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Epoch confirms GPT5.4 Pro solved a frontier math open problem

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Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#181

Post by razorbeamz »

fenomas wrote: post #166
razorbeamz wrote: post #124

Earlier quoted context omitted.

No, it does not reason anything. LLM "reasoning" is just an illusion. When an LLM is "reasoning" it's just feeding its own output back into itself and giving it another go.

This is like saying chess engines don't actually "play" chess, even though they trounce grandmasters. It's a meaningless distinction, about words (think, reason, ..) that have no firm definitions.

Chess engines are not a comparable thing. Chess is a solved game. There is always a mathematically perfect move.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#182

Post by tovej »

fnordpiglet wrote: post #77
qnleigh wrote: post #74

Their 'Open Problems page' linked below gives some interesting context. They list 15 open problems in total, categorized as 'moderately interesting,' 'solid result,' 'major advance,' or 'breakthrough.' The solved problem is listed as 'moderately interesting,' which is presumably the easiest category. But it's notable that the problem was selected and posted here before it was solved. I wonder how long until the other…

I’d hope this isn’t a goal post move - an open math problem of any sort being solved by a language model is absolute science fiction.

It is not. You're operating under the assumption that all open math problems are difficult and novel.

This particular problem was about improving the lower bound for a function tracking a property of hypergraphs (undirected graphs where edges can contain more than two vertices).

Both constructing hypergraphs (sets) and lower bounds are very regular, chore type tasks that are common in maths. In other words, there's plenty of this type of proof in the training data.

LLMs kind of construct proofs all the time, every time they write a program. Because every program has a corresponding proof. It doesn't mean they're reasoning about them, but they do construct proofs.

This isn't science fiction. But it's nice that the LLMs solved something for once.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#183

Post by number6 »

NitpickLawyer wrote: post #167
snemvalts wrote: post #65

Earlier quoted context omitted.

Math and coding competition problems are easier to train because of strict rules and cheap verification. But once you go beyond that to less defined things such as code quality, where even humans have hard time putting down concrete axioms, they start to hallucinate more and become less useful. We are missing the value function that allowed AlphaGo to go from mid range player trained on human moves to superhuman by p…

> I don't see this getting better. We went from 2 + 7 = 11 to "solved a frontier math problem" in 3 years, yet people don't think this will improve?

But can it count the R's in strawberry?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#184

Post by locknitpicker »

storus wrote: post #55
Validark wrote: post #33

I have long said I am an AI doubter until AI could print out the answers to hard problems or ones requiring tons of innovation. Assuming this is verified to be correct (not by AI) then I just became a believer. I would like to see a few more AI inventions to know for sure, but wow, it really is a new and exciting world. I really hope we use this intelligence resource to make the world better.

AI is a remixer; it remixes all known ideas together. It won't come up with new ideas though; the LLMs just predict the most likely next token based on the context. That means the group of characters it outputs must have been quite common in the past. It won't add a new group of characters it has never seen before on its own.

> AI is a remixer; it remixes all known ideas together.

I've heard this tired old take before. It's the same type of simplistic opinion such as "AI can't write a symphony". It is a logical fallacy that relies on moving goalposts to impossible positions that they even lose perspective of what your average and even extremely talented individual can do.

In this case you are faced with a proof that most members of the field would be extremely proud of achieving, and for most would even be their crowning achievement. But here you are, downplaying and dismissing the feat. Perhaps you lost perspective of what science is,and how it boils down to two simple things: gather objective observations, and draw verifiable conclusions from them. This means all science does is remix ideas. Old ideas, new ideas, it doesn't really matter. That's what they do. So why do people win a prize when they do it, but when a computer does the same it's role is downplayed as a glorified card shuffler?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#186

Post by bandrami »

59nadir wrote: post #158
bandrami wrote: post #135

It's deeply surprising to me that LLMs have had more success proving higher math theorems than making successful consumer software

Software developers have spent decades at this point discounting and ignoring almost all objective metrics for software quality and the industry as a whole has developed a general disregard for any metric that isn't time-to-ship (and even there they will ignore faster alternatives in favor of hyped choices). (Edit: Yes, I'm aware a lot of people care about FP, "Clean Code", etc., but these are all red herrings that d…

But we don't even seem to be getting faster time-to-ship in any way that anybody can actually measure; it's always some vague sense of "we're so much more productive".

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#187

Post by wobfan »

trick-or-treat wrote: post #126
energy123 wrote: post #122

Earlier quoted context omitted.

I can't really make that claim about human cognition, because I don't have enough understanding of how human cognition works. But even if I could, why is that relevant? It's still helpful, from both a pedagogical and scientific perspective, to specify precisely why there is seeming novelty in AI outputs. If we understand why, then we can maximize the amount of novelty that AI can produce. AlphaGo didn't teach itself…

> The verifier taught AlphaGo that move Ok so it sounds like you want to give the rules of Go credit for that move, lol.

It feels like you're purposefully ignoring the logical points OP gives and you just really really want to anthropomorphize AlphaGo and make us appreciate how smart it (should I say he/she?) is ... while no one is even criticising the model's capabilities, but analyzing it.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#188

Post by famouswaffles »

slopinthebag wrote: post #162
famouswaffles wrote: post #151

Earlier quoted context omitted.

>The capabilities of a human far surpass every single AI to date What does this mean ? Are you saying every human could have achieved this result ? Or this ? https://openai.com/index/new-result-theoretical-physics/ because well, you'd be wrong. >, and much more efficiently as well. That we are able to brute-force a simulacrum of intelligence in a few narrow domains is incredible, but we should not denigrate humans wh…

> The capabilities of a human far surpass every single AI to date Meaning however you (reasonably) define intelligence, if you compare humans to any AI system humans are overwhelmingly more capable. Defining "intelligence" as "solving a math equation" is not a reasonable definition of intelligence. Or else we'd be talking about how my calculator is intelligent. Of course computers can compute faster than we can, that…

>Meaning however you (reasonably) define intelligence, if you compare humans to any AI system humans are overwhelmingly more capable.

Really ? Every Human ? Are you sure ? because I certainly wouldn't ask just any human for the things I use these models for, and I use them for a lot of things. So, to me the idea that all humans are 'overwhelmingly more capable' is blatantly false.

>Defining "intelligence" as "solving a math equation" is not a reasonable definition of intelligence.

What was achieved here or in the link I sent is not just "solving a math equation".

>Or else we'd be talking about how my calculator is intelligent.

If you said that humans are overwhelmingly more capable than calculators in arithmetic, well I'd tell you you were talking nonsense.

>Of course computers can compute faster than we can, that's aside the point.

I never said anything about speed. You are not making any significant point here lol

>No, I don't mean how the intelligence evolved or was created.

Well then what are you saying ? Because the only brute-forced aspect of LLM intelligence is its creation. If you do not mean that then just drop the point.

>But if you want to make that argument you're essentially asserting we have a creator, because to "brute force" something means it was intentional.

First of all, this makes no sense sorry. Evolution is regularly described as a brute force process by atheist and religious scientists alike.

Second, I don't have any problem with people thinking we have a creator, although that instance still does necessarily mean a magic 'poof into existence' reality either.

>But my point is that LLM's essentially arrive at answers by brute force through search.

Sorry but that's just not remotely true. This is so untrue I honestly don't know what to tell you. This very post, with the transcript available is an example of how untrue it is.

>or the amount of energy it takes to do things humans can do with orders of magnitude less (our brain runs on %20 of a lightbulb!).

Meaningless comparison. You are looking at two completely different substrates. Do you realize how much compute it would take to run a full simulation of the human brain on a computer ? The most powerful super computer on the planet could not run this in real time.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#189

Post by number6 »

jamesfinlayson wrote: post #125
otabdeveloper4 wrote: post #95

Earlier quoted context omitted.

LLMs can often guess the final answer, but the intermediate proof steps are always total bunk. When doing math you only ever care about the proof, not the answer itself.

Yep, I remember a friend saying they did a maths course at university that had the correct answer given for each question - this was so that if you made some silly arithmetic mistake you could go back and fix it and all the marks were for the steps to actually solve the problem.

This would have greatly helped me. I always was at a loss which trick I had to apply to solve this exam problem, while knowing the mathematics behind it. Just at some point you had to add a zero that was actually a part of a binomial that then collapsed the whole fromula

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#190

Post by staticassertion »

parasubvert wrote: post #164
slg wrote: post #60

Earlier quoted context omitted.

Yes, but is it "intelligence" is a valid question. We have known for a long time that computers are a lot faster than humans. Get a dumb person who works fast enough and eventually they'll spit out enough good work to surpass a smart person of average speed. It remains to be seen whether this is genuinely intelligence or an infinite monkeys at infinite typewriters situation. And I'm not sure why this specific example…

Someone actually mathed out infinite monkeys at infinite typewriters, and it turns out, it is a great example of how misleading probabilities are when dealing with infinity: "Even if every proton in the observable universe (which is estimated at roughly 1080) were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons might no longer exist), they would still need a far greate…

> So no. LLMs are not brute force dummies. We are seeing increasingly emergent behavior in frontier models.

Woah! That was a leap. "We are seeing ... emergent behaviors" does not follow from "it's not brute force".

It is unsurprising that an LLM performs better than random! That's the whole point. It does not imply emergence.

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