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.
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.
Comments
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.
Ah right, thank you for clarifying.
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.