Comment by danielmarkbruce
4 months ago
a - a + a = b when a and b map to the same vector (or in practice, extremely close together). Your assumptions about invertibility etc don't hold in this world.... embeddings are just a bunch of empirically learned coordinates in a dense space.
So an example: a maps to [1,2,3] and b maps to [1,2,3] . Again in practice b could map to [1,2,3.0001] or something.
To summarize: king, man etc aren't symbols, they get mapped to vectors. + is element wise addition. = is "equal to or very close in multi dimensional space".
Maybe tone down the attitude. You clearly aren't in this field. The properties you have assumed to be true are not. People in AI/ML are using terms and conventions differently than you assume. When someone says "vector addition" they really do mean just element wise addition in practically every case. You are the fool here.
Yes? Thats what I've said lol. That's what the above example shows. THAT WAS THE ENTIRE POINT
I'm glad you finally decided to agree with me. But it would have been a lot faster had you actually read my comments.
Except you were suggesting it's due to the definition of +, and your silly, irrelevant rant about abstract algebra started when I noted it's plain old addition.
It holds for integers too, floating point arithmetic quirks are irrelevant.
You are applying a bunch of ideas that are irrelevant because you don't have any idea how embedding models actually work.