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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#221
post #190

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.

Eventually recursive self-improvement includes reducing bottlenecks.

Re: On the Navier–Stokes Millennium Prize Problem

#222
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…

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

Re: On the Navier–Stokes Millennium Prize Problem

#223

Earlier quoted context omitted.

They should have used a zero data retention agreement, user error

I suspect this controversy will blow the case for ZDR wide open. Whatever the facts (possibly unknowable), it's going to become a very public lesson that data sovereignty was never about "having nothing to hide". If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.

Yeah if I was Anthropic this would be part of my marketing strategy.

Re: On the Navier–Stokes Millennium Prize Problem

#224

Earlier quoted context omitted.

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. "People" are just misinformed and keep…

> The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to O…

Wow, this sentence is doing a lot of work in that tweet: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Re: On the Navier–Stokes Millennium Prize Problem

#225

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

the model is a set of weights, you can take a snapshot and test it. Reinforcement learning itself is largely testing and tuning.

Re: On the Navier–Stokes Millennium Prize Problem

#226
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…

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.

> could trace whether that data was used

The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.

Re: On the Navier–Stokes Millennium Prize Problem

#227

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

Interesting that they quote the mathematician directly: “there is nothing you can do, I simply do not trust you”

but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."

Re: On the Navier–Stokes Millennium Prize Problem

#228

Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..

I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.

I also think the trope is a little overused, but do wonder if there is an interesting analogy for what this will do to research: Massively incentivize keeping results secret, to avoid being scooped by someone willing to throw enormous compute at your partial solution.

So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.

Re: On the Navier–Stokes Millennium Prize Problem

#229
post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

>there's still the problem of does this logical result actually prove the initial question that was asked?

In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you have a logical statement which only assumes the axioms of the system you're working with and which shows that the statement you're trying to prove is deduced through that statement.

Basically, they already have the "answer" in the sense that the statement they want to prove/disprove/etc. is already known. What everyone doesn't/didn't have is the argument which starts from axioms and leads to that statement which is logically valid. A Lean proof IS this argument. Since it is just logic, it can be checked computationally.

For example, if I assert "2 is an even number," then I haven't proven that 2 is actually an even number yet, but I know that a valid proof of my assertion will end with the statement "2 is an even number". So the question I'd be trying to answer is "what is the line of logic, starting with axioms, which leads to the statement '2 is an even number'"? If I have that line of logic (as a Lean proof), then I can check that it is logically consistent, and if it turns out to be valid, then I can now assert that "2 is an even number" knowing that there is a proof of that statement.

This problem is no different. There is a logical statement corresponding to "Navier–Stokes Millennium Prize Problem" that everyone knows, but which nobody had been able to provide a proof (or counterexample, etc.) for until now.

Re: On the Navier–Stokes Millennium Prize Problem

#230
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…

Will history look back at comments like these as people being dumb, or people trying to cope?
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