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

epoch.ai

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

#701

Post by hnfong »

eru wrote: post #643
hnfong wrote: post #635

Earlier quoted context omitted.

> Turing's test is a famous example Ironically, the Turing test is the OG functionalist approach. The GP's comment basically sums up with the Turing test was designed for.

Yes, but I interpret Turing's paper not as saying "souls don't matter", but as "here's a good proxy that we can actually measure". (I don't know what Turing's opinion on souls is, and it doesn't matter for that paper!)

I think it's generally accepted that Turing thinks soul doesn't matter when we try to determine whether things have intelligence/ability to think.

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

#702

Post by My_Name »

There seems to be a focus on understanding when talking about LLMs and solving problems. Personally, I do not think understanding is required. I can write a very small program that can calculate Pi to however many digits I like, or calculate any digit in the sequence on demand, without the program or computer having any understanding at all of what Pi is or what it means. I could get Claude to output that same code when prompted to find a solution to generating Pi, also with no understanding of what Pi is, or what it means.

IMO the ability to provide an accurate solution to a problem is not always based on understanding the problem.

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

#703

Post by staticassertion »

fenomas wrote: post #700
staticassertion wrote: post #614

Earlier quoted context omitted.

This is great observational data but it's an early "step 1", I'd definitely need to see an actual analysis of these cases and likely want to have that analysis involve a review of relevant training data.

What you're asking for is exactly what's in the link you replied about. It collects analysis of each solution (or attempt), and info about whether the AI's solution could be found anywhere in the literature.

Where?

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

#704

Post by hnfong »

scoofy wrote: post #650
hnfong wrote: post #631

Earlier quoted context omitted.

> distinction between deductive and inductive knowledge There's also intuitive knowledge btw. Anyway, the recent developments of AI make a lot of very interesting things practically possible. For example, our society is going to want a way to reliably tell whether something is AI generated, and a failure to do so pretty much settles the empirical part of the Turing test issue. Or alternatively if we actually find som…

I don't want to do the thing where we fight on the internet. I don't know your background, but I'll push back here just because this type of comment that non-philosophers seem to present to me, which misses a lot of the points I'm trying to make. (1) "intuitive knowledge" - whether or not you want to take "intuitive knowledge" as a type of knowledge (I don't think I would) is basically immaterial. The deductive-induc…

Your response is... interesting.

I thought I agreed with most of your original comment that I replied to, and here you are ready to fight. I'm not even sure what you're fighting, and I certainly didn't have in mind the things you responded to.

Well, I guess I learned not to talk to philosophers (especially those who went through school) the hard way. Sometimes I forget my lesson and it's always sad when this happens. Have a good day.

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

#705

Post by fenomas »

staticassertion wrote: post #703
fenomas wrote: post #700

Earlier quoted context omitted.

What you're asking for is exactly what's in the link you replied about. It collects analysis of each solution (or attempt), and info about whether the AI's solution could be found anywhere in the literature.

Where?

The high-order bit for for each case is the category it's in and the "Outcome" column - that summarizes if the solution was full/partial/wrong, if AI had assistance, etc. Then further discussion for each one is linked from the number.

Then the "Literature result" columns have a citations for where similar published results were found. The ones with no "Literature" column, like in the first section, are cases where no similar published results have been found (implying that the solution would not have been trained on). Note that in some cases a published solution was found but it wasn't similar to the AI's.

(this is all explained with more detail and caveats at the top of the page)

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

#706

Post by botro »

datsci_est_2015 wrote: post #336
NitpickLawyer wrote: post #167

Earlier quoted context omitted.

> 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?

I’ve seen this style of take so much that I’m dying for someone to name a logical fallacy for it, like “appeal to progress” or something. Step away from LLMs for a second and recognize that “Yesterday it was X, so today it must be X+1” is such a naive take and obviously something that humans so easily fall into a trap of believing (see: flying cars).

How about 'slippery incline'?

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

#707

Post by srean »

scoofy wrote: post #690
thaumasiotes wrote: post #679

Earlier quoted context omitted.

> Math is a perfect field for machine learning to thrive because theoretically, all the information ever needed is tied up in the axioms. Not really; the normal way that math progresses, just like everything else, is that you get some interesting results, and then you develop the theoretical framework. We didn't receive the axioms; we developed them from the results that we use them to prove.

Axioms are, again, by definition, arbitrary. It is effectively irrelevant that we try to develop axioms so that the framework mirror the real world. Everything falls out of the axioms, period. If you want to change the axioms to better reflect some aspect about life, that's all well and good, but everything will still fall out of the new axioms.

I agree and not all mathematicians care about or are motivated by how well a set of axioms model the real world. To a mathematician the richness of the consequences of a set of axioms is its own reward.

In this sense mathematicians are board-game designers. It matters less how well the game describes nature's reality than how fun it is to play the game that results.

Now if you were a physicist, the game has already been design by some other mechanism and you have to probe to understand the rules and discover its consequences.

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

#708

Post by staticassertion »

fenomas wrote: post #705
staticassertion wrote: post #703

Earlier quoted context omitted.

Where?

The high-order bit for for each case is the category it's in and the "Outcome" column - that summarizes if the solution was full/partial/wrong, if AI had assistance, etc. Then further discussion for each one is linked from the number. Then the "Literature result" columns have a citations for where similar published results were found. The ones with no "Literature" column, like in the first section, are cases where no…

Sorry, I suppose I'm asking for a lot of handholding here, which isn't really fair. I'm actually just sick right now and have crazy brain fog. Thanks for the assistance! I'll read through.

FWIW I've wavered on this topic quite a bit. Not too long ago I leaned more heavily towards "complex cognitive capabilities can be expressed using statistical token generation", I've started leaning the other way, but I'm not committed so it's great to circle back on the state of things.

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

#709

Post by fenomas »

staticassertion wrote: post #708
fenomas wrote: post #705

Earlier quoted context omitted.

The high-order bit for for each case is the category it's in and the "Outcome" column - that summarizes if the solution was full/partial/wrong, if AI had assistance, etc. Then further discussion for each one is linked from the number. Then the "Literature result" columns have a citations for where similar published results were found. The ones with no "Literature" column, like in the first section, are cases where no…

Sorry, I suppose I'm asking for a lot of handholding here, which isn't really fair. I'm actually just sick right now and have crazy brain fog. Thanks for the assistance! I'll read through. FWIW I've wavered on this topic quite a bit. Not too long ago I leaned more heavily towards "complex cognitive capabilities can be expressed using statistical token generation", I've started leaning the other way, but I'm not commi…

Not at all - didn't mean to sound snarky, I just wanted to add that I was omitting details and caveats.

FWIW, personally I think it muddies things to frame the question as if "..using statistical token generation" was a limitation. NNs are Turing-complete, so what LLMs do can just be considered "computation" - the fact that they compute via statistical token generation is an implementation detail.

And if you're like most people, "can cognition happen via computation?" is a less controversial question, which then puts LLMs/cognition topics easily into the "in principle, obviously, but we can debate whether it's achievable or how to measure it" category.

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

#710

Post by acuozzo »

snemvalts wrote: post #76
virgildotcodes wrote: post #56

I don't know why I am still perpetually shocked that the default assumption is that humans are somehow unique. It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window. People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whethe…

The ability to learn and infer without absorbing millions of books and all text on internet really does make us special. And only at 20 watts!

20 watts ignores the startup cost: Tens of millions of calories. Hundreds of thousands of gallons of water. Substantial resources from at least one other human for several years.
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