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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

#111

Post by ben_w »

William_BB wrote: post #85
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

Ever heard of the infinite monkey theorem? This is basically what LLMs do on really hard tasks. Prompt it a million times on a really hard problem and it might output the correct answer once.

The infinite monkey theorem assumes random distribution of symbols*.

Given the tokenizers have a vocabulary in the 10k-100k range, "a million attempts" will generally still only get the first token of the answer correct.

Even really rubbish models, e.g. talkie, the "what if we only use pre-1930s data to train a model?"** model, had to be almost all the way to the right answer to reach the really low HumanEval pass@100 score of ~0.04 (I'm only eyeballing the relevant chart).

* Actual monkeys not being like this is, while amusing, irrelevant

** https://talkie-lm.com/introducing-talkie

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

#112

Post by cromka »

xg15 wrote: post #51
cromka wrote: post #19

Earlier quoted context omitted.

That doesn't make any sense; you can't have one LLM to read your mind to prompt another LLM.

Waiting for the next Neuralink announcement...

That's still prompting, just justing a different interface.

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

#113

Post by d4rkp4ttern »

In the Reddit post there was clarification that this was done with Sol Pro not Ultra - curious what is everyone’s mental model of the difference.

My understanding is that ChatGPT Pro is effectively a multi agent system, or somehow uses multiple LLMs in parallel and selects a best answer. And Ultra is more similar to Claude-Code UltraCode where the main agent can choose to create a dynamic JS workflow that deterministically orchestrates multiple agents to handle different parts of a task and have adversarial checkers etc.

Is that more or less the difference? Any substantiating sources would be great to see.

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

#114

Post by timcobb »

georgemcbay wrote: post #94
timcobb wrote: post #30

Earlier quoted context omitted.

I can't stop wondering myself.... I'm writing some software with AI and wondering, why am I doing this? Will anyone need this? Will anyone have money to buy this? Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days

> Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days Continually progressing AI (combined with our current socioeconomic systems) throws a lot of uncertainty into our mid to long term future, but I don't think this is going to be what happens. There are billions more of "us" than of "them", people don't respond well en masse to a drastic worsening…

Humans aren't sheep but in the broad average it seems like we have a strong tendency to fall inline.

Fwiw I was mostly joking. I agree that the techno overlords have no reason to keep us, unlike in Roman times.

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

#115

Post by _alternator_ »

hodgehog11 wrote: post #92
LPisGood wrote: post #86

Earlier quoted context omitted.

It should be noted that optimization of a convex bounded lipschitz function is exactly what most modern statistical learning (AI) models are based on.

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 encouraged a lot of research, but it's more of the kind aimed at resolving tension: these methods are probably good for convex functions, why do they continue to work for nonconvex problems, and are there tweaks we can make to improve them in that setting? It's not a lot of de novo theory; more standing on the shoulders of giants, etc etc.

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

#116

Post by sashank_1509 »

This is all a depressing and bleak future that I don’t look forward to.

One solution is to ban LLM’s, to artificially create a demand for human thought, that just feels like living in an artificially constructed zoo.

Another solution is humans don’t do anything that AI can do better , / doesn’t need the human touch. So I suppose we will all become artists, sportsmen or politicians, the only jobs that will remain except for select few. Maybe this is ok, I don’t know.

Another solution is we find a way to mind-meld with AI so that human + Ai >> AI alone. This is dystopian, who gets to decide who mind melds with AI, how much will it cost etc etc.

For the stupid copes that the prompt required human ingenuity, let me first add that the author used GPT5.6 to write most of the prompt. He just gave some mild direction. That amount of direction does not require deep expertise and the expertise required will keep falling with time, eventually an undergrad can create this loop and then maybe a high school student.

  And prompt engineering / loop engineering nonsense is not real. Calling it engineering is a psy-op because it is something simple, imprecise and future models will be much better at it than you.
In fact, in the future the most likely outcome is you tell the agent what you want (I want this app, or I want this theorem solved) and it will set up the loop, or loop of loops and use all its computing effort to come up with a result. This is completely dystopian to a human life.

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

#117

Post by ben_w »

lvl155 wrote: post #63
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

Intelligence was always relatively cheap. You can pick up a phone and get answers for free in most academic settings.

You've not seen how they react to noobs asking physics questions, I think.

Even when you've got an interesting idea, if you're an enthusiastic amateur who don't yet know enough to phrase the question right but does actually know the basics, they'll put you in the same category as the people who think healing crystals can power hyperspace telepathy with Anubis: "oh no not another one".

LLMs have infinite patience, but unfortunately come (came?) with too much sycophancy, giving even more people far too much confidence.

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

#118

Post by barnacs »

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.

I hold my stance that LLMs are stochastic parrots.

Making the parrots ever more complex and training on ever more data produced by intelligent, creative beings may make them more useful or convincing but does at no point give rise to intelligence or creativity.

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

#119

Post by fsmv »

vatsachak wrote: post #91
rakel_rakel wrote: post #29

> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed. I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the professio…

Math is way more automatable than programming. In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part. In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convolut…

I think the difference is in math the problem is fully specified and easily verifiable and in programming it's not. I don't agree that we always know we can solve the problem.

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

#120

Post by fsmv »

sashank_1509 wrote: post #103
vatsachak wrote: post #91

Earlier quoted context omitted.

Math is way more automatable than programming. In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part. In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convolut…

> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store,…

Have you not seen vend bench?
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