491–500 of 1001 posts
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What's happening is the verbal/linguistic equivalent of the invention of calculus. No intellectual field will ever be the same again. Who wouldn't find that exciting, and want to experience it?
People who enjoy thinking. Ya know, the "intellectual" part.
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A lot of the space outside of the convex hull is just untried things. You can brute-force trying random things and checking the result and eventually learn something new. With a better heuristic, you can make better guesses and learn new things much more efficiently. There’s no reason to believe that kind of guess-and-check is outside of the reach of LLMs, or that most of our new discoveries are not found the same wa…
I think of most things you can get to by guess and checking as definitionally inside of the hull; most forms of guess and checking are you take some existing thing, randomize a bunch of its parameters, and see what you get. Whereas with something like relativity, there's not even a starting point that you can randomize and guess/check from the pre-existing knowledge space that will lead you to relativity. That's more…
Like, “take a random sequence of bits and interpret it as Unicode” is at one end of a scale, and “take a random sequence of words in a language” is just a tad away from it, and the scale continues in that direction for quite a while.
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So you think that OpenAI paid some mathematicians to either solve this conjecture problem, or a bunch of related unpublished math related to it, then fed it into an LLM model so they could announce it as being solved by the model? How is that not a conspiracy theory?
It is just a theory, the conspiracy part is not really applicable. I don't see what is controversial about it. Are you implying the machine taught itself the mathematics to do all this?
Are you asking me how LLMs work?
The theory proposed by the original commenter was that there could have been some secret training data the model was trained on that made it possible to solve this problem set. So the only conclusion is they are implying it's a conspiracy by OpenAI to hide some novel math research they funded merely to do marketing about solving math problems (then convincing multiple math experts to verify and support it with papers). That is the definition of a conspiracy.
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Are you saying this result is uninteresting and therefore AI slop or puffery? Obviously OpenAI has a motivation to "market" the accomplishment as much as possible, but surely you agree it IS a remarkable achievement?
I'll let the mathematicians in the field determine the level of "interest" in this result, but saying "you may want to make sure you are sitting down" is pure puffery. > has a motivation to "market" the accomplishment as much as possible I am so sick of HN promoting unethical behaviour as virtuous due to it's financialization worship at the foot of "valuations". > but surely you agree it IS a remarkable achievement?…
A lot of the weight this holds is the fact that it's an old problem and that its difficulty hinges on the lack of investigation the disproof side of hypothesis. The model basically took a contrarian path and found tools and methods that support that a disproof is viable. So the (unquantified amount of) mathematicians out there were all dedicating their resources on the notion that this can be proved. Some with hindsight would say that if they a had team of experts who are driven to the goal of disproof that this would have been achievable by humans, and one of the mathematicians of the paper state as much,this still has value in terms of reliability measurement, and possibly human-aided endeavors when the methods scrounged by the model can be used in other solutions.
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I find it understandable, it is common to evaluate human intelligence vs AI as a zero-sum competition, because that is how employers typically understand it and LM providers market it. AI proving itself moves the needle in an uncomfortable direction for all of us without very robust job security. > I wonder if we’ll still be doing this two years hence. It is going to take some time for people to recognize that AI has…
It isn't necessarily the case. Another wishful/hopeful thought is that the human experience itself is valuable, that competing for resources and living within a social network and having physical needs somehow creates value that is essential for companies to operate. But is it really the case? I don't think we know that, and I don't know if the economy that results when all the white collar and much of the blue colla…
If LLMs were improving significantly independent of scaling up compute resources, I would be a lot more worried. The economic instability (on several levels) of the current trajectory cannot last. Countries and companies that don't take a more sustainable approach will eventually find themselves outclassed by those that do. Unfortunately that is not a guarantee against some sort of dark age in the short term.
Speaking 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…
Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.
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I don't have enough information about the announcement for it to mean much to me. I don't know much about this field of maths. I don't know how many mathematicians were actively working on this problem. It could be zero, which would indicate it's not really that interesting. The article gushes about how it's a Very Important Problem, but it's not even mentioned on https://en.wikipedia.org/wiki/List_of_conjectures_by_…
You don't have enough knowledge to dismiss them, but you still laugh? For?
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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…
But if you actually try to take a convex hull of, some encoding of sentences as vectors? It isn’t true. The outputs are not in the convex hull of the training data.
I guess it’s supposed to be a metaphor and not literal, but in that case it’s confusing. Especially seeing as there are contexts in machine learning where literal interpolation vs literal extrapolation, is relevant. So, please, find a better way to say it than saying that “it can only interpolate”?
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"new kind of math" Well I think the point is there is no "new kind of math". There's just types of math we've discovered and what we haven't. No new math is created, just found.
Where does this mathematics exist before we discover it? I know of no realm where mathematical objects live except human minds. No, it seems clear to me that mathematics is a creation of our minds.
"Where" mathematics exists is in the abstract combinatorical space of an infinite repeating application of logical rules. This space doesn't exist in a substantive sense, but it is accessible/navigable by studying the consequences of logical rules. It is the space of possible structure.