrote: post #119

OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.

Or paying for API use.

It should be clear to everyone reading this now that those generous compute quotes with the flat rate plans aren't charity.

Re: On the Navier–Stokes Millennium Prize Problem

#198

Post by Aboutplants »

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.

I’m of zero knowledge on model training, but how is a model accessible while performing training at the same time, especially so early in its run? I’m obviously thinking a little too narrowly in terms of how it actually works

Re: On the Navier–Stokes Millennium Prize Problem

#199

Post by [deleted] »

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

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#200

Post by fantasizr »

nbulka wrote: post #166

There's a loophole in the terms of service at least for Anthropic which allows the use of dark patterns to "borrow" your (even paid) data. talking about this... Was this chat helpful? 1 That button you always click, gotcha! 2 Slightly 3 Good 0 Dismiss PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS. There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!

reminds me of the TOS episode of South Park. By Checking this box you forfeit your millennium prize solution and may be turned into a human centipede at future date.
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