Comment by danielmarkbruce

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.