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Comment by danielmarkbruce

19 hours ago

You really don't understand that the illogical sounding results from that website are due to the vectors themselves huh. It has zero to do with the definition of +.

Please, tell me more. I was naively under the impression that normal addition had Abelian group properties[0]. Maybe you can inform me as what the inverse element is. That will get me to change my mind

[0] https://en.wikipedia.org/wiki/Abelian_group

  • You’re lost in abstractions. ‘King’ and ‘queen’ and 'man' etc etc aren’t algebraic symbols, they’re mapped to vectors of real numbers. The model learns those mappings, then we just add and subtract numbers element wise. That’s it. You’re giving a group theory lecture about an operation that’s literally just a[i] + b[i]. The semantics come from training, not from some deep mathematical revelation you think everyone missed.

    •   > they’re mapped to vectors of real numbers
      

      Yes, I'm in agreement here. But you need to tell me how

        a - a + a = b
      

      Use what ever the fuck you want for a. A vector (e.g. [1,2,3]), a number (e.g. 1), an embedding (e.g. [[1,2,3],[4,5,6]]), words (e.g. "man"), I really don't give a damn. You have to tell me why b is a reasonable answer to that equation. You have to tell me how a==b while also a!=b.

      Because I expect the usual addition to be

        a - a + a = a
      

      This is the last time I'm going to say this to you.

      You're telling me I'm lost in abstraction and I'm telling you is not usual addition because a != b. That's it! That's the whole fucking argument. You literally cannot see the contradiction right in front of you. The only why it is usual addition is if you tell me "man == woman" because that is literally the example from several comments ago. Stop being so smart and just read the damn comment