Your Vector Database Already Speaks Hyperbolic

This post introduces hyperbolic embeddings and demonstrates how they can be searched in Milvus using the standard inner product metric with a simple transformation. It explains that hyperbolic embeddings, which live in a curved space, naturally represent hierarchical data and that the "height" dimension acts as a built-in specificity score. The key technical contribution is showing that searching these embeddings in Milvus with inner product is achievable by flipping a sign in the vector representation and performing a subtraction at ingest to ensure indexability. This enables Milvus to support advanced embedding types without requiring dedicated hyperbolic distance metrics or separate reranking steps, improving recall on common index types like HNSW, IVF_FLAT, and IVF_SQ8.