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.
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.
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
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.
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
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.
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.
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.