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The Navier–Stokes Millennium Prize Problem

simonwillison.net

221–230 of 234 posts

Re: The Navier–Stokes Millennium Prize Problem

#221

Earlier quoted context omitted.

Put down the pitchfork. It's a toggle in their settings.

If you trust a "toggle" I have a bridge to sell. Users data is just too precious to ignore.

Which bridge? Do share the contract.

Re: The Navier–Stokes Millennium Prize Problem

#222
post #216

Earlier quoted context omitted.

I not only think it is not trivial, I know it is not solved.

I don't trust your judgment, it's in my opinion even hilarious given that we're talking about companies worth almost a trillion dollar (4 trillion in the case of Google). Be that as it may, it was nice chatting with you!

I also find it hilarious. I wonder what will happen if they don't solve this.

Re: The Navier–Stokes Millennium Prize Problem

#223

Earlier quoted context omitted.

If you trust a "toggle" I have a bridge to sell. Users data is just too precious to ignore.

Which bridge? Do share the contract.

Tower Bridge suits you? But hurry up, there are a lot of pretenders.

Re: The Navier–Stokes Millennium Prize Problem

#224

Earlier quoted context omitted.

But this is different, right? The equivalent would be taking a (fully offline) LLM and asking it about the ending of one specific Goosebumps book, and it revealing the twist. And although that specific book was (probably) only once in the training data, a high parameter LLM can usually "remember" the twist.

The only way it would be able to tell you the ending is if it was somehow given more importance in pretraining, loaded into context, or represented in multiple sets of training samples. I have a blog that I make very LLM friendly and usually load posts up into context when I’m working on something relevant. I’ve also opted to improve models for everyone. Despite this, the model can’t recognize my site or any of my po…

That's not correct for a SOTA model with trillions of parameters. Those have immense amounts of knowledge trained into their parameters. Try it. It "remembers" the ending of random books, Goosebumps and otherwise.

That's the entire point of why knowledge cutoff is so important (if you use them offline).

I find it entirely believable that the Navier-Stokes conversation was auto-flagged as high value training data, and burned-in the models knowlegdge base.

Re: The Navier–Stokes Millennium Prize Problem

#225

Earlier quoted context omitted.

I don't believe HN boosts their algo but I think people recognize posters like celebs. I recognize tosh, simonw, etc. Also it's an easy way to farm karma. The pelican guy posted a pelican, let's upvote it? It's at least a bit of psychosis / mass effect in this. For what it's worth, I like the pelicans but just making an observation

> It's at least a bit of psychosis I know semantic shift is inevitable, but can we put the brakes on this one at least a little? This doesn't even connect to the original meaning.

Fair enough. Hivemind, mass effect, happy to have a replacement word in this case.

Re: The Navier–Stokes Millennium Prize Problem

#226
post #133
post #15

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence»,…

This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the…

That doesn't really matter. Currently we're in the "this is a dog" (marks a muffin) stage of "AI as a scientist". It's totally reasonable to expect that considering how rapidly AI is advancing, the frontier of knowledge and research won't be universities anymore, but rather AI companies running their models in a loop.

Imagine that 20 years from now nobody really does science by hand because AI is just better at it, everyone just runs models, but these models require so much memory that only datacenters can realistically handle them, and it just so happens that the public gets access to nerfed models, while privately, companies actually break all asymmetrical encryption ciphers.

Re: The Navier–Stokes Millennium Prize Problem

#227
post #146
post #24

> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as…

I have a similar story, but perhaps even stranger. I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick. The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters. There are always a few competitive guys who spend the entire conference taking tu…

I think it's largely due to psychology. If 210m is considered the best, then as they approach it they may start to tense up and choke. When the goal and possibility is known as 500m, then there's no point being concerned near 210m.

Re: The Navier–Stokes Millennium Prize Problem

#228

I think this drama was blown up a bit out of proportion. The entire discourse I am seeing online seems to revolve around this: > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models I mean... yeah? What do you expect? What else can they say? How could you prove a negative in this case? I do not want to comment on specific OAI employee chat messa…

The claim that they 'cannot rule out' using Buckmaster's data isn't true in principle. Trivially, imagine that the model had been trained on data only since Jan 1, but a discovery was published on Jan 2.

Whether it's true in practice that's a matter of how their systems' functioning & its current state. If they really care about proving this, it's worth an audit. In fact, if anything, they may be able to prove that it hadn't used Buckmaster's inputs, but wouldn't be able to prove that it had.

Re: The Navier–Stokes Millennium Prize Problem

#229
post #13

I’ll go back to the point about authorship. I’m Not a mathematician but I am in academia. if you are fucking around with authorship you are immediately suspect. That aspect alone would/should be unthinkable to any serious academic. Authorship reflects who did the work and changing it for business competition reasons should be a red flag for multiple different reasons. They include, the sheer tactlessness of treating…

OAI's side of the story is that they discovered the approaches (and indeed solved problems - Euler equations vs NS equations) differed. They then offered Buckmaster lead authorship of OAI's proof, without Alpöge. But they never demanded that Alpöge be stripped of coauthorship on resolving the regularity of the Euler equations. At least that's the claim. https://xcancel.com/SebastienBubeck/status/20973794116915163...

To me it’s telling that the screen shot he posted doesn’t really support any of what he says in the post and the screenshot doesn’t contradict the other sides claims

Re: The Navier–Stokes Millennium Prize Problem

#230
post #146

Earlier quoted context omitted.

I have a similar story, but perhaps even stranger. I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick. The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters. There are always a few competitive guys who spend the entire conference taking tu…

I like to leverage that when brainstorming solutions to hard problems. Instead of contemplating small percentage improvements, try to think about what's in the way of improvements that are orders of magnitude better (e.g., don't take time to run a big task from 100s to 90s, take it to milliseconds). Sometimes it unlocks big ideas.

I work in software deployment for large orgs. I use this technique to optimize. "How can I provision or deploy this with one package install, and launch instance." Typically take multi-page or multi-step deployments down to fully automated.
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