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GPT-5.6 used a prompt to close a 30-year gap in convex optimization

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Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#321

Post by dudul »

piloto_ciego wrote: post #302
qarl2 wrote: post #296

Earlier quoted context omitted.

> WTF does the pandemic have to do with this? I'm not sure, but if I may guess, I suspect he's talking about the fact that the entire US shut down for a year and people survived because the US Government printed money and gave it away free to businesses so they wouldn't collapse. (PPP loans.) If we can do something like that for the pandemic, we can do something similar when push really comes to shove.

Thank you! We can decide to just... you know... do things. Like, am I crazy here? The rules that we live by are largely made up and the points don't matter - we can decide to live in a better world if we want to. It's hard, and there are obstacles, for sure, but this appeal to doom for the sake of doom just... why? We have made unfathomable progress over the last century and if we keep trying we can make progress lik…

> We can decide to just... you know... do things.

OK, this is Twitter-level conversation here, not interested. But hey, stay positive, more power to you.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#322

Post by sandspar »

pydry wrote: post #153
p-e-w wrote: post #139

Earlier quoted context omitted.

Unless you’re claiming that AIs will suddenly (and very soon) stop improving, they are obviously a threat to everyone’s job. Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.

>Unless you’re claiming that AIs will suddenly (and very soon) stop improving Most technologies level off sharply after bouts of boundless improvements. In 1968 they thought we'd be flying to the moon by now but instead we're flying across the ocean in planes not that different from the 747 that existed back then.

Even if AI stops merely at solving Erdos problems (merely...), metabolizing it would take decades.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#323

Post by WarmWash »

piloto_ciego wrote: post #301
vanuatu wrote: post #292

Earlier quoted context omitted.

I play the game for a manufactured challenge People in the real world all having god mode cheats is good, actually

yeah! Like can you imagine a world where you could just effectively "conjure" new furniture for your house and robots would assemble it in a few hours? Or molecular assemblers would grow it while you slept? Or imagine a world where we could basically cure every disease? Or a world where people could assume any form factor that they wanted? I don't know, the list goes on and on in a post-scarcity world... and we're se…

The rub is that we already live in that world relative to people who lived 1000 year ago, and yet somehow we aren't bursting with euphoria 24/7.

We also have humans who essentially live post scarcity lives on the back of a monetary windfall, yet their stories are strangely quite often depressing ones.

I think their is good reason to believe most human desires are illusions.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#324

Post by moomoo11 »

cornell532 wrote: post #319
moomoo11 wrote: post #294

Earlier quoted context omitted.

just ignore these people gig economy is a blessing to keep the LCD busy and doing something productive instead of being nihilistic losers it’s better to focus on how to keep these “knowledge” workers busy for the AI age they don’t like to work and complain even on a w2 job (where someone else had to figure out how to capitalize them) so in many ways they’re far more dangerous and hopeless.

Don’t be so nasty about w2 workers. Incredibly unbecoming. Also see comparative advantage re best roles for each actor in an economy

cool

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#325

Post by slopinthebag »

amelius wrote: post #70
mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

Everybody can be an armchair mathematician now. Just fling some thoughts in the direction of your AI setup and let it do breadth first search with AI based pruning heuristics.

I imagine there are hundreds of thousands of people doing this, yet all we seem to get is a handful of solved problems. So it would seem the success rate is extremely low.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#326

Post by YeGoblynQueenne »

So if you dig down a bit it turns out the author had been trying to solve that problem for a year with GPT 5.4 and 5.5 and he fed all that information to the prompt he gave to Sol Pro which may or may not had direct access to the author's chat history. So the claimed "148 minutes" was really "a year plus 148 minutes".

Moreover, it seems the prompt included the technique used to solve the problem:

https://old.reddit.com/r/math/comments/1uxj3cy/after_openais...

In the prompt I basically just throw all reasonable approaches at it, without making a big distinction for what to explore most, and these approaches would all be reasonable for someone who knows the area. Sol helped me with the prompt as well, for which I gave it the CDC prompt, some ideas and specifications, a crystal clear problem description, and then modified things slightly myself after. One thing I do wonder is how much it accessed memory of previous chats, since as mentioned I had worked with 5.5 and 5.4 on this previously, and the main construction is not so different from something I discussed there. But, the function class max of affine functions that worked in the end was also in my prompt, so I'm not totally sure.

So it's not clear to me the degree to which "GPT-5.6 used a prompt" to close the gap etc, or the author basically did all the work himself and assigned it to GPT-5.6 out of enthusiasm.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#327

Post by YeGoblynQueenne »

andy12_ wrote: post #198
applfanboysbgon wrote: post #10

Two points: - Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too! - The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting th…

> but it is worth noting that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." It wasn't the case for this, but when OpenAI disproved the Unit Distance Conjecture, it was really done autonomously by an automated AI pipeline with a completely AI-generated prompt. No human expertise required at all in the process (well, except for the final human verification).

Without human verification, an LLM can generate correct or incorrect proofs but it can't tell the difference. A human is necessary to be able to tell one from the other.

Saying that's a solution "done autonomously by an automated AI pipeline" is like saying that a self driving car that can only take you to the nearest train station after which you have to ride the rain to where you're going is "autonomously" driving you to your destination. Which is exaggerating the autonomy of the system, rather.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#328

Post by slopinthebag »

threethirtytwo wrote: post #108

Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.

They aren’t really stochastic parrots, they’re next token prediction machines. They aren’t intelligent nor creative imo. However they are quite useful at some tasks. Why would you assume people who don’t kneel at the alter of AI are somehow fearful or hate AI? Most of the hate I’ve seen have been for the people and companies involved with AI not the technology itself.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#329

Post by samdhar »

_alternator_ wrote: post #115
hodgehog11 wrote: post #92

Earlier quoted context omitted.

Very confused by this comment. The older (poorer) parts of the ML literature focus on models with convex and (gradient-)Lipschitz objectives, but that's not representative of reality, not even close. Modern objectives for AI models are famously nonconvex (catastrophically, from the point of view of classical optimisation theory), and that's where the interesting research is.

I'd push back on this. Most of the core optimization techniques (eg, ADAM, stochastic gradient descent) are straight out of the convex optimization literature. Generally you need to use optimizers that work well on convex objectives because near minimizers, functions tend to be convex. (Proof by contradiction: a non-convex point has a strict descent direction.) The fact that neural networks are highly nonconvex has e…

[flagged]

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#330

Post by cindyllm »

slopinthebag wrote: post #328
threethirtytwo wrote: post #108

Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.

They aren’t really stochastic parrots, they’re next token prediction machines. They aren’t intelligent nor creative imo. However they are quite useful at some tasks. Why would you assume people who don’t kneel at the alter of AI are somehow fearful or hate AI? Most of the hate I’ve seen have been for the people and companies involved with AI not the technology itself.

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