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Harnessing the Universal Geometry of Embeddings

arxiv.org

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Re: Harnessing the Universal Geometry of Embeddings

#11

Post by sdenton4 »

rhelz wrote: post #6

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 a…

/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.

Re: Harnessing the Universal Geometry of Embeddings

#12

Post by rhelz »

odyssey7 wrote: post #10
rhelz wrote: post #7

Earlier quoted context omitted.

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.

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, i…

// 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.

Re: Harnessing the Universal Geometry of Embeddings

#13

Post by rhelz »

sdenton4 wrote: post #11
rhelz wrote: post #6

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 a…

/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 guarant…

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.

Re: Harnessing the Universal Geometry of Embeddings

#14

Post by canjobear »

rhelz wrote: post #7
ironSkillet wrote: post #5

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.

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.

It was accepted to NeurIPS.

Re: Harnessing the Universal Geometry of Embeddings

#15

Post by canjobear »

rhelz wrote: post #6

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 a…

The weights aren’t compressed. So there are interpretable redundancies in practice.

Re: Harnessing the Universal Geometry of Embeddings

#16

Post by rhelz »

canjobear wrote: post #15
rhelz wrote: post #6

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 a…

The weights aren’t compressed. So there are interpretable redundancies in practice.

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.

Re: Harnessing the Universal Geometry of Embeddings

#17

Post by canjobear »

rhelz wrote: post #16
canjobear wrote: post #15

Earlier quoted context omitted.

The weights aren’t compressed. So there are interpretable redundancies in practice.

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.

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.

Re: Harnessing the Universal Geometry of Embeddings

#18

Post by Nail2680 »

ironSkillet wrote: post #5

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.

It isn't a maths paper, so the conventions are different.

Re: Harnessing the Universal Geometry of Embeddings

#19

Post by robrenaud »

srean wrote: post #4

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 i…

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.

Re: Harnessing the Universal Geometry of Embeddings

#20

Post by robrenaud »

ironSkillet wrote: post #5

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.

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.

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