I'm not sure the question is about factorization but more about having the proper coordinates. Right now our basis vectors are pointing in... well... random dir

I'm not sure the question is about factorization but more about having the proper coordinates. Right now our basis vectors are pointing in... well... random directions. So when we naively interpolate between two vectors we're certainty going to pass through different semantical concepts. Our basis vectors aren't aligned to those concepts. And certainly LERPing is not the right way to move along this geometry either, and we should actually be thinking about the geodesics of our surface. We've gone about all this as if we're working with a 2D cartesian coordinate system. I'm actually impressed things have worked this well! Crazy how we've done all this without care for the structural preservation of our data. But I guess with scale you can kinda side step that, forcing the manifold hypothesis. But to move forward and tackle these challenges? Might be time to get back into the weeds.