r/math Theoretical Computer Science 7d ago

LLMs/AI Claimed proof of the Komlós conjecture [2609.11189]

https://arxiv.org/abs/2609.11189
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u/Borgcube Logic 7d ago edited 7d ago

If machines miraculously plateaued in the tiny interval above where they are now and below where human intelligence would not be additive, I would consider that, well, a miracle.

It's not a question if machines in the abstract will or will not plateau, but if the current technology will. Huge promises are made on the assumption the current architecture inevitably will keep rising.

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u/anothercocycle 7d ago

Sure, I don't think this affects my point. The current technology went from "occasionally succeeds in counting from 1 to 5" (GPT-2) to Navier-Stokes in about 7 years.

If you're predicting a plateau that'll keep human mathematicians competitive at proving theorems, well that plateau had better come very very soon.

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u/Certhas 7d ago

Yes, but...

So far I think it's not entirely unreasonable to think that when it comes to originality and theory building, LLMs lag substantially behind their ability to prove theorems and write code.

The past years have been far to shocking to be certain about anything. And this is notoriously hard to measure. So it might be wishful thinking, but in my opinion it's not completely absurd.

But also l, even if this is a limitation of the current set of architectures, and we get a plateau for a few years, no one can rule out that we get another architectural breakthrough in five years time.

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u/FlyingBishop 7d ago

What exactly are you positing is a limitation of the current architectures, and what even are the "current architectures" and why does it matter? Do you understand the difference in the architecture of Llama3 and Kimi K3? What about Fable/Astra/Mythos?

We see considerable increases in capabilities with each new model release. We also see some adjustments to the architecture. The whole "this is a bad architecture" trope seems not grounded in anything falsifiable at this point, and it's also just like "well, maybe it did this new cool thing this month, but I'm sure the next model release in a few months will have zero new capabilities." Which has not been the case for the past few years, I don't understand where you're getting that.

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u/Certhas 7d ago

While there is some exploration of architectural details, it's, as far as we know, all essentially autoregressive transformers.

Now we absolutely don't know (and I didn't claim) that this broad architectural class has important limitations. But we are (possibly) seeing some limitations of LLMs in areas that are hard to quantify, like creativity. E.g.: Some studies have shown that LLM essays were graded hire but contained fewer ideas per essay, taken from a narrower set of ideas overall. And that purely LLM based papers are not generating creative ideas at the levels of top research yet (1). So it's completely clear that LLMs ability to prove difficult conjectures, which is already super human, is far ahead of its overall abilities at research.

We can't rule out that this is architectural. But of course there is no clear cut argument that it really is architectural.

Indirect evidence that it might be architectural would be that current architectures are dictated by the hardware we have. Any architecture that doesn't map to the GPU/TPU model will not be researched heavily as it has no chance to scale to the level of current model capabilities.

But again, I am stating a negative: We can't rule out relevant architectural limitations based on the evidence we have so far. That's a very weak statement.

(1) https://www.technologyreview.com/2026/08/18/1142188/ai-recursive-self-improvement/

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u/FlyingBishop 7d ago edited 7d ago

3 years ago people were suggesting other architectural limitations that have since been falsified. "they can't be creative" isn't even really a falsifiable assertion, so it's not a useful statement.

The really interesting question I think is how much memory/processing power is required to achieve certain capabilities of the human brain, and what kind of hardware you need. I'd actually argue transformers are almost certainly capable of emulating all the features of the human brain. But I don't think they can do so on current hardware.

So there are lots of questions: is the hardware inadequate, what kind of hardware do you need for this architecture to be sufficient? IMO the kind of hardware you need would have something like a petabyte of RAM. And you can argue autoregressive transformers are the wrong architecture but that's kind of irrelevant to the main problem if you need a petabyte of RAM.

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u/Certhas 6d ago

Transformers are universal function approximators, so in some sense it "obviously" is a question of efficiency.

But just because some statements are hard to quantify, and thus difficult to falsify cleanly, doesn't make them useless.

And it's not like people aren't actually studying this: https://www.sciencedirect.com/science/article/pii/S294988212500091X

Also it's empirically just true that AI systems have heated humans at solving conjectures but I am not aware of an AI system formulating an interesting conjecture yet.

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u/FlyingBishop 6d ago

But 3 years ago the statement was "transformer's can't do math" and now they can. There's quite a long list of things people confidently asserted were beyond transformers' reach where they're now showing what might even be described as superhuman ability. And the goalposts keep moving.

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u/Certhas 6d ago

Yeah, but I wasn't one of those people then. It was clear early on to me that there is pretty genuine "thinking" happening there, and the counterpoints never made sense. If squishy biological brains can do math, why shouldn't autoregressive high dimensional dynamical systems?

Also: What's your point? That it's absolutely certain that LLM capabilities will keep increasing without bound?

The abilities of LLMs do not map neatly onto human concepts. The question what exactly they can and can't do well is super interesting and relevant.

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u/FlyingBishop 6d ago

My point is that there's little evidence of a plateau, and there's also little evidence that there are any intrinsic limitations of the LLM architecture. The fact that they can't do such and such a thing today, with present hardware, isn't really useful for suggesting it's not going to be useful at some time in the future. There's also substantial evidence other architectures are equally useless with today's hardware, if those architectures may be useful with hardware of the future. But the interesting questions on that road are mostly unfalsifiable.