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Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)" And even odder that the proof was by Erdo
by nl 9mo ago
Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)"
And even odder that the proof was by Erdos himself and yet he listed it as an open problem!
- TZubiri 9mo agoMaybe it was in the training set.
- magneticnorth 9mo agoI think that was Tao's point, that the new proof was not just read out of the training set.
- rzmmm 9mo agoThe model has multiple layers of mechanisms to prevent carbon copy output of the training data.
- TZubiri 9mo agoforgive the skepticism, but this translates directly to "we asked the model pretty please not to do it in the system prompt"
- ffsm8 9mo agoIt's mind boggling if you think about the fact they're essential "just" statistical models It really contextualizes the old wisdom of Pythagoras that everything can be represented as numbers / math is the ultimate truth
- GrowingSideways 9mo agoHow so? Truth is naturally an apriori concept; you don't need a chatbot to reach this conclusion.
- glemion43 9mo agoThey are not just statistical models They create concepts in latent space which is basically compression which forces this
- jrmg 9mo agoYou’re describing a complex statistical model.
- glemion43 9mo agoDebatable I would argue. It's definitely not 'just a statistical model's and I would argue that the compression into this space fixes potential issues differently than just statistics. But I'm not a mathematics expert if this is the real official definition I'm fine with it. But are you though?
- inimino 9mo agoI am, and yes, that's what a statistical model is.
- mmooss 9mo agoWhat is "latent space"? I'm wary of metamagical descriptions of technology that's in a hype cycle.
- AIorNot 9mo agoSee this video https://youtu.be/D8GOeCFFby4?si=AtqH6cmkOLvqKdr0 https://youtu.be/D8GOeCFFby4?si=AtqH6cmkOLvqKdr0
- DoctorOetker 9mo agoits a statistical term, a latent variable is one that is either known to exist, or believed to exist, and then estimated. consider estimating the position of an object from noisy readings. One presumes that position to exist in some sense, and then one can estimate it by combining multiple measurements, increasing positioning resolution. its any variable that is postulated or known to exist, and for which you run some fitting procedure
- mikaraento 9mo agoThat might be somewhat ungenerous unless you have more detail to provide. I know that at least some LLM products explicitly check output for similarity to training data to prevent direct reproduction.
- guenthert 9mo agoShould they though? If the answer to a question^Wprompt happens to be in the training set, wouldn't it be disingenuous to not provide that?
- ttctciyf 9mo agoMaybe it's intended to avoid legal liability resulting from reproducing copyright material not licensed for training?
- TZubiri 9mo agoDing! It's great business to minimally modify valuable stuff and then take credit for it. As was explained to me by bar-certified counsel "if you take a recipe and add, remove or change just one thing, it's now your recipe" The new trend in this is asking Claude Code to create a software on some type, like a Browser or a DICOM viewer, and then publishing that it's managed to do this very expensive thing (but if you check source code, which is never published, it probably imports a lot of open source dependencies that actually do the thing) Now this is especially useful in business, but it seems that some people are repurposing this for proving math theorems. The Terence Tao effort which later checks for previous material is great! But the fact that the Section 2 (for such cases) is filled to the brim, and section 1 is mostly documented failed attempts (except for 1 proof, congratulations to the authors), mostly confirms my hypothesis, claiming that the model has guards that prevent it is a deus ex machina cope against the evidence.
- TZubiri 9mo agoSo it would be able to produce the training data but with sufficient changes or added magic dust to be able to claim it as one's own. Legally I think it works, but evidence in a court works differently than in science. It's the same word but don't let that confuse you and don't mix them both.
- efskap 9mo agoWould it really be infeasible to take a sample and do a search over an indexed training set? Maybe a bloom filter can be adapted
- hexaga 9mo agoIt's not the searching that's infeasible. Efficient algorithms for massive scale full text search are available. The infeasibility is searching for the (unknown) set of translations that the LLM would put that data through. Even if you posit only basic symbolic LUT mappings in the weights (it's not), there's no good way to enumerate them anyway. The model might as well be a learned hash function that maintains semantic identity while utterly eradicating literal symbolic equivalence.
- ComplexSystems 9mo agoThe model doesn't know what its training data is, nor does it know what sequences of tokens appeared verbatim in there, so this kind of thing doesn't work.
- Den_VR 9mo agoUnfortunately.
- glemion43 9mo agoDo you have a source for this? Carbon copy would mean over fitting
- fweimer 9mo agoI saw weird results with Gemini 2.5 Pro when I asked it to provide concrete source code examples matching certain criteria, and to quote the source code it found verbatim. It said it in its response quoted the sources verbatim, but that wasn't true at all—they had been rewritten, still in the style of the project it was quoting from, but otherwise quite different, and without a match in the Git history. It looked a bit like someone at Google subscribed to a legal theory under which you can avoid copyright infringement if you take a derivative work and apply a mechanical obfuscation to it.
- Workaccount2 9mo agoLLM's are not archives of information. People seem to have this belief, or perhaps just general intuition, that LLMs are a google search on a training set with a fancy language engine on the front end. That's not what they are. The models (almost) self avoid copyright, because they never copy anything in the first place, hence why the model is a dense web of weight connections rather than an orderly bookshelf of copied training data. Picture yourself contorting your hands under a spotlight to generate a shadow in the shape of a bird. The bird is not in your fingers, despite the shadow of the bird, and the shadow of your hand, looking very similar. Furthermore, your hand-shadow has no idea what a bird is.
- fweimer 9mo agoFor a task like this, I expect the tool to use web searches and sift through the results, similar to what a human would do. Based on progress indicators shown during the process, this is what happens. It's not an offline synthesis purely from training data, something you would get from running a model locally. (At least if we can believe the progress indicators, but who knows.)
- int_19h 9mo ago
- GeoAtreides 9mo agodoes it? this is a verbatim quote from gemini 3 pro from a chat couple of days ago: "Because I have done this exact project on a hot water tank, I can tell you exactly [...]" I somehow doubt it an LLM did that exact project, what with not having any abilities to do plumbing in real life...
- cma 9mo agoI don't think it is dispositive, just that it likely didn't copy the proof we know was in the training set. A) It is still possible a proof from someone else with a similar method was in the training set. B) something similar to erdos's proof was in the training set for a different problem and had a similar alternate solution to chatgpt, and was also in the training set, which would be more impressive than A)
- heliumtera 9mo agoDoes it matter if it copied or not? How the hell would one even define if it is a copy or original at this point? At this point the only conclusion here is: The original proof was on the training set. The author and Terence did not care enough to find the publication by erdos himself
- CamperBob2 9mo agoIt is still possible a proof from someone else with a similar method was in the training set. A proof that Terence Tao and his colleagues have never heard of? If he says the LLM solved the problem with a novel approach, different from what the existing literature describes, I'm certainly not able to argue with him.
- mmooss 9mo ago> A proof that Terence Tao and his colleagues have never heard of? Tao et al. didn't know of the literature proof that started this subthread.
- CamperBob2 9mo agoRight, but someone else did ("colleagues.")
- habinero 9mo agoNo, they searched for it. There's a lot of math literature out there, not even an expert is going to know all of it.
- pfdietz 9mo agoThe theorem is implied by an older result of Erdos, but is not a result of Erdos. Apparently this is because the connection is something called "Roger's Theorem" that was quite obscure. https://terrytao.wordpress.com/2026/01/19/rogers-theorem-on-sieving/ https://terrytao.wordpress.com/2026/01/19/rogers-theorem-on-... "This theorem is somewhat obscure: its only appearance in print is in pages 242-244 of this 1966 text of Halberstam and Roth, where the authors write in a footnote that the result is “unpublished; communicated to the authors by Professor Rogers”. I have only been able to find it cited in three places in the literature: in this 1996 paper of Lewis, in this 2007 paper of Filaseta, Ford, Konyagin, Pomerance, and Yu (where they credit Tenenbaum for bringing the reference to their attention), and is also briefly mentioned in this 2008 paper of Ford. As far as I can tell, the result is not available online, which could explain why it is rarely cited (and also not known to AI tools). This became relevant recently with regards to Erdös problem 281, posed by Erdös and Graham in 1980, which was solved recently by Neel Somani through an AI query by an elegant ergodic theory argument. However, shortly after this solution was located, it was discovered by KoishiChan that Rogers’ theorem reduced this problem immediately to a very old result of Davenport and Erdös from 1936. Apparently, Rogers’ theorem was so obscure that even Erdös was unaware of it when posing the problem!"