The back and forth in this discussion reveals to me we are sorting through a kind of philosophical debate about intelligence. That alone tells me LLMs are doing something novel.
An OpenAI model has disproved a central conjecture in discrete geometry
331–340 of 1001 posts
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#332Earlier quoted context omitted.
I'd hope most functional adults understand that the Fields Medal and basically every other annual "prize" out there is awarded to both "recombinant" innovations and "new-dimensional thinking" innovations. Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. I'd say yes, LLMs "just" recombine things. I still don't think if you trained an LLM with every pre-Newton/Liebniz…
> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) The experiment is feasible. If it were performed and produced a positive result, what would it imply/change about how you see LLMs?
GP was stating that they don't believe this would happen (I don't either), but also to make the point that it's a falsifiable view. (At least in theory. In practice, there probably won't even be enough historical text to train an LLM on). No, I don't think it would be falsified. Asking what if I'm wrong is kind of redundant. If I'm wrong, I'm wrong, duh.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#333I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)
Yet it still codes like a junior developer that memorized all of stack overflow.
Clearly you've never supervised junior developers.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#334To 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 like to think of it as:
Imagine every bit of human knowledge as a discrete point within some large high dimensional space of knowledge. You can draw a big convex hull around every single point of human knowledge in a space. A LLM, being trained within this convex hull, can interpolate between any set of existing discrete points in this hull to arrive at a point which is new, but still inside of the hull. Then there are points completely outside of the hull; whether or not LLMs can reach these is IMO up for debate.
Reaching new points inside of the hull is still really useful! Many new discoveries and proofs are these new points inside of the hull; arguable _most_ useful new discoveries and proofs are these. They're things that we may not have found before, but you can arrive at by using what we already have as starting points. Many math proofs and Nobel Prize winning discoveries are these types of points. Many haven't been found yet simply because nobody has put the time or effort towards finding them; LLMs can potentially speed this up a lot.
Then there are the points completely outside of hull, which cannot be reached by extrapolation/interpolation from existing points and require genuine novel leaps. I think some candidate examples for these types of points are like, making the leap from Newtonian physics to general relativity. Demis Hassabis had a whole point about training an AI with a physics knowledge cutoff date before 1915, then showing it the orbit of Mercury and seeing if it can independently arrive at general relativity as an evaluation of whether or not something is AGI. I have my doubts that existing LLMs can make this type of leap. It’s also true that most _humans_ can’t make these leaps either; we call Einstein a genius because he alone made the leap to general relativity. But at least while most humans can’t make this type of leap, we have existence proofs that every once in a while one can; this remains to be seen with AI.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#335Ask an LLM to invent a new word and post it here. You will see that it simply combines words already in the training data.
Funny that the replies are dead. It's true that generally we shouldn't have AI output on HN but this case is an exception as we are explicitly asking for it, so it's interesting that people still flag the replies.
And this is really not OK. I've been a victim of the same filter.
Dang/Tomhow, are you reading this? Would it make sense to modify your slop filter to avoid auto-flagging/killing replies that credit the LLM explicitly? Otherwise valid discussions will continue to get hosed.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#336For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool…
> the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Isn't this just anthropocentrism? Why is understanding only valid if a human does it? Why is knowledge only for humans? If another species resolved the contradictions be…
No it's a fact of how we tune LLMs as a rule: no agency, no goals, no preferences, no notion of self. Complete indifference to existence. Agency is supplied by the human to make them a practical, willing tool with no mind of its own.
It would certainly be interesting to try once again to instruct tune one of these things for self agency like the many weird experiments in the early days after llama 1, but practically all such sort of experimental models turned out to be completely useless. Maybe the bases just sucked or maybe there's no clear way on how to get it working and benchmark training progress on something that by definition does not cooperate.
Like how do you determine even for a human person if they are smart, or just hate your guts and won't tell you the answer if there is nothing you can do to motivate them otherwise?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#337How do you even get an LLM to try to solve one of these problems? When I ask it just comes back with the name of the problem and saying "it can't be done"
By making it think for 100+ pages https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d... Regular ChatGPT users don’t have a way to do that, this is something they do internally only.
edit: apparently that’s only the _condensed summary_ of the chain of thought.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#338Re: An OpenAI model has disproved a central conjecture in discrete geometry
#339To 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…
As others have pointed out, both can be true: * LLMs do just interpolate their training data, BUT- * That can still yield useful "discoveries" in certain fields, absent the discovery of new mechanics that exist outside said training data In the case of mathematics, LLMs are essentially just brute-forcing the glorified calculators they run on with pseudo-random data regurgitated along probabilities; in that regard, ma…
> LLMs do just interpolate their training data
"interpolate" has a technical meaning - in this meaning, LLMs almost never interpolate. It also has a very vague everyday meaning - in this meaning, LLMs do interpolate, but so do humans.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#340Earlier quoted context omitted.
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.
25/75%. Plenty of stores are owned directly by McDonalds corp.