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dankai 3 hours ago [-]
I've been working on research related to this in the context of diferent LLMs, and I can tell you that similarity != executability.
While you can make embeddings across different LLMs similar (i.e. universally looking) the few percentage of R2 that you are missing in translating the universal representation into a native representation are precisely those that make the hidden states executable in the LLM (which makes them useful).
They do this with simple embedding models because there the purpose of the embeddings is to measure similarity, but if you would like to use this principle to turn latent representations of one LLM into latent representations that are understandable/executably by a different LLM, you will fail.
One way to pose/(think about) the problem is that there are two finite metric spaces linked by an unknown odometry (damn you autocorrect). The problem is to recover that unknown isometry.
This, like graph isometry, can be very computationally intensive in the worst case. However, heuristics to aid matching one vertex on one graph to another vertex on another graph using local, semilocal structural signatures can be very effective on particular cases.
One can of course argue that the spaces are not designed as metric spaces. Even if true, these might be metrizable topological spaces.
More generally, if these are indeed non-metric spaces one can still pose it as finding the unknown isomorphism between two poset spaces.
In my other comment I was using the property of maximal chains -- Identify the longest chains in both posets. The isomorphism must map the longest chain in Poset 1 directly to a longest chain in Poset 2, preserving the exact linear order.
ironSkillet 14 hours ago [-]
I am not familiar with the standards of publishing in machine learning, but as someone trained in a mathematics background, this paper seems relatively light on details and heavy on exposition. Is that typical? Is this a really novel idea? Not trying to be snarky, just trying to understand how meaningful this is.
robrenaud 11 hours ago [-]
It's cool that it proves that a bunch of vectorized outputs from an unknown embedder on an unknown dataset is in no way private, because of this ability to reverse engineer the embedder.
I talked to the author at his poster session at neurips and was able to get the gist, though I had read a lot about the platonic representation hypothesis, and this was one of my top 10 favorite papers in the conference.
7 hours ago [-]
wging 9 hours ago [-]
They link to their code on GitHub - see footnote 2 on page 2. I don't see it linked anywhere else, which makes it easy to miss. https://github.com/rjha18/vec2vec/
Nail2680 12 hours ago [-]
It isn't a maths paper, so the conventions are different.
adastra22 11 hours ago [-]
This isn’t math. The exposition IS the details.
rhelz 14 hours ago [-]
You are not wrong. But this has by no means proven its up to the standard of being publishable in a machine learning journal. Its on arXiv.org, which, lets face it, at the end of the day is a vanity press.
contubernio 9 hours ago [-]
Calling the arxiv a vanity press shows you aren't a researcher. In math and physics all the best stuff is on the arxiv and the general level is well above the level of most journals. Journals mainly serve as accreditation and many are basically mediocre - the review process resta more value than it adds overall.
canjobear 13 hours ago [-]
It was accepted to NeurIPS.
efavdb 14 hours ago [-]
At a minimum posting to arxiv gives others a standard way to cite the work.
odyssey7 14 hours ago [-]
The pace of things is moving along so rapidly right now, I’m not sure that waiting for peer reviews is always a wise move. Doubly so if there’s a paywall; why limit your article’s impact by placing it where practitioners’ agents might not be able to access it? The rapid progress right now is challenging for conventional academic processes.
If the value of the paper is difficult to independently verify, for example, if it depends on the credibility of the author, then the academic ritual can add something. If it’s a mathematical result, one that can be automatically verified, or a machine learning technique that anyone can try with Claude code reconstructing it for them, this sort of pre-print publishing model is advantageous.
rhelz 13 hours ago [-]
// why limit your article's impact //
Because...science? It's not science until it passes peer review.
I'm not advocating that everybody stops posting to arXiv, and I'm not saying you can't find good stuff there. I'm just saying, it's a vanity press, there is absolutely no guarantee of the paper's quality.
And being published by a famous professor from a prestigious university is also no guarantee. If we've learned anything from the non-reproducibility crisis, it is that a paper's origin story is no guarantee.
Xmd5a 6 hours ago [-]
> It's not science until it passes peer review.
You mean Robert Maxwell's quasi-monopoly on scientific publications ?
Peer reviewers don't generally reproduce the work in the publications they are asked to review, at least not during the review process itself. Neither do journal editors.
If you want a real vanity press, check vixra and its origin story.
ArXiv does have moderators and endorsers in each area, although they are usually light-touch, weeding out literally unreadable submissions, ones that so obviously ignore formatting guidelines that it beggars belief they could comply with a typical journal's rules, and ones that are clearly submitted to the wrong area.
Having a stable document early (a pre-print) tends to widen the scrutiny of papers that may ultimately be published to a journal whose editor's expertise lies in a very different area from the submission; this can and does lead to author corrections being made before journal publication.
There are plenty of peer-reviewed papers which are hot garbage that have found their way into prestigious high-impact journals like Nature and Science (see <https://retractionwatch.com/the-retraction-watch-leaderboard...> for examples, and note none of the top 10 are in areas covered by the arXiv).
> being published by a famous professor from a prestigious university is also no guarantee
Everyone in academia knows this, including the vast majority of famous professors from prestigious universities, because of online repositories like <https://retractionwatch.com/retractions-by-nobel-prize-winne...> (and much more sadly because of <https://en.wikipedia.org/wiki/Nobel_disease>, lower-profile versions of which academic paper-writers -- and dissertation writers -- tend to encounter as they chase the history of the problem before them or read late citations to works they are relying upon). This particular part of your set of claims is is not a real problem in academia or with the arXiv in particular.
Finally, what value does publication in a predatory journal bring? Do you believe that peer review and editing were actually even performed in the majority of MDPI's most predatory journals, for example? <https://www.predatoryjournals.org/news/list-of-all-mdpi-pred...> Some papers published in some of their pay-for-publication open access journals don't even get submitted to the arXiv; one might hope this is out of embarrassment by the authors, although the (low) bar set by the arXiv itself is certainly a factor.
The remedy for a reasonably argued but wrong academic paper isn't lack of publication, failed peer review, or editorial alteration, but rather reply papers. That's the academic dialogue.
anon48293 10 hours ago [-]
Then again neither is peer review. Reproducing research is the only way to prove reproducibility and thereby lend credibility to the claims.
fennecfoxy 6 hours ago [-]
I'm not as heavy on the maths stuff involved in this as other people commenting appear to be.
But the idea makes sense, of course there is still recoverable data in embeddings, that's the point. Though as I constantly find the more you try to squeeze into an n bit vector the more watered down everything gets.
I suppose a latent space could be encrypted/mapped in some way to resolve that, but how many people are exposing their vectors in the first place?
ViscountPenguin 4 hours ago [-]
The point of the paper isn't that embeddings contain information, it's that even if you don't know what model generated a set of embeddings you can still recover information from the geometry of the point cloud itself.
The fact that this is possible also adds some pretty strong restriction to the set of possible maps you could use to remove that information. No linear map will work since all embedding spaces are ~an orthonormal matrix apart, so some form of encryption is necessary. This wasn't known until very recently.
srean 16 hours ago [-]
Let's assume that monotonocity of pair-wise distances are preserved.
Without knowing the details of how the paper solved the problem, my first attempt would be to find the diametrically distant pair of points in the two different embeddings and assume that the pair is the same pair. Then find the next distant pairs and so on.
After sufficiently many such pairs have been found, or better still, the largest d-simplex is found, find that scaled rigid body transformation that makes the corresponding pairs coincide. Proceeding this way ought to be less work than solving a generic graph isomorphism problem.
robrenaud 11 hours ago [-]
I think a less stringent, but still workable assumption is that for very similair objects, their distances will be small. This is much easier to accomplish than agreement across all pairs.
srean 7 hours ago [-]
Could you explain a bit more. What you say about similar objects is obviously true. However the algorithm sketch that you have in your mind is a little implicit. Could you make it more explicit. I am quite curious.
I’ve never liked that this was called “the platonic representation hypothesis”.
Lots of weird baggage attached and seems like a waste of a good name.
pksebben 51 seconds ago [-]
"We believe these representations are not serious, they're just really good friends."
rhelz 14 hours ago [-]
Cyberphrenology. In any two random graphs, you'll find an isomorphic graph which is can be up to log of the size of the graphs.
And if the LLM has been trained up to the limit of what data it can hold, it is going to be random. Proof below if it isn't obvious.
The entire effort of all people who are trying to understand how LLMs work, how they represent their data, its all bound to fail.
Proof: a LLM is a very good approximation of the Solomonov/Levin/Kolmogorov universal probability function on tokens. As such, it will be random--pure white noise--because if you found any patterns in there, you could exploit the regularity and come up with a smaller set of weights for the same LLM.
There are no patterns there to be found. They have all been factored out by training the neural net until it couldn't learn any more.
sdenton4 14 hours ago [-]
/a smaller set of weights for the same LLM./
Distillation is alive and well... Earlier work on model printing also found that it's pretty easy to find smaller sets of parameters which can replicate the behavior of the entire network with pretty good fidelity.
Large parameter counts give space to explore, and give routes out of what would be local minima in a lower dimensional space.
In other words, there's no guarantee that any given trained model is a minimal representation of its training set.
rhelz 13 hours ago [-]
I'm not claiming any arbitrary set of weights is a minimal representation. But typically, if people could achieve the same quality of results with a smaller set of weights, or weights which have been quantized to lower bit representations, etc, they would have published the smaller one instead.
andrewflnr 10 hours ago [-]
You kind of are claiming they're minimal, though. Because if they're not, your statement that "if you found any patterns in there, you could exploit the regularity..." implies nothing. Yeah, the patterns are there, and people are exploiting them.
Your socioeconomic argument just doesn't hold either. People don't delay releasing models until they've minimized it to the theoretical limit. They ship it when it's good enough for whatever job they're making it for.
canjobear 13 hours ago [-]
The weights aren’t compressed. So there are interpretable redundancies in practice.
rhelz 12 hours ago [-]
If the weights arn't compressed, then a smaller set of weights would perform as well. Sure, you can always induce as much symmetry and patterns as you want by bloating the data set, but that hardly gives us insight into how a set of weights which is "as full as it can be" of information.
canjobear 12 hours ago [-]
The point of TFA is that there are regularities you can exploit in the actually existing weights of machine learning systems, not in some hypothetically maximally efficient weights. The maximally efficient weights would indeed have no structure, but that’s not what anyone is working with.
measurablefunc 17 hours ago [-]
What is the (co)homology of this space?
chombier 8 hours ago [-]
That of the underlying, hypothetical universal brain topology?
While you can make embeddings across different LLMs similar (i.e. universally looking) the few percentage of R2 that you are missing in translating the universal representation into a native representation are precisely those that make the hidden states executable in the LLM (which makes them useful).
They do this with simple embedding models because there the purpose of the embeddings is to measure similarity, but if you would like to use this principle to turn latent representations of one LLM into latent representations that are understandable/executably by a different LLM, you will fail.
Note this is version 4 of the paper and the original post was version 1 (I think?)
OpenReview (for NeurIPS) for the curious: https://openreview.net/forum?id=jiCLUPq5xv
This, like graph isometry, can be very computationally intensive in the worst case. However, heuristics to aid matching one vertex on one graph to another vertex on another graph using local, semilocal structural signatures can be very effective on particular cases.
One can of course argue that the spaces are not designed as metric spaces. Even if true, these might be metrizable topological spaces.
More generally, if these are indeed non-metric spaces one can still pose it as finding the unknown isomorphism between two poset spaces.
In my other comment I was using the property of maximal chains -- Identify the longest chains in both posets. The isomorphism must map the longest chain in Poset 1 directly to a longest chain in Poset 2, preserving the exact linear order.
I talked to the author at his poster session at neurips and was able to get the gist, though I had read a lot about the platonic representation hypothesis, and this was one of my top 10 favorite papers in the conference.
If the value of the paper is difficult to independently verify, for example, if it depends on the credibility of the author, then the academic ritual can add something. If it’s a mathematical result, one that can be automatically verified, or a machine learning technique that anyone can try with Claude code reconstructing it for them, this sort of pre-print publishing model is advantageous.
Because...science? It's not science until it passes peer review.
I'm not advocating that everybody stops posting to arXiv, and I'm not saying you can't find good stuff there. I'm just saying, it's a vanity press, there is absolutely no guarantee of the paper's quality.
And being published by a famous professor from a prestigious university is also no guarantee. If we've learned anything from the non-reproducibility crisis, it is that a paper's origin story is no guarantee.
You mean Robert Maxwell's quasi-monopoly on scientific publications ?
https://www.theguardian.com/science/2017/jun/27/profitable-b...
Peer reviewers don't generally reproduce the work in the publications they are asked to review, at least not during the review process itself. Neither do journal editors.
If you want a real vanity press, check vixra and its origin story.
ArXiv does have moderators and endorsers in each area, although they are usually light-touch, weeding out literally unreadable submissions, ones that so obviously ignore formatting guidelines that it beggars belief they could comply with a typical journal's rules, and ones that are clearly submitted to the wrong area.
If anything, I think sometimes the net is too fine. Will Kinney just this week had a version of <https://www.acsu.buffalo.edu/~whkinney/SpecialRelativityBoot...> rejected by the arXiv, for example. The reasons for arXiv-rejection can be opaque.
Having a stable document early (a pre-print) tends to widen the scrutiny of papers that may ultimately be published to a journal whose editor's expertise lies in a very different area from the submission; this can and does lead to author corrections being made before journal publication.
There are plenty of peer-reviewed papers which are hot garbage that have found their way into prestigious high-impact journals like Nature and Science (see <https://retractionwatch.com/the-retraction-watch-leaderboard...> for examples, and note none of the top 10 are in areas covered by the arXiv).
> being published by a famous professor from a prestigious university is also no guarantee
Everyone in academia knows this, including the vast majority of famous professors from prestigious universities, because of online repositories like <https://retractionwatch.com/retractions-by-nobel-prize-winne...> (and much more sadly because of <https://en.wikipedia.org/wiki/Nobel_disease>, lower-profile versions of which academic paper-writers -- and dissertation writers -- tend to encounter as they chase the history of the problem before them or read late citations to works they are relying upon). This particular part of your set of claims is is not a real problem in academia or with the arXiv in particular.
Finally, what value does publication in a predatory journal bring? Do you believe that peer review and editing were actually even performed in the majority of MDPI's most predatory journals, for example? <https://www.predatoryjournals.org/news/list-of-all-mdpi-pred...> Some papers published in some of their pay-for-publication open access journals don't even get submitted to the arXiv; one might hope this is out of embarrassment by the authors, although the (low) bar set by the arXiv itself is certainly a factor.
The remedy for a reasonably argued but wrong academic paper isn't lack of publication, failed peer review, or editorial alteration, but rather reply papers. That's the academic dialogue.
But the idea makes sense, of course there is still recoverable data in embeddings, that's the point. Though as I constantly find the more you try to squeeze into an n bit vector the more watered down everything gets.
I suppose a latent space could be encrypted/mapped in some way to resolve that, but how many people are exposing their vectors in the first place?
The fact that this is possible also adds some pretty strong restriction to the set of possible maps you could use to remove that information. No linear map will work since all embedding spaces are ~an orthonormal matrix apart, so some form of encryption is necessary. This wasn't known until very recently.
Without knowing the details of how the paper solved the problem, my first attempt would be to find the diametrically distant pair of points in the two different embeddings and assume that the pair is the same pair. Then find the next distant pairs and so on.
After sufficiently many such pairs have been found, or better still, the largest d-simplex is found, find that scaled rigid body transformation that makes the corresponding pairs coincide. Proceeding this way ought to be less work than solving a generic graph isomorphism problem.
I explained my thoughts in a comment here
https://news.ycombinator.com/item?id=49595424
And if the LLM has been trained up to the limit of what data it can hold, it is going to be random. Proof below if it isn't obvious.
The entire effort of all people who are trying to understand how LLMs work, how they represent their data, its all bound to fail.
Proof: a LLM is a very good approximation of the Solomonov/Levin/Kolmogorov universal probability function on tokens. As such, it will be random--pure white noise--because if you found any patterns in there, you could exploit the regularity and come up with a smaller set of weights for the same LLM.
There are no patterns there to be found. They have all been factored out by training the neural net until it couldn't learn any more.
Distillation is alive and well... Earlier work on model printing also found that it's pretty easy to find smaller sets of parameters which can replicate the behavior of the entire network with pretty good fidelity.
Large parameter counts give space to explore, and give routes out of what would be local minima in a lower dimensional space.
In other words, there's no guarantee that any given trained model is a minimal representation of its training set.
Your socioeconomic argument just doesn't hold either. People don't delay releasing models until they've minimized it to the theoretical limit. They ship it when it's good enough for whatever job they're making it for.