“I can’t really see a reasonable way for the symmetry to be implemented at all.”
Yeah, same.
Here’s an example, although it is not reasonable.
You could implement embedding in a vector database. If X1 and X2 are equivalent, embed them with an anti-collinear relationship i.e X1 = - X2. and implement the ‘is’ operator as a multiplication by −1.
But this fails when there are three vectors that should be equivalent, and it is not very elegant to embed items that should be “equivalent” with an anti-collinear relationship.
Yeah, same.
Here’s an example, although it is not reasonable.
You could implement embedding in a vector database. If X1 and X2 are equivalent, embed them with an anti-collinear relationship i.e X1 = - X2. and implement the ‘is’ operator as a multiplication by −1.
But this fails when there are three vectors that should be equivalent, and it is not very elegant to embed items that should be “equivalent” with an anti-collinear relationship.