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Language models are injective and hence invertible

arxiv.org

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Re: Language models are injective and hence invertible

#3
I don't like the title of this paper, since most people in this space probably think of language models not as producing a distribution (wrt which they are indeed invertible, which is what the paper claims) but as producing tokens (wrt which they are not invertible [0]). Also the author contribution statement made me laugh.

[0] https://x.com/GladiaLab/status/1983812121713418606

Re: Language models are injective and hence invertible

#4
post #3

I don't like the title of this paper, since most people in this space probably think of language models not as producing a distribution (wrt which they are indeed invertible, which is what the paper claims) but as producing tokens (wrt which they are not invertible [0]). Also the author contribution statement made me laugh. [0] https://x.com/GladiaLab/status/1983812121713418606

Yeh it would be fun if we could reverse engineer the prompts from auto generated blog posts. But this is not quite the case.

Re: Language models are injective and hence invertible

#7
>we confirm this result empirically through billions of collision tests on six state-of-the-art language models, and observe no collisions

This sounds like a mistake. They used (among others) GPT2, which has pretty big space vectors. They also kind of arbitrarily define a collision threshold as an l2 distance smaller than 10^-6 for two vectors. Since the outputs are normalized, that corresponds to a ridiculously tiny patch on the surface of the unit sphere. Just intuitively, in such a high dimensional space, two random vectors are basically orthogonal. I would expect the chance of two inputs to map to the same output under these constraints to be astronomically small (like less than one in 10^10000 or something). Even worse than your chances of finding a hash collision in sha256. Their claim certainly does not sound like something you could verify by testing a few billion examples. Although I'd love to see a detailed calculation. The paper is certainly missing one.

Re: Language models are injective and hence invertible

#9
post #3

I don't like the title of this paper, since most people in this space probably think of language models not as producing a distribution (wrt which they are indeed invertible, which is what the paper claims) but as producing tokens (wrt which they are not invertible [0]). Also the author contribution statement made me laugh. [0] https://x.com/GladiaLab/status/1983812121713418606

Still, it is technically correct. The model produces a next-token likelihood distribution, then you apply a sampling strategy to produce a sequence of tokens.
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