Are proximity scores symmetric in reverse vector queries across identical indexes?

I’m a newbie exploring a specific use case.

Scenario (assuming same dimensions, same index setup, and same embedding engine):

  • Index_1 contains many vectors, including Vector_1
  • Index_2 contains many vectors, including Vector_2

If I query Index_1 with search vector Vector_2, I will get a score characterizing the proximity between Vector_1 and Vector_2 (assuming Vector_1 is returned).

Now, if I do the reverse and query Index_2 with Vector_1, should I assume that the proximity score with Vector_2 will be identical (again, assuming same index setup and same embedding methods)? Or will the score differ?