Debatable 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?
its 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
I'm disappointed that you had to add the 'metamagical' to your question tbh
It doesn't matter if ai is in a hype cycle or not it doesn't change how a technology works.
Check out the yt videos from 1blue3brown he explains LLMs quite well.
.your first step is the word embedding this vector space represents the relationship between words. Father - grandfather. The vector which makes a father a grandfather is the same vector as mother to grandmother.
You the use these word vectors in the attention layer to create a n dimensional space aka latent space which basically reflects a 'world' the LLM walks through. This makes the 'magic' of LLMs.
Basically a form of compression by having higher dimensions reflecting kind a meaning.
Your brain does the same thing. It can't store pixels so when you go back to some childhood environment like your old room, you remember it in some efficient (brain efficient) way. Like the 'feeling' of it.
That's also the reason why an LLM is not just some statistical parrot.
So 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.
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.
The 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.
It'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.
I 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.
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.
For 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.)
While true in general, they do know many things verbatim. For instance, GPT-4 can reproduce the Navy SEAL copypasta word for word with all the misspellings.
Threatening violence*, even in this virtual way and encased in quotation marks, is not allowed here.
Edit: you've been breaking the site guidelines badly in other threads as well. (To pick one example of many: https://news.ycombinator.com/item?id=46601932.) We've asked you many times not to.
I don't want to ban your account because your good contributions are good and I do believe you're well-intentioned. But really, can you please take the intended spirit of this site more to heart and fix this? Because at some point the damage caused by poisonous comments is worse.
* it would be more accurate to say "using violent language as a trope in an argument" - I don't believe in taking comments like this literally, as if they're really threatening violence. Nonetheless you can't post this way to HN.
I 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)
It 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.
There's an update from Tao after emailing Tenenbaum (the paper author) about this:
> He speculated that "the formulation [of the problem] has been altered in some way"....
[snip]
> More broadly, I think what has happened is that Rogers' nice result (which, incidentally, can also be proven using the method of compressions) simply has not had the dissemination it deserves. (I for one was unaware of it until KoishiChan unearthed it.) The result appears only in the Halberstam-Roth book, without any separate published reference, and is only cited a handful of times in the literature. (Amusingly, the main purpose of Rogers' theorem in that book is to simplify the proof of another theorem of Erdos.) Filaseta, Ford, Konyagin, Pomerance, and Yu - all highly regarded experts in the field - were unaware of this result when writing their celebrated 2007 solution to #2, and only included a mention of Rogers' theorem after being alerted to it by Tenenbaum. So it is perhaps not inconceivable that even Erdos did not recall Rogers' theorem when preparing his long paper of open questions with Graham in 1980.
(emphasis mine)
I think the value of LLM guided literature searches is pretty clear!
This whole thread is pretty funny. Either it can demo some pretty clever, but still limited, features resulting in math skills OR it's literally the best search engine ever invented. My guess is the former, it's pretty whatever at web search and I'd expect to see something similar to the easily retrievable, more visible proof method from Rogers' (as opposed to some alleged proof hidden in some dataset).
Either it can demo some pretty clever, but still limited, features resulting in math skills OR it's literally the best search engine ever invented.
Both are precisely true. It is a better search engine than anything else -- which, while true, is something you won't realize unless you've used the non-free 'pro research' features from Google and/or OpenAI. And it can perform limited but increasingly-capable reasoning about what it finds before presenting the results to the user.
Note that no online Web search or tool usage at all was involved in the recent IMO results. I think a lot of people missed that little detail.
Does 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
YMMV whether this will fly in your company culture, but I titled mine "Focus time, please ask before scheduling".
And when people inevitably didn't ask, I'd just decline unless I especially wanted to attend. I find myself getting invited to meetings sometimes just because the organizer wants to be inclusive and make sure everyone is looped in who might want to be, and I figure that's what's going on if they added me without asking.
If it's really important for me to be there, they'll see my time block and ask me.
The idea of the heimlich is to put sudden force on the diaphragm and force air upward. You can do that alone by pushing your upper abdomen against a chair back, counter, railing, whatever. Not something I've ever tried, but good to know about in case.
Yes, seconding this one too. I've opted for ugly black electrical tape squares over the worst offenders in sleeping spaces, but why is that the only option?
Ha, I've done the same. I never thought I'd become like my old grandpa, who didn't like when TV stations started adding crawls to the bottom of the screen for certain news/information so put electric tape across the bottom of the screen.
If they're going to do LEDs, at least do red ones, which don't obliterate night vision. Making them togglable is the ideal unless they're literally a life-or-death piece of equipment.
It used to be dim red LEDs but then in the early 2010s everyone switched to blue to look more fancy and modern. Sometimes really bright ones too, I used to have an ASUS router that had bright enough (blinking!) blue LEDs to light the entire room up. Without any option to disable them, of course.
With all public debate around the effects of blue light on sleep, it's weird more people haven't found that concerning.
> my old grandpa, who didn't like when TV stations started adding crawls to the bottom of the screen for certain news/information so put electric tape across the bottom of the screen.
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