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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#121

Post by voooduuuuu »

peterlk wrote: post #120
voooduuuuu wrote: post #98

Earlier quoted context omitted.

I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

Ask an LLM to invent a new word and post it here, I will be waiting. You will see that it simply combines words already in the training data.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#122

Post by nemomarx »

pear01 wrote: post #82
throw-the-towel wrote: post #54

Earlier quoted context omitted.

The capability they lack is being able to be sued.

Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them. https://en.wikipedia.org/wiki/Qualified_immunity Assuming you can still sue McDonalds I am not sure if this is a problem in the robotic llm case. I'm also trying to imagine a case where you would want to sue the llm and not the company. Given robots/llm don't have free will…

McDonald's are franchises - you generally want to sue the local owner or threaten them in addition to the holding company.

That only requires someone own the ai managed McDonald's though. so long as they can't avoid responsibility by pointing to the AI I don't see why you couldn't sue them.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#123

Post by sunshowers »

voooduuuuu wrote: post #98
m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.

One might argue that the composition of higher abstractions is the next token predicted after "here is a higher abstraction:"

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#124

Post by truncate »

Tenobrus wrote: post #96
dvt wrote: post #61

Earlier quoted context omitted.

> I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibniz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like an art than a science. For example, many belive that to…

what basis do you have for assuming an LLM is fundamentally incapable of doing this?

What's your basis for assuming LLM is capable of doing this?

I honestly don't know personally either way. Based on my limited understanding of how LLMs work, I don't see them be making the next great song or next great book and based on that reasoning I'm betting that it probably wont be able to do whatever next "Descartes, Newton, Leibnitz, Gauss, Euler, Ramanujan, Galois" are going to do.

Of course AI as a wider field comes up with something more powerful than LLM that would be different.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#126

Post by [deleted] »

voooduuuuu wrote: post #98
m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.

[deleted]

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#127

Post by kilotaras »

phkahler wrote: post #21

I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.

Both 3n and 2n are linear, the broken conjecture is that you can't do better than linear.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#128

Post by cubefox »

Fraterkes wrote: post #37

I guess if this stuff is going to make my employment more precarious, it’d be nice if it also makes some scientific breakthroughs. We’ll see

Breakthroughs in pure mathematics aren't scientific though. They say us nothing about the world, and they are not useful.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#129

Post by fnordpiglet »

dvt wrote: post #105
Tenobrus wrote: post #96

Earlier quoted context omitted.

what basis do you have for assuming an LLM is fundamentally incapable of doing this?

Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)

I prefer to think of it as they’re interpolation machines not extrapolation machines. They can project within the space they’re trained in, and what they produce may not be in their training corpus, but it must be implied by it. I don’t know if this is sufficient to make them too weak to create original “ideas” of this sort, but I think it is sufficient to make them incapable of original thought vs a very complex to evaluate expected thought.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#130

Post by bossyTeacher »

voooduuuuu wrote: post #121
peterlk wrote: post #120

Earlier quoted context omitted.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

Ask an LLM to invent a new word and post it here, I will be waiting. You will see that it simply combines words already in the training data.

Does a random sequence of letters qualify as a new word?
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