You’re right, I mixed intuitions and math about the inner product and cosines similarity, which resulted in many errors. I added a disclaimer at the top of my comment. Sorry for my sloppy math, and thank you for pointing it out.
I think my math is right if only looking at the inner product between d and theta, not about the cosine similarity. So I think my original intuition still hold.
You’re right, I mixed intuitions and math about the inner product and cosines similarity, which resulted in many errors. I added a disclaimer at the top of my comment. Sorry for my sloppy math, and thank you for pointing it out.
I think my math is right if only looking at the inner product between d and theta, not about the cosine similarity. So I think my original intuition still hold.