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.
But I think my point still stands, isn't the geometry information THE information I referred to in the first place? Obviously the vector size gives you the granularity but it's kind of unavoidable to positionally encode information in a latent space...that's literally what they're for?
But yes, it is very cool to know that regardless of exact implementation finding x,y,z representations of some dataset with various relationships (like language) creates similar geometry/clues across all the implementations.