Why do we still flatten embedding spaces?

ost dense retrieval systems rely on cosine similarity or dot-product, which implicitly assumes a flat embedding space. But embedding spaces often live on curved manifolds with non-uniform structure—dense regions, semantic gaps, asymmetric paths.

I’ve been exploring the use of:

- Ricci curvature as a reranking signal

- Soft-graphs to preserve local density

- Geodesic-aware losses during training

Curious if others have tried anything similar? Especially in information retrieval, QA, or explainability. Happy to share some experiments (FiQA/BEIR) if there's interest.