You'd think a billion dollar company would be able to normalize the sound level on their video :/
An OpenAI model has disproved a central conjecture in discrete geometry
711–720 of 1001 posts
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#712Earlier quoted context omitted.
If you interpret “interpolate” in the literal sense, and apply it to the mechanisms behind LLMs, then the claim that they only interpolate, is straightforwardly false. Taking it instead as a metaphorical claim may be more valid, but in that case it doesn’t depend on our understanding of how LLMs work.
LLMs are statistical models by construction, so depending on how liberal you want to be with terminology, "interpolate" is not so bad. Might make a statistician upset.
But people aren’t giving a (less literal) definition of what they mean by “interpolate” that relies on the internal mechanisms of these models, just a vague metaphor, which, as this vague metaphor, there’s nothing it uses about LLMs that makes the question “do LLMs just interpolate” less of a type error than “do people just interpolate”.
And I don’t think it’s a good metaphor.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#713Earlier quoted context omitted.
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.
Are you saying comments are getting shadow banned?
From what I can tell, anything that triggers some sort of AI post filter gets automatically flagged. Several posts in this thread are visible only with showdead enabled.
My argument is that this rule should apply only to people who post LLM output under their own user names without acknowledgment, or otherwise post it where it doesn't belong. If the topic of a (sub)thread involves LLM output, it should be OK to cite examples without getting your post flagged.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#714The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…
To me, AI feels like the morbidity of Star Trek teleportation, where it's actually copying the person at to the other end and zapping the original one out of existence. The original human never benefits from the fast transportation. Similarly, we're creating tools to improve knowledge, but we're progressively zapping the human out of the equation. Knowledge is created for something, but it's unclear if very soon huma…
You lost me at “except billionaires”. I don’t see how Jeff Bezos benefits from this one much more than let’s say Terence Tao.
Can a tech news stay a tech news, without getting bombardes with leftist subtexts all the time?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#715Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…
Maybe I'm misunderstanding how these models work, but isn't it more the responsibility of the harness and its prompts rather than the model itself to make sure that a result is generated with explicit sources?
Probably.
"All" a model is doing is predicting the next words, based on the statistical distribution of words it has seen similar to the ones read/produced so far.
We push a model towards a particular set of distributions through context. If I ask a model "What is the capital of France?", there is a non-zero chance it goes down the dad joke answer of "The letter F". The far more likely option is "Paris", because the joke appears much less often in training material, but if I wanted to be absolutely sure of getting a consistent geography answer I'd address that with additional context. We can add context via prompts, RAG, agents, skills and so on.
However, when training a model, we select the material. We could show it a lot more geography information (or dad jokes!), and skew the statistical distribution in the direction we wanted. We could also decide to design the system prompt towards the direction we prefer - which the user would interpret as "the model" - and so nudge the context model-wide. We can also construct the interaction to iterate on context with a specific framing and call it "reasoning".
In this specific example, you could therefore solve the problem by a) training skewed towards mathematical papers, which likely degrades performance in general and likely for the specific case too, b) train the user to provide better context/prompts for mathematical work, shifting the workload to them which feels very "a la 2024", c) publish agents and skills that are tailored to mathematics work (very "a la 2026"), d) tweak the system prompt for when the model is doing mathematics work, which the user would see as "the model" doing the change, but you and I might look under the hood and say that is in the harness or a specific type of prompt, or e) add "reasoning" execution that is set to focus on mathematical formatting, or f) a mixture of the above.
Right now we're probably looking at agents and skills. I think over time we're going to see smaller models targets towards domains with a mixture of all of it, where some of this sits at user configurable levels, and some is "baked in" via training, system prompts and execution modes, but from a user perspective it's all just "the model".
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#716Earlier quoted context omitted.
Terence Tao gave a recent talk about this issue (lack of attribution). He called it the decoupling of implicit and explicit goals. AI is only good at solving the explicit goals for now, and humans don't have the bandwidth or the institutions to know how to integrate AI into the field. https://youtu.be/Uc2zt198U_U?si=OkwO3xT8-zhSABwh
That is an odd summary of the talk. He was talking about how the explicit goal of solving a problem is kind of becoming trivialized, but the abundance of 100-page AI generated proofs will not help the implicit goal of furthering human understanding, because we lack the bandwidth to really digest them. Adhering to things like (human-focused) academic etiquette is a different problem and can probably easily be solved b…
I feel like that’s already becoming true. I sometimes work on problems/projects where the AI agent is definitely more qualified than me to call the shots.
For example, this library here for deep learning is 100% ai generated and far beyond my technical capabilities.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#717Earlier quoted context omitted.
LLM's? I doubt it. Systems with Prolog, Common Lisp and the like with proof solvers? For sure. LLM's are doomed to fail. By design. You can't fix them. It's how do they work.
You can have a word with Terrence Tao, he had different opinions here
Yeah, and Knuth, but that's a fallace of authority. Wait until the errors raise.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#718Earlier quoted context omitted.
> But, for scientists, I find that these tools address the problem of the exploding complexity barrier in the frontier. Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. AI is going to both help and hinder this process though. At the end of the day, mathematics is mostly a social process at this point. The goal is not raw number of…
> Only a rare few new theorems in mathematics nowadays have direct real world applicability. I am no mathematician and very naïve about this, but in a world that is rapidly becoming extremely calculation and network dependent that sounds hard to believe. > If AI produced legitimate theoretical breakthroughs at a pace mathematicians are unable to absorb, then the impact will be neutral to negative. I think the idea he…
The key word in that sentence is “new.” New math is typically explored without expectation of practical use. There are exceptions, but it is generally true.
On the other hand, there are many applied mathematicians and theorists from other fields that mine new maths for applications to their fields. But they are almost always not the ones that come up with the new math.
Historically, of course, mathematics was always driven by the need to explain things. Many of the mathematicians from the 17th and 18th centuries were physicists (or, less commonly, engineers). But for the last hundred years or so that really hasn’t been the case.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#719Absolutely no proof that any LLM actually found the result, and just a mention of an "internal model". Served to you by one of the biggest liars in the world. Why would anyone believe this to be true even for a split second?
This has been an unsolved open problem for 80 years. What you're suggesting is that someone connected to Open AI solved this very hard math problem, but then rather than taking credit for it, falsely attributed it to AI? The point of having an AI solve an unsolved problem, is to make it very clear that the insight must have come from the AI and wasn't in the training data. Sure, it's possible OpenAI had access to som…
> That human would be turning down a potential Fields Medal for this discovery.
While interesting, this result is not Fields Medal material.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#720Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…
Maybe I'm misunderstanding how these models work, but isn't it more the responsibility of the harness and its prompts rather than the model itself to make sure that a result is generated with explicit sources?
I don't think you are misunderstanding how models work, but I think the parent comment meant that the training of the models should push them to include attributions in their native output so they will more likely do so without reinforcement through the harness.