Hyperbolic Embeddings in Milvus

This post details the practical implementation and performance evaluation of hyperbolic embeddings within Milvus. It demonstrates that by applying a simple sign flip to the query vector's first dimension and centering the stored document vectors, standard inner product search (`metric_type="IP"`) can achieve hyperbolic ranking. The post quantifies the recall improvements across HNSW, IVF_FLAT, and IVF_SQ8 indexes on the ImageNet dataset, showing significant gains, especially for IVF indexes. It also introduces a server-side function chain for reranking in Milvus 3.0.1+, enabling Strategy B (shortlist then rerank) to be executed within a single database request with comparable recall to application-level reranking.